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Economic risk quantification of toll highway projects Hatakama, Toshiaki 1994

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ECONOMIC RISK QUANTIFICATION OF TOLL HIGHWAY PROJECTS BY TOSHIAKI HATAKAMA B.Eng., Hokkaido University, Japan. 1983  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTERS OF APPLIED SCIENCE  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING  We accept this thesis as conforming to the required  UNIVERSITY  standard  OF BRITISH COLUMBIA July 1994  © TOSHIAKI HATAKAMA , 1994  In presenting this thesis  in partial fulfilment  of  the  requirements  for  an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of  this thesis for scholarly purposes may be granted by the head of  department  or  by  his  or  her  representatives.  It  is  understood  that  copying  my or  publication of this thesis for financial gain shall not be allowed vtithout my written permission.  (Signature)  Department ofCivilEngineering The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  July  27,  1994  Abstract  The objectives of this thesis are to model economic and financial performance of user-pay highway facilities, to explore the sensitivity of project performance to changes in primary variables, to measure the uncertainty surrounding user-pay highway facilities, and to explore ways of reducing the uncertainty.  Special attention is  given to the revenue phase.  The model consists of three levels: work package/revenue stream level; project performance level; and project decision level.  The model calculates work package  duration, work package cost, and revenue stream for the work package/revenue stream level; project duration, project cost, and project revenue for the project performance level; and project's net present value (NPV) for the project decision level.  They are described by  their expected value, standard deviation, skewness, and kurtosis.  This model is applied to a numerical example patterned after a Japanese project to carry out a sensitivity and risk analysis, and highly sensitive primary variables are  ii  identified.  The case study may be viewed as a comparison  of current Japanese deterministic feasibility analysis with a probabilistic one, using the same underlying project model.  Risk management strategies are presented, and their  impacts on overall project risks are measured. Results from applying the model to a sample project show that it is very difficult for a highway operator alone to reduce risks.  It is suggested that it is very important  that risk sharing be negotiated with the government and some guarantee of support be received.  iii  Table of Content  Abstract  ii  List of Tables  viii  List of Figures  xvii  Acknowledgement  xxi  1. Introduction  1  1.1 General  1  1.2 Background of the Research  2  1.2.1 Toll Highway Concept  2  1.2.2 Analytical Method for Quantification of Economic Risks  6  1.3 Objectives of the Research  10  1.4 Structure of the Research  11  2. Analytical Model  13  2.1 General  13  2.2 Cash Flows  22  2.3 Structure of the Economic Analysis  23  2.3.1 Work Package/Revenue Stream Level  . .  24  2.3.2 Project Performance Level  29  2.3.3 Project Decision Level  31  2.4 Work Package  32  IV  2.5 Toll Revenue  33  2.5.1 General  33  2.5.2 General Input Data  37  2.5.3 Traffic Volume  38  2.5.4 Toll Rate  40  2.5.5 General Form of Toll Revenue  44  2.6 Maintenance and Operation Cost Model . . . .  48  2.6.1 Maintenance Costs  49  2.6.2 Operation Costs  56  2.6.4 General Form of Maintenance and Operation Costs  61  3 . Application  62  3.1 General  62  3.2 Sample Project  63  3.2.1 Sample Project General Information . .  63  3.2.2 Work Packages  66  3.2.3 Revenue Streams  74  3.2.4 Calculation Results 3.3 Sensitivity Analysis  .  87 95  3.3.1 Results  95  3.3.2 Summary of Sensitivity Analysis 3.4 Summary  . . . 104 105  4. Risk Management  106  4.1 General  106  V  4.2 Strategies for Risk Management  107  4.2.1 Revenue Stream Early Start Time (case-2)  108  4.2.2 Toll Rate Growth Parameters (case-3)  112  4.2.3 Traffic Volume Growth Parameters (case-4)  116  4.2.4 Tolls (case-5)  119  4.2.5 Traffic Volume (case-6)  122  4.2.6 Inflation Rate (case-7)  126  4.2.7 Parameter for Consignment Cost of Toll Collection (case-8)  129  4.2.8 Combination of Case-2 to Case-8 (case-9)  132  4.3 Conclusions  135  5. Conclusions and Recommendations  140  5.1 Conclusions  140  5.2 Recommendations for Future Work  142  5.2.1 Computer Programs  142  5.2.2 Correlation between Primary Variables for Revenue Streams  . . . .  143  5.2.3 Deterministic Input for Primary Variables  144  Bibliography  145  Appendices  149 vi  A Discounted Work Package Cost  149  B Input Data for Revenue Stream  152  B.l Closed System (Fixed Toll Rate)  152  B.2 Closed System (Distance Proportional Toll Rate) B.3 Open System (Fixed Toll Rate)  157 162  C Interchange Pair Traffic Volume and Traffic Volume and Toll Rate Growth Parameters  167  C.l Interchange Pair Traffic Volume  167  C.2 Traffic Volume Growth Parameters  177  C.3 Toll Rate Growth Parameters  178  D Source Code of the Model  179  Vll  List of Tables  1.1  Derived Variables at Each Level  2.1  Work Package Components  32  2.2  Input Data for Revenue Streams  35  2.3  Interchange Pair Daily Traffic Volume  36  2.4  Interchange Pair Toll  36  2.5  Interchange Pair Annual Toll Revenue  36  2.6  Vehicle Type and Toll Ratio  41  2.7  Input Data for Toll Revenue  2.8  Daily Traffic Volume Q{1,k,1,1)  46  2.9  Daily Traffic Volume Q{1,k,1,2)  46  (Example)  7  45  2.10 Tolls r(l,A:,l,l)  46  2.11 Tolls r{l,k,l,2)  46  2.12 Daily Traffic Volume Q{2,k,1,1)  46  2.13 Daily Traffic Volume Q{2,k,1,2)  46  2.14 Toll r(2,k,l,l)  46  2.15 Toll r{2,k,l,2)  46  2.16 Annual Revenue R(1,1,A:,1,1)  46  2.17 Annual Revenue R (1, 1, ;c, 1, 2 ) 2.18 Annual Revenue R{1,2,k,1,1)  46 47  2.19 Annual Revenue R (1, 2 , A:, 1, 2 )  47  2.20 Annual Revenue R(2,1,A:,1,1)  47  2.21 Annual Revenue R{2,1,k,1,2)  47 viii  2.22 Annual Revenue R{2,2,k,1,1)  47  2.23 Annual Revenue R(2,2,k,1,2)  47  2.24 Annual Revenue R(2,3,A:,1,1)  47  2.2 5 Annual Revenue R(2,3,A:,1,2)  47  2.26 Total Revenues for an Example  47  2.27 Maintenance Costs  48  2.28 Operation Costs  49  2.29 Road Length  49  2.30 Tunnel Length by Ventilation Methods  50  2.31 Road Length  51  (Example)  2.32 Tunnel Length by Ventilation Methods  (Example)  .  51  2.33 Road Cleaning Costs  51  2.34 Road Maintenance Costs  52  2.35 Road Lighting Costs  52  2.36 Bridge Maintenance  (Repairing) Costs  53  2.37 Bridge Maintenance  (Repainting) Costs  53  2.38 Tunnel Maintenance Costs  54  2.39 Snow and Ice Control Costs  55  2.40 Overlay Costs  55  2.41 Manpower Required for Operation Office  57  2.42 Labour Cost for Operation Office  57  2.43 Manpower Required for Toll Collection  59  3.1  General Feature of the Sample Project  63  3.2  Statistics Data for Inflation, Interest, Discount Rates, and Equity Fraction  3.3  65  Five Percentile Estimate Parameters for W.P. Duration  68 ix  3.4  Five Percentile Estimate Parameters for W.P. Costs  3.5  68  Deterministic Values for Work Package Durations and Costs  3.6  71  Statistics for Work Package Durations and Costs  72  3.7  Discounted Work Package Costs  73  3.8  Five Percentile Estimate Parameters for Revenue  3.9  Streams  74  Interchange Distances  75  3.10 Toll for Light Motor Vehicle  75  3.11 Toll for Ordinary Motor Vehicle  76  3.12 Toll for Medium-sized Motor Vehicle  76  3.13 Toll for Large-sized Motor Vehicle  76  3.14 Toll for Special Large-sized Motor Vehicle 3.15 Spot Traffic Volume between  . . .  76  Interchange  #1 and #2  77  3.16 Spot Traffic Volume between  Interchange  #2 and #3  78  3.17 Spot Traffic Volume between  Interchange  #3 and #4  79  3.18 Spot Traffic Volume between  Interchange  #4 and #5  80  3.19 Spot Traffic Volume between Interchange #5 and #6  81  3.20 Deterministic Annual Revenues and Annual Maintenance and Operating Costs (Constant Dollar)  85 X  3.21 Discounted Revenues for the Original Feasibility Analysis  86  3.22 Statistics for Discounted Work Package Costs  87  3.23 Statistics for Discounted Revenues  88  3.24 Statistics for Project Duration, Discounted Project Cost, Project Revenue, and Project Net Present Value(NPV)  88  3.25 Cumulative Probability of Project Duration .  89  3.26 Cumulative Probability of Project Cost  91  . . .  3.27 Cumulative Probability of Project Revenue  92  3.28 Cumulative Probability of Project Net Present Value  94  3.29 Total sensitivity Coefficients for RVS #1  97  3.30 Total sensitivity Coefficients for RVS #2  97  3.31 Total sensitivity Coefficients for RVS #3  98  3.32 Total sensitivity Coefficients for RVS #4  98  3.33 Total sensitivity Coefficients for RVS #5  99  3.34 Total sensitivity Coefficients for RVS #6  100  3.35 Total sensitivity Coefficients for RVS #7  101  3.36 Total sensitivity Coefficients for RVS #8  102  3.37 Total sensitivity Coefficients for RVS #9  103  4.1  Five Percentile Estimate Parameters for W.P. Durations  4.2  109  Five Percentile Estimate Parameters for W.P. Durations  4.3  (case-1)  (case-2)  109  Comparison of the Project Revenue (case-1 and case-2)  110  xi  4.4  Cumulative probability of the Project Revenue (case-1 and case-2)  4.5  llO  Comparison of the Project NPV (case-1 and case-2)  4.6  Ill  Cumulative Probability of the Project NPV (case-1 and case-2)  4.7  Ill  Five Percentile Estimate Parameters for Toll Rate Growth Parameters  4.8  113  Statistics Information of Five Percentile Estimate Parameters for Toll Rate Growth Parameters  4.9  113  Comparison of the Project Revenue (case-1 and case-3)  113  4.10 Cumulative probability of the Project Revenue (case-1 and case-3)  114  4.11 Comparison of the Project NPV (case-1 and case-3)  114  4.12 Cumulative Probability of the Project NPV (case-1 and case-3)  115  4.13 Five Percentile Estimate Parameters for Traffic Volume Growth Parameters  116  4.14 Statistics Information of Five Percentile Estimate Parameters for Traffic Volume Growth Parameters  116  4.15 Comparison of the Project Revenue (case-1 and case-4)  116  4.16 Cumulative probability of the Project Revenue (case-1 and case-4)  117 xii  4.17 Comparison of the Project NPV (case-1 and case-4)  117  4.18 Cumulative Probability of the Project NPV (case-1 and case-4)  118  4.19 Five Percentile Estimate Parameters for Tolls  119  4.20 Statistics Information of Five Percentile Estimate Parameters for Tolls  119  4.21 Comparison of the Project Revenue (case-1 and case-5)  120  4.22 Cumulative probability of the Project Revenue (case-1 and case-5)  120  4.23 Comparison of the Project NPV (case-1 and case-5)  121  4.24 Cumulative Probability of the Project NPV (case-1 and case-5)  121  4.25 Five Percentile Estimate Parameters for Traffic Volume  123  4.26 Statistics Information of Five Percentile Estimate Parameters for Traffic Volume  123  4.27 Comparison of the Project Revenue (case-1 and case-6)  123  4.28 Cumulative probability of the Project Revenue (case-1 and case-6)  124  4.29 Comparison of the Project NPV (case-1 and case-6)  124  4.30 Cumulative Probability of the Project NPV (case-1 and case-6)  125 xiii  4.31 Five Percentile Estimate Parameters for Inflation Rate  126  4.32 Statistics Information of Five Percentile Estimate Parameters for Inflation Rate  126  4.33 Comparison of the Project Revenue (case-1 and case-7)  126  4.34 Cumulative probability of the Project Revenue (case-1 and case-7)  127  4.35 Comparison of the Project NPV (case-1 and case-7)  127  4.36 Cumulative Probability of the Project NPV (case-1 and case-7)  128  4.37 Five Percentile Estimate Parameters for Parameter for Consignment Cost of Toll Collection  129  4.38 Statistics Information of Five Percentile Estimate Parameters for Consignment Cost of Toll Collection  129  4.39 Comparison of the Project Revenue (case-1 and case-8)  129  4.40 Cumulative probability of the Project Revenue (case-1 and case-8)  130  4.41 Comparison of the Project NPV (case-1 and case-8)  130  4.42 Cumulative Probability of the Project NPV (case-1 and case-8)  131  4.43 Comparison of the Project Revenue (case-1 and case-9)  132 xiv  4.44 Cumulative probability of the Project Revenue (case-1 and case-9)  132  4.45 Comparison of the Project NPV (case-1 and case-9)  133  4.46 Cumulative Probability of the Project NPV (case-1 and case-9)  133  4.47 Five Percentile Estimate Parameters for Traffic Volume  136  4.48 Statistics Information of Five Percentile Estimate Parameters for Traffic Volume  . . . .  136  4.49 Comparison of the Project Revenue (case-1 and case-10)  136  4.50 Cumulative probability of the Project Revenue (case-1 and case-10)  137  4.51 Comparison of the Project NPV (case-1 and case-10)  138  4.52 Cumulative Probability of the Project NPV (case-1 and case-10)  B.l  138  Input Data for Closed System (Fixed Toll Rate)  B.2  152  Input Data for Closed System (Distance Proportional Toll Rate)  B.3  Input Data for Open System (Fixed Toll Rate)  C.l  157  162  Interchange Pair Traffic Volume at Base Year for RVS #1  168 XV  C.2  Interchange Pair Traffic Volume at Base Year for RVS #2  C.3  169  Interchange Pair Traffic Volume at Base Year for RVS #3  C.4  170  Interchange Pair Traffic Volume at Base Year for RVS #4  C.5  171  Interchange Pair Traffic Volume at Base Year for RVS #5  C.6  172  Interchange Pair Traffic Volume at Base Year for RVS #6  C.7  173  Interchange Pair Traffic Volume at Base Year for RVS #7  C.8  174  Interchange Pair Traffic Volume at Base Year for RVS #8  C.9  175  Interchange Pair Traffic Volume at Base Year for RVS #9  176  C.IO Traffic Volume Growth Parameters  177  C 11 Toll Rate Growth Parameters  178  D.l  181  Program List  XVI  List of Figures  1.1  Flowchart for the Analytical Approach  9  2.1  Generalized Cash Flow Diagram for an Engineering Project  15  2.2  Cash Flow Diagram for a Toll Highway Project  . .  2.3  Feasibility Study Components for a Toll Highway  15  Project  16  2.4  General Pattern of Traffic Growth  17  2.5  Organizational Structure  21  2.6  Derived Variables at Each Level  24  2.7  Cash Flow Diagram for Work Package  26  2.8  Cash Flow Diagram for Net Revenue Stream  2.9  Cost/Revenue Components  . . . .  27 28  2.10 Revenue Stream and Base Years  34  2.11 Interchanges  36  (Example)  2.12 Toll Rate Increase  (Case-1)  41  2.13 Toll Rate Increase  (Case-2)  42  2.14 Toll Growth Parameters  (Case-1)  42  2.15 Toll Growth Parameters  (Case-2)  43  2.16 Road Structure  3.1  (Example)  50  Expenditure Profiles for the Construction Phase  64 xvii  3.2  Expenditure and Revenue Profiles for the Revenue Phase  64  3.3  Time Line for a Sample Project  66  3.4  Precedence Network for the Sample Project  3.5  Spot Traffic Volume between  . . .  Interchange  #1 and #2 3.6  82  Spot Traffic Volume between  Interchange  #2 and #3 3.7  82  Spot Traffic Volume between  Interchange  #3 and #4 3.8  83  Spot Traffic Volume between  Interchange  #4 and #5 3.9  70  83  Spot Traffic Volume between  Interchange  #5 and #6  84  3.10 Cumulative Probability of Project Duration  ...  3.11 Cumulative Probability of Project Cost 3.12 Cumulative Probability of Project Revenue  90 91  . . .  93  3.13 Cumulative Probability of Project Net Present Value  4.1  94  Cumulative Probability of the Project Revenue (case-1 and case-2)  4.2  Ill  Cumulative Probability of the Project NPV (case-1 and case-2)  4.3  112  Cumulative Probability of the Project Revenue (case-1 and case-3)  4.4  114  Cumulative Probability of the Project NPV (case-1 and case-3)  115 xviii  4.5  Cumulative Probability of the Project Revenue (case-1 and case-4)  4.6  117  Cumulative Probability of the Project NPV (case-1 and case-4)  4.7  118  Cumulative Probability of the Project Revenue (case-1 and case-5)  4.8  121  Cumulative Probability of the Project NPV (case-1 and case-5)  4.9  122  Cumulative Probability of the Project Revenue (case-1 and case-6)  124  4.10 Cumulative Probability of the Project NPV (case-1 and case-6)  125  4.11 Cumulative Probability of the Project Revenue (case-1 and case-7)  127  4.12 Cumulative Probability of the Project NPV (case-1 and case-7)  128  4.13 Cumulative Probability of the Project Revenue (case-1 and case-8)  130  4.14 Cumulative probability of the Project NPV (case-1 and case-8)  131  4.15 Cumulative Probability of the Project Revenue (case-1 and case-9)  133  4.16 Cumulative Probability of the Project NPV (case-1 and case-9)  134  4.17 Cumulative Probability of the Project Revenue (case-1 and case-10)  137  4.18 Cumulative Probability of the Project NPV (case-1 and case-lO)  138 xix  D.l  Program S t r u c t u r e  180  XX  Acknowledgement I wish to express my most  sincere gratitude  to Dr. Alan  Russell, my teacher and supervisor, who has had a profound and  positive  attitudes.  impact  on  my  academic  professional  I greatly appreciate his advice, guidance, and  support throughout my graduate studies. not  and  exist  without  his  patient  This thesis would  efforts  and  valuable  suggestions.  To  Michael  Granstrom,  J.  Wise,  Jerry  Kevin  Froese,  Yu,  fellow  Francois  Medori,  colleagues  and  Bruce  friends,  many thanks for your moral support and encouragement.  I  would  like  to  thank  my  parents  for  their  support,  encouragement, and instilling in me a dedication that was invaluable in performing this work.  To Daiki, thank for your encouragement.  You made the bad  times more tolerable and the good times more enjoyable.  Finally,  to  Mitsuyo,  your  patience,  support,  encouragement are most gratefully acknowledged.  XXI  and  Chapter 1 Introduction 1.1 General This thesis describes an application of an analytical method for time and economic risk quantification for large toll highway projects.  The methodology facilitates the investigation of the  sensitivity  of  project  performance  variables for a toll highway project. to model  the economic  and  to  changes  in  primary  The goal of this thesis is  financial performance  of user-pay  highway facilities, to measure the uncertainty surrounding such projects, and to explore ways of reducing the uncertainty.  This chapter presents the background of the research, including the  toll  highway  concept  and  the  analytical  method  for  quantification of economic risks, the objectives of the research, and the structure of the thesis.  Chapter  1: Introduction  2  1.2 Background of the Research 1.2.1 Toll Highway Concept The concept of toll highway is not new at all. and researchers  Many economists  (Atkins, Bade, and Fisher, 1972; Beesley and  Hensher, 1990; Geltner and Moavenzadeh, 1987; Gittings, 1987; Johansen, 1987; Robertson, 1987; Rusch, 1984; Schneider, 1985; Wuestefeld, 1988; et al) have discussed the toll highway concept for a long time.  Many toll highways have been built in a variety  of countries, particularly in Italy, France, Spain, and Japan. On the other hand, the former West Geinnany developed its national highway  system  without  the  use  of  toll  financing.  It  is  recognized that toll financing can be an effective method for developing and improving urgently needed highway systems within limited  national  budgets,  unavoidable disadvantages.  although  such  an  approach  has  In addition to using the toll system  for the construction of new highways, several countries are also considering toll financing in order to provide funds for the improvement and rehabilitation of existing free highway networks.  The primary objectives of toll financing are described as follows by Rusch(1984): •  to obtain funds for urgently needed projects;  •  to shift the burden of capital, operating, and maintenance costs to specific users; and  Chapter I.- Introduction  •  to provide  3  an immediate  and direct  source  of revenue to  discharge the obligations created.  Potential advantages and disadvantages have been also described by Atkins, Bade, and Fisher(1972); Beesley and Hensher(1990); Geltner and Moavenzadeh  (1987); Gittings(1987); Johansen(1987);  Robertson(1987); Rusch(1984); Schneider(1985); Wuestefeld (1988) et al as follows.  Advantages include: • a more precise form of pay-as-you-go financing; • rapid construction; • fewer inflationary effects on capital cost; • better quality maintenance; • an ability to use toll rates as a form of congestion pricing; and • a better safety record.  Disadvantages include: • extra financing costs; • extra costs of toll collection; • extra costs for toll collection facilities; • the payment of a fuel tax while traveling on a toll facility; • time delays, increased fuel consumption, and worse air quality when motorists are stopped; • putting more traffic back onto underpriced roads; • creating an undesirable private monopoly of management; and  Chapter 1: Introduction  •  4  less frequent access.  According Office  to the analysis conducted by the Congressional  (Gittings,  1987),  exceed the additional built  4  or more  the benefits  facility  only  years  2  of toll-financing may  costs if a needed highway facility can be sooner  conventional tax financing. a  Budget  than  would  be possible  under  However, if toll financing produces  or fewer  years  sooner,  the use of toll  financing is probably not worth the additional costs.  Toll collection systems are generally classified into three basic categories  (Gittings, 1987).  (1) Closed  (ticket) system  This  system  Tollbooths Examples  limits  access  are located  to  at each  toll-paying  point  are the New Jersey,  motorists.  of entry  Ohio,  and  and exit.  Pennsylvania  turnpikes. (2) Open (main-line barrier) systems This system allows local, short distance traffic to use the facility  without  intermittently  paying  along  tolls.  the main  Barriers  line  are located  of the road,  tollbooth is located on the interchange ramps.  and  no  All traffic  must stop at the barriers to pay the toll.  However,  traffic  is no barrier  between  may avoid entry  paying  and exit.  tolls  if there  Examples  local  are the Connecticut  Turnpike and the Bee Line Expressway in Florida.  Chapter  l:  Introduction  5  (3) Hybrid (barrier-ramp) system This system is a hybrid of the above two systems. a closed and an open system.  There is  In the closed system, toll  barriers are located at intervals along the main line and on most interchange ramps.  Every motorist has to pay the toll.  An example is the Illinois Tollway.  The open system, on the  other hand, allows some toll free traffic.  Toll barriers  are located at the main lines and on selected high-revenue interchange ramps.  An example is the Garden State Parkway  in New Jersey.  Gittings  (1987) mentioned  that  significant  cost  savings  are  dependent on the design of the toll collection system - e.g. type of toll collection system, the number of collection points, the location of collection points - and the degree of automation in the system, and also that toll collection design decisions depend on cost, user access, traffic route choice, toll revenue, safety, and highway financing equity.  There are usually two levels of feasibility studies required: preliminary engineering studies, and more detailed and definitive engineering studies,  studies  aspects  alignment,  toll  (Rusch, 1984) . In preliminary engineering  examined rate,  include  traffic  consideration  projections,  and  of location, estimates of  construction, operation, maintenance, and financing costs.  If  preliminary studies indicate project feasibility, more detailed  Chapter 1: Introduction  and definitive  6  engineering  studies are required  in order to  produce reliable cost and revenue estimates.  Benefit-cost analysis for highway projects, which includes social benefits and impacts, has been discussed and reported on by many researchers  (Andersson,  1985;  Campbell  and Humphrey,  1988;  Christofferson, 1980; Davis and et al, 1953; Sharp, Button, and Deadman, 1986; Waters and Meyers, 1987; Weisbrod and Beckwith, 1992).  Atkins, Bade, and Fisher(1972) introduced a computer  based model roads.  for analysing the financial  feasibility  of toll  However, there seem to be very few academic studies which  focus on toll highway projects and the measurement of economic risk.  1.2.2 Analytical Method for Quantification of Economic Risks This  research  Quantification  is based of Economic  Ranasinghe (1990).  on  the Analytical  Risks,  which  Method for  was developed by  A brief outline is given below.  By way of background, several probabilistic estimate methods for project decision and performance variables have been developed. They are: Probabilistic Time Methods, Probabilistic Cost Methods, Probabilistic Time/Cost Methods, and Probabilistic Present Value Methods.  However, among them, only Probabilistic Present Value  Methods, which evaluate a project's net present value (NPV) and internal  rate  of return  (IRR),  are suitable  for economic  Chapter 1: Introduction  7  feasibility studies because they employ criteria necessary to the proper evaluation  of a project.  The Analytical  Method for  Quantification of Economic Risks belongs in this category. An engineering project can be described in terms of a hierarchy which consists of three levels, namely, project decision, project performance, and work package/revenue stream.  The  project  decision  level  is the highest  level,  and  the  individual work package/revenue stream level is the lowest level. At each level, derived variables are described by Y=sr(X) , where Y is the derived variable and X is a vector of primary variables. Derived variables at the lower level are primary variables at the higher  level.  See Table  1.1 for the variable  hierarchy  described.  Level Project Decision  Project Performance  W.P/Revenue Stream  Primary Variables Project Duration Project Cost Project Revenue W.P Duration W.P Cost Net Revenue Stream input data  Derived Variables NPV IRR Project Duration Project Cost Proj ect Revenue W.P Duration W.P Cost Net Revenue Stream  Table 1.1 Derived Variables at Each Level  The  framework  for quantifying  the uncertainty  variable is based on four assumptions:  of a derived  Chapter 1: Introduction  8  (l)The derived and the primary variables are continuous and their probability  distributions  are approximated  by the Pearson  family of distributions; (2)An expert can provide estimates for the percentiles of his subjective  prior  probability  distribution  for a primary  variable at the input level; (3)A derived variable can be more accurately estimated from a set of primary variables that are functionally related to it than by direct estimation; and (4)The correlations between primary variables are linear.  See Ranasinghe (1990) for justification of these assumption. Figure 1.1 shows the flowchart for the analytical approach.  Chapter  1:  Introduction  Analyst/Expert Input * Precedence Relations among Work Packages and Revenue Streams * Functions for Work Package Duration, Cost and Revenue Streams * Subjective Estimates for Percentiles of Primary Variables and Correlation Matrices, and Shared Variables in Functions for Work Package Durations, Costs and Revenue Streams  W.P Durations  W.P Start Times  W.P Costs and Revenue Streams  Work Package/Revenue Stream Level  First Four Moments for Work Package and Revenue Stream Start Times, Work Package Durations, Cost and Net Revenue Streams  I Project Performance Level  I  First four Moments for Project Duration, Cost and Revenue  I Project Decision Level  First Four Moments for Project Net Present Value and Cumulative Distribution Function for Project Internal Rate of Return  Figure 1.1 Flowchart for the Analytical Approach (Ranasinghe, 1990)  Chapter  1: Introduction  10  1.3 Objectives of the Research The primary objectives of this research are: 1. to model economic and financial performance of user-pay highway facilities, with special emphasis on modeling revenues and costs during the operating phase; 2. to explore the sensitivity of project performance to change in primary variables (input data).  Sensitivity  analysis for the revenue phase(traffic volume and toll rate) are emphasized; 3. to measure the uncertainty surrounding user-pay highway facilities; and 4. to explore ways of reducing the uncertainty.  The case study presented in chapter 4 is a comparison of current Japanese  (Japan  Highway  Public  Corporation)  deterministic  feasibility analysis with a probabilistic one, using essentially the same underlying project model. To achieve the objectives of the thesis, extensive work had to be done on the original main frame program developed by Ranasinghe (1990) called TIERA which was converted to a PC based program called AMMA. this thesis.  This program was extensively revised as part of It is listed in Appendix D.  Large toll highway projects consume large quantities of time, cost, and resources.  The economic  failure of a large toll  highway project would undoubtedly cause serious damage to both  Chapter 1: Introduction  11  the owner/operator of the highway and to the society in which it has been built. feasibility  Therefore, it is critical that a detailed  analysis  potential risks.  be carried  out in order  to minimize  Feasibility analyses for toll highway projects  require long-term forecasts of usage and unit rates because of long project durations, especially for the revenue phase.  This  means that such projects are executed in an environment of high uncertainty.  Although many traffic forecast methods are now  available (Bushell, 1970; Dalton and Harmelink, 1974; Davinroy, 1962; Duffus, Alfa, and Soliman,  1987; Huber, Boutwell, and  Witheford, 1968; Kadiyali, 1983; Morellet, 1981; Neveu, 1982; Newell, 1980; Thomas, 1991; et al), it is difficult to accurately estimate future traffic, because traffic volume is dependent on an  uncertain  economic  environment,  conditions and many other factors. quantification  should  be done  changing  road  network  In these situations, risk  carefully  during  feasibility  analysis.  1.4 Structure of the Thesis Chapter 2 develops an analytical model for toll highway projects, with particular  emphasis  on the revenue  phase.  The model  consists of three levels, work package/revenue stream level (the lowest level), project performance level, and project decision level (the highest level) .  As they are functionally related,  this  primary  model  requires  that  variables  for the work  Chapter 1: Introduction  12  package/revenue stream level only are inputted. be applied  to the closed, open, and hybrid  This model can systems of toll  collection.  Chapter 3 presents a numerical example patterned after a Japanese project.  Results  from a sensitivity  and risk analysis are  presented.  Chapter 4 examines strategies for risk management, and explores these impact on overall risks. Conclusions and recommendations are presented in Chapter 5.  Appendix A contains the mathematical derivation of an equation for discounted work package costs.  Appendix B contains detailed input data required by the model.  Appendix C contains interchange pair traffic volumes and growth parameters for both traffic volumes and toll rates for the sample project.  Appendix D contains source code of the model.  Chapter 2  Analytical Model 2.1 General This chapter presents an analytical model for the feasibility analysis of a toll highway project. analytical  method  for  time  and  developed by Ranasinghe (1990).  The model is based on an  economic  risk  quantification  Extensions are made in the form  of generalized revenue and operating cost models which draw on the approach used by the Japan Highway Public Corporation. Figure 2.1 shows the generalized cash flow diagram for a civil engineering project.  However, a modified cash flow diagram,  shown in Figure 2.2, is used for this model in order to make it more appropriate to a toll highway project.  In this scenario,  several basic assumptions have been made in order to simplify the model: (1)Since a project financing approach where funds are advanced during  the  construction  phase,  and  repaid  during  the  operation phase is assumed, there is no distinction between interim and permanent financing; 13  Chapter 2: Analytical  Model  (2)The  of financing  repayment  construction  phase  14  is  is assumed  completed,  to begin  although  after the  the model  is  compatible with projects involving overlapping operation and construction phases as well; (3)The repayment of financing is assumed to last until the end of the  operation  phase, but a shorter  repayment  period  or a  balloon payment at the end of the revenue phase could also be assumed; and (4)The repayment profile is assumed to be uniform and to consist of principal and interest. A more detailed explanation of each cash flow component is given in section 2.2.  Figure 2.3 shows a flow chart of the components of a general feasibility study for a toll highway project used in Japan (Japan Highway Public Corporation, 1983).  It is generally divided into  seven basic steps as follows. (1) Traffic Survey Traffic surveys to elicit base traffic and travel speed for traffic forecasts are carried out. traffic  volume  survey,  These surveys include a  a motor vehicle  origin-destination  (OD) survey, and a travel speed survey. (2) Traffic Forecast Traffic forecasts are needed for the first year and years when relevant traffic conditions change - such as a new road opening or a big industrial area being completed.  In these  'base years', traffic volume is often discontinuous because  Chapter  2: Analytical  15  Model  Permanent Financing  i k Salvage Values  Revenue Time (years)  Amortization of Permanent Financing Operating Expenses \ [ Repayment of Interim Financing  Balloon Payment  Figure 2.1 Generalized Cash Flow Diagram for an Engineering Project  i I Salvage Values  Time (years)  Balloon Payment  Figure 2.2 Cash Flow Diagram for a Toll Highway Project  Chapter  2: Analytical  16  Model  Traffic Survey  Base Traffic  Travel Speed  Traffic Volume Growth Rate  Divertible Traffic Volume  Diversion Rate  Benefit Accounting  -L Toll Rate  Travel Time Difference  Toll Travel Time Difference  Designed Daily Volume at the first year and base years  Design  Project Costs  Traffic Volume Growth Rate  Operation Costs at the first year and base years  Designed Daily Volume at each year Annual maintenance and operation costs  Annual Toil Revenue  Redemption Table  Figure 2.3 Feasibility Study Components for a Toll Highway Project  Chapter  2: Analytical  of  discrete  conditions.  Model  17  additions  to  capacity  or  changes  in  road  See Figure 2 . 4 .  traffic volume  year  r o a d opens  road c o n d i t i o n / c a p a c i t y  (base year)  (base year)  changes  Figure 2.4 general pattern of traffic growth  Future traffic volume is calculated on the basis of toll rates, results of traffic  surveys, road length, and the  traffic volume growth parameters that are based on future projections  of  economic  conditions,  population,  road  development plans, other national development plans, and so on. (3) Estimation of Annual Traffic Volume Annual traffic volume is calculated on the basis of traffic forecasts for the base years.  It is not practical to carry  out a traffic forecast for every year because of the cost and time involved.  Therefore, traffic volume in non-base  years is interpolated by parameters.  Chapter  2: Analytical  For  Model  example,  if  18  traffic  volume  derived from a t r a f f i c f o r e c a s t ,  (Qo)  in  a base  year  is  t r a f f i c volume (Qi) at year  i is:  Qi = ki/koxQo  (2.1)  where ko and ki are parameters, based on economic forecasts, national development plans, and so on.  These parameters for  the analytical model are described in more detail in section 2.5. (4) Design Toll highway  facilities are designed on the basis of the  traffic volume forecasts, topographical and geological data, political and other factors. estimated.  Then, construction costs are  The design of toll highway  facilities may be  dependent not only on traffic volume during base years, but also on that of other years. (5) Estimation of Annual Revenue In  its  simplest  form,  toll  revenue  is  calculated  by  multiplying traffic volume by toll rate. toll revenue = (traffic volume) x (toll rate) Complexity  arises  when  consideration  has  (2.2)  to be  given  to  different vehicle types, volume between interchange points, changing rates versus time, and open versus closed systems. (6) Estimation of Annual Maintenance and Operation Costs Annual maintenance and operation costs are calculated on the basis of  traffic volume, the toll  collection  system,  the  Chapter  2: Analytical  Model  19  organizational structure adopted, weather conditions, and so on. (7) Calculation of Project's Future Value (Redemption Table) The future value of the project at the end of every fiscal year  during  computed  the  in  construction  order  to  and  measure  revenue  the  phase  project's  can  be  financial  condition.  If the projected value at the end of the revenue  phase  positive,  is  calculation  the  is based  project  is  feasible.  on the above-mentioned  This  construction  costs, toll revenue, and maintenance and operation costs.  This paper forecasts  focuses  on  the procedure  followed  for base years have been completed,  after  traffic  and uses the  project's net present value as a decision criterion.  The organizational structure required for the administration of a toll road is one important factor that affects project expenses in terms of overheads.  The organizational structure assumed for  this model is shown in Figure 2.5, and reflects the structure of the  Japan  Highway  Corporation, 1992). basic  plans  and  Public  Corporation  (Japan  Highway  Public  Headquarters is in charge of formulating  policies  financing, and auditing.  for  execution,  setting  standards,  A bureau is an executing body for  performing the actual work, such as road construction, operation, etc.  Construction Bureaus are mainly in charge of construction,  and Operation Bureaus are mainly in charge of executing road operation and collecting tolls.  Each Bureau controls several on-  Chapter 2: Analytical  Model  20  site offices: a survey office for performing survey and design of road  construction;  a construction  office  in charge  of road  construction work and negotiations for acquiring rights of way; an operation office in charge of collecting tolls, operating traffic, performing road maintenance work, and management of properties.  In addition, a laboratory that performs technical  surveys, tests and research and development required for the construction and operation of roads is assumed. This structure is designed for organizations that operate several toll highway projects simultaneously, but can also be used for organizations that have only a single project. Overheads are usually allocated to each project in proportion to its construction costs and toll revenue.  The remainder of this chapter is structured as follows: section 2.2 describes the cash flows that this model assumes, section 2.3 presents the structure of the model, section 2.4 describes work packages, section 2.5 describes revenue streams, and section 2.6 describes maintenance and operation costs.  Chapter  2: Analytical  Model  Figure 2.5 Organizational Structure  21  Chapter  2: Analytical  Model  22  2.2 Cash Flows  It  is  assumed  inflation  that  rate,  with time.  all  interest  cash  flows  are  continuous,  rate, and discount  rate  and  the  are invariant  The model consists of seven categories of cash flows.  (1) Current Dollar Expenditure This  cash  include  flow  category  survey  consists  and design  of work  costs,  land  fraction  /,  package  costs  acquisition  which  costs,  and  construction costs. (2) Financing In  this model,  an equity  time, is assumed.  which  is invariant  with  Financing is described as follows:  Financing = (1-/) x current dollar expenditure of each work package.  (2.3)  (3) Revenue Revenue usually consists of toll revenue and others such as rent from  the  other  toll  highway's  miscellaneous  toll revenue only.  associated  revenues.  facilities,  However,  this  interest,  thesis  and  considers  Toll revenues are calculated by using annual  traffic volumes and toll rates. (4) Amortization of Financing It  is  assumed  that  repayment  of  financing  begins  after  the  construction phase is completed, and continues for the remaining operation  period  (recall  that  before the end of construction).  the operation  phase  could  start  Chapter  2: Analytical  Model  23  (5) O p e r a t i n g Expenses Operating expenses consist primarily of two types, maintenance costs and operation costs. (6) Salvage Values After  the  revenue  phase  expires,  toll  highway  facilities  are  usually transferred to the government, federal, provincial, or municipal. political  The salvage values are dependent on the contract, the environment, and other factors.  zero, and sometimes not.  They are  sometimes  This model can be applied to either  case. (7) Balloon Payment At the end of the revenue phase, the loan balance is discharged by the balloon payment if there is a balance left.  2.3 Structure of the Economic Analysis Model This  analytical  package/revenue  model stream  consists level,  of  project  three  levels:  performance  level,  work and  project decision level, as well the risk measurement framework. Figure 2.6 shows derived variables at each level.  Chapter  2: Analytical  24  Model Derived Variables  NPV  Project Duration  Work Pacl<age Duration  Project Decision Level  IRR  Project Performance Level  Project Cost  Project Revenue  Work Package Cost 1  Net Revenue Stream  1  Work Package/Revenue Stream Level  r  Traffic Volume  Input Data (primary variables for tfie work package/revenue stream level)  Figure 2.6 Derived Variables at Each Level  2.3 1 Work Package/Revenue Stream Level This is the lowest level, and each work package and revenue item is  linked  by  way  of  a  precedence  network.  The  work  package/revenue stream level has three derived variables: work package duration, work package cost, and net revenue stream including usage (traffic volume).  (1) Work Package Duration Work package duration can be estimated directly by experts, or derived using functional relationships that are dependent on work scope and productivity. depends  on  what  the  The selection of estimation methods  model  is  used  for.  For  preliminary  engineering studies or the early stages of feasibility studies, a  Chapter 2: Analytical  Model  25  direct estimate may be chosen.  On the other hand, for more  detailed and definitive engineering studies and for monitoring a project during the operation phase, a decomposed estimate may be used.  (2) Work Package Cost Work package cost can also be estimated directly, or derived using a functional relationship in terms of constant, current, or total dollars. The discounted cost of a typical work package is described as follows.  See Appendix A for the detailed derivation.  WPCi =  /•e^^-''^-^'^-f'Coi(T)'e^^-'''>-'dT  (2.4)  where WPCi is the discounted cost for the ith work package; Coi (T) and  Ci (T) are the functions for constant dollar cash flow and  current  dollar  cash  flow  for  the  ith  work  package  respectively (note: Ci(r) = C<.i(r)-e*''^^"'""^''^) ; Ted, Td are work package start  time  and duration;  TT, Tp and TRT are total  project  duration, construction phase finish time, and total revenue phase duration respectively; f is the equity fraction; dd, r and y are inflation, interest and discount rates, which are invariant with time, respectively. See figure 2.7 for reference.  Chapter  2: Analytical  26  Model  TT  TRT  Tsci  (l-f)Ci(T)  uniform amortization of  financing  Tmve  Ci(T)  Tci  TT-TP  Figure 2.7 Cash Flow Diagram for Work Package  (3) Net Revenue Stream Net revenue stream can be estimated directly, or derived using functional relationships. However, it is usually derived from traffic volume and toll rate.  A discounted net revenue stream is described as follows:  NRSi  =  e'-^"'f(Ri{T)-Mi{T))-e'''dT  (2.5]  where NRSi is the discounted ith net revenue stream; Ri (r) is the function for current dollar cash flow for the ith toll revenue; Moi (T) and Mi (T) are the functions for constant dollar cash flow  Chapter 2: Analytical  and  current  maintenance  Model  dollar cost  cash  27  flow  respectively  for the ith operation and  (note: Mf(r) = M?/(T-)-e^'^'^^'"""^^^) ;  TSRI  and TRI are revenue stream start time and duration of the revenue stream;  ^i,  respectively.  r  and y  are inflation  and discount  rates  See Figure 2.8 for reference.  $ TsRi  RVS#i  Time  Moi(T) Mi(T)  Tki  Figure 2.8 Cash Flow Diagram for Net Revenue Stream  Figure  2.9  shows  cost  and revenue  package/revenue stream level. later.  factors  at  the work  They are described in more detail  Chapter  2: Analytical  28  Model  r" construction costs  work paclcage costs headquarters and construction bureau overhead  Toll Highway Project  revenue  toll revenue streams  maintenance and operation costs  maintenance costs  road cleaning — road maintenance road lighting  I  bridge maintenance - i — repairing bridge repainting bridge  — tunnel maintenance — snow and ice control overlay '— others operation costs  labor costs  operation office overhead operation bureau overhead headquarters overhead  consignment costs  — others  I  toll collection toll collection machine maintenance building and repainting relevant expenses of operation  — cost for machine and equipment '— others  Figure 2.9 Cost/Revenue Components  Chapter  2: Analytical  Model  29  2.3 2 Project Performance Level The project performance level has three derived variables, project duration, project cost, and project revenue.  (1) Project duration The duration of a path is described as follows:  Tj = Y,WPDij  (2.6)  1=1  where Tj is the duration of the jth path and WPDij is the duration of the ith work package on the jth path. For  this  research,  the  probability  project in time t, denoted as p(t), basis  of  Although  the  Modified  PNET  assumes  statistically considered  that  independent,  to  activities.  PNET  be  the  as  completing  the  is calculated on the  method  two  correlated  of  (Ranasinghe,  activity  durations  different a  1990) .  result  paths of  are are  common  Then, the correlation between two paths i and  J having m common activities  is defined  as  (Ang et al. ,  1975) ,  where  cP'ijk is  the variance  paths i and j, (Ji and duration  of  paths  i  of  the  k"'  common  activity  q? are the standard deviations and  j,  and  py  is  the  on for  correlation  Chapter  2: Analytical  Model  30  coefficient between paths i and j . are  represented  by  path  assumption that p,  0.5  i  (the  pu^p  Those paths with  longest  path)  from  the  for this research, represents the  transition between high and low correlation. Therefore, the probability, p(t)  of completing the project  in time t is given by  p(t) = P(Ti < t)P(T2 < t)  where  P{T\<t)P{Ti<t)  P{Tr <t)  P{Tr<t)  are  (2.8)  the  probabilities  of  each  representative path completing the project in time t, for r representative  paths.  See Ranasinghe  (1990)  for a more  extensive description.  (2) Project Cost  The d i s c o u n t e d p r o j e c t c o s t i s d e s c r i b e d as  follows:  «  Discounted p r o j e c t  cost  =^JVPCi  (2.9)  (3) Project Revenue The discounted project revenue is described as follows: «  Discounted project revenue =^NRSi  (2.10)  Chapter  2: Analytical  Model  31  2.3.3 Project Decision Level The project decision level has two derived variables, net present value  (NPV) and internal rate of return (IRR).  (1) Net Present Value NPV = Discounted Project Revenue - Discounted Project Cost (2.11) (2) Internal Rate of Return IRR = Discount Rate when NPV = 0  (2.12)  Chapter  2: Analytical  32  Model  2.4 Work Package A  toll  highway  packages.  project  consists  of  a  variety  of  work  Therefore, it is not practical to consider every  detail of activities such as form work and concrete pouring for a feasibility  study,  especially  at  the  early  stage.  Table 2.1 shows factors considered as work packages in this model.  Attention has not been placed  developing  cost estimating  in this thesis on  relationships  for  construction  related work.  Phase (1)Survey & Design (2)Land Acquisition (3)Construction  Work Package Survey & Design Land Acquisition Earth Work Bridge Tunnel Interchange Junction Rest Area Pavement Traffic Control Facility Toll Collection Facility Building & Repairs Overhead Others (4)Revenue Stream Revenue Stream for (Finish W.P) Different Vehicle Types Maintenance Costs Operation Costs Table 2.1 Work Package Components  Chapter  2: Analytical  Model  33  2.5 Toll Revenue 2.5.1 General Toll revenue is dependent on the toll collection method, traffic volume, and toll rate.  As stated previously, toll  collection  methods can be classified into three major categories: (1) closed (ticket) system; (2) open (main-line barrier) system; (3) hybrid system. In addition, each system has several variations such as manual toll  collection,  automatic  toll  collection,  collection, e.g. Automatic Vehicle  and non-stop  Identification  (AVI).  toll This  model is designed for all of them. Each revenue stream is divided by base years.  In other words,  the first year of each revenue stream is a base year.  See Figure  2.10. The toll revenue of each revenue  stream is calculated  on the  basis of information from the base year and growth parameters. This is described in more detail later.  Chapter  2: Analytical  34  Model  duration of RVS#3 Traffic Volume  year  (base year)  (base year)  (base year)  Figure 2.10 Revenue Stream and Base Years  The revenue phase of this model requires three kinds of input data, namely, general information, toll revenue information, and maintenance and operation cost information. these  data  probabilistic physical  data  for  a  closed  variables for  a  system.  are noted. toll  highway,  interchanges, are deterministic.  Table 2.2 shows  Deterministic It is assumed such  as  the  versus  that the number  of  On the other hand, forecasts of  future events such as traffic volume and growth rate are treated as probabilistic.  See Appendix D for more detailed input data.  Although the number of primary variables for each revenue stream depends on the number of interchanges, toll collection method, revenue stream duration, and the number of vehicle types, it can be over 200.  Therefore, in order to simplify the probabilistic  treatment of the model, correlation between primary variables for the revenue phase is not considered in the present model.  Chapter  2: Analytical  Model  35  Input Data Type (1) General  Components the number of revenue streams ( = the number of base years) the number of interchanges the number of vehicle types revenue stream duration (2) Toll Revenue interchange pair toll toll growth rate interchange pair traffic volume traffic volume growth rate (3) Maintenance and weather classification Operation Cost periodic overlay periodic bridge repainting maintenance cost estimate criteria operation cost estimate criteria Table 2.2 Input Data for Revenue Streams where D : deterministic variable P : probabilistic variable  D D D P P P P P P D D D P P  In its simplest form, toll revenue is computed as: R = QX r  (2.13)  where R is toll revenue, Q is traffic volume, and r is toll rate. Q and r are usually described as an interchange pair traffic volume and interchange pair tolls when calculating toll revenue (enter at interchange 1, exit at m, pay fare rim) .  For  example,  if  there  are  5  interchanges  in  year  i,  and  interchange pair traffic volume and tolls from vehicle type j are as shown in Tables 2.3 and 2.4, the toll revenue from vehicle type j 2.14.  in year i can be described as in Table 2.5 and equation  Chapter  2: Analytical  36  Model  a-  o  IC #1  Figure 2.11 Interchanges  o#4  —o-  #2  #3  -o #5  (Example) I.e. I.e. I.e.  I.e. I.e.  #1  #2  Q ( i , l , 2 , j)  #3  #4  #5  Q ( i , 4 , 5 , j)  Q ( i , 3 , 4 , j)  Q ( i , 3 , 5 , j)  Q ( i , 2 , 3 , j)  Q { i , 2 , 4 , j)  Q ( i , 2 , 5 , j)  Q ( i , l , 3 , j)  Q ( i , l , 4 , j)  Q ( i , l , 5 , j)  Table 2.3 Interchange Pair Daily Traffic Volume I.e. I.e. I.e. I.e. I.e.  #1  #2  r ( i , i , 2 , j)  #3  #4  #5  r ( i , 4 , 5 , j)  r ( i , 3 , 4 , j)  r ( i , 3 , 5 , j)  r(i,2,3,j)  r ( i , 2 , 4 , j)  r ( 1 , 2 , 5 , j)  r{i,i,3,j)  r ( i , i , 4 , j)  r(i,i,5,j)  Table 2.4 Interchange Pair Toll I.e. I.e.  #4  #5  Q ( l , 4 , 5 , j)X r (1,4,5,j) X  365 I.e.  #1  Q(l,3,4, j)X  Q(l,3,5, j)X  r  r (1, 3,5,j) X  (1,3,4,j)X  365  365  Q(l,2,3, j)X  Q(l,2,4, j)X  Q(l,2,5, j)X  r ( i , 2 , 3 , j) X  r ( 1 , 2 , 4 , j) X  r(1,2,5,j)X  365  365  365  Q ( i , l , 2 , j)X  Q ( l , l , 3 , j)X  Q ( l , l , 4 , j)X  Q(l,l,5,j)X  r(1,1,2, j)X  r (1,1,3, j)X  r ( 1 , 1 , 4 , j) X  r(1,1,5,  365  365  365  365  I.e.  I.e.  #3  #2  j)x  Table 2.5 Interchange Pair Annual Toll Revenue  R(i.J) = 2  '^Q(i,l.m,J)  /=1 m=/+l  •r(i.l.m,j)  (2.14)  Chapter  2: Analytical  Model  37  where /?(,-^^)  : toll revenue of vehicle type j  in year i  Q(i.i,m.j) •• interchange pair traffic volume between interchanges #1 and #m for vehicle type #j in year i r(i,i.m,j)  • interchange pair toll between interchanges #1 and #m for vehicle type #j in year i  2.5.2 General Input Data For the closed system, input data required for the computer implementation of this model are:  the number of revenue streams; the number of interchanges; the number of vehicle types; and revenue stream start time revenue stream duration  For the open system, input data required in this model are:  the number of revenue streams; the number of interchanges; the number of vehicle types; the number of toll gates; location of toll gates; and  Chapter  2: Analytical  Model  38  •  revenue stream s t a r t time  •  revenue stream d u r a t i o n .  For example, if a toll gate is located at interchange #2, the location of the toll gate is indicated by 2.  If a toll gate is  located between interchanges #2 and #3, the location of the toll gate is indicated by 2.5.  2.5.3 Traffic Volume As the operation period of a toll highway project is very long, e.g. 30 years, it is very difficult to accurately forecast future traffic volumes, even though many traffic forecasting methods are available (Bushell, 1970; Dalton and Hannelink, 1974; Davinroy, 1962; Duffus, Alfa, and Soliman,  1987; Huber, Boutwell, and  Witheford, 1968; Kadiyali, 1983; Morellet, 1981; Neveu, 1982; Newell, 1980; Thomas, 1991; et al) .  In addition, because each  forecasting method has its own characteristics, tendency, and validity, it is important to consider them carefully when the five percentile subjective estimates are done. The calculation of annual  revenue  requires information about  every interchange-pair traffic volume of every vehicle type for every year during the revenue phase.  However, as mentioned  previously, it is not practical to carry out a detailed traffic forecast  for  every  year.  Therefore,  this  model  requires  information on traffic volume for base years only, and traffic volume  in non-base  years  is  interpolated  by  parameters, as  Chapter 2: Analytical  described  Model  39  in equation  (2.1).  As also mentioned previously,  traffic growth parameters in equation (2.1) are based on economic forecasts, national development plans, and so on, and the growth rate  is not constant.  parameters.  In  There may be several  this  thesis,  forecasted  kinds  annual  of the vehicle-  kilometers, which are probabilistic, are used.  This model can deal with any kind of traffic forecasting method as long as it satisfies these requirements.  In this thesis, it  is assumed that each traffic volume is independent, as mentioned in 2.5.1.  An annual discrete traffic growth model similar to that shown in Figure 2.10 is used for this model in order to calculate annual revenue and expenses.  As  mentioned  traffic  volume  in a later have  high  section,  estimates  uncertainty  among  related to the primary  variables that describe a toll highway project.  Input data required in this model are: every interchange pair traffic volume for every vehicle type in a base year for every revenue stream; and •  a traffic volume growth parameter for every year during the revenue phase.  Chapter 2: Analytical  It  is  assumed  parameters  Model  here  40  that  the traffic  are the same for each vehicle  based on the current procedure in Japan. to  the model  should  facilitate  volume type.  growth This is  Future extensions  the input  of different  growth parameters for each vehicle type, thereby rendering the model greater flexibility.  2.5.4 Toll Rate Toll rates are generally classified into 2 categories, the distance proportional toll rate and the flat(fixed) rate. The general form of the distance proportional toll rate is:  r=rpxd+rf  (2.15)  where rp -, proportional part of toll rate ($/km) rf : fixed part of toll rate ($) d  : travel distance (km)  Tolls are calculated on the basis of the above toll rate and vehicle types. types  and toll  Table 2.16 shows an example of vehicle  ratios  between  them.  This  model  also  considers the long distance discount.  It is very important to discuss whether or not future toll increases are to be considered in a feasibility analysis. Considering future toll increases may cause  overestimates  of toll revenue, especially if there is no guarantee that  Chapter  2: Analytical  Model  41  class  description  class 1  Light motor vehicle  Class 2  Ordinary motor vehicle  class 3  Medium-sized motor vehicle  b  class 4  Large-sized motor vehicle  c  class 5  Special large-sized motor vehicle  d  toll ratio a 1.00  Table 2.6 Vehicle Type and Toll Ratio  toll rates can be increased over time. cases,  it  is more  realistic  to  take  However, in some them  into  account.  Therefore, this model is applicable in both cases. Two kinds shown  of toll  in Figure  increase  2.12  and  considered  2.13.  in this model are  Figure  2.12  rates that increase annually, and Figure 2.13 rates that increase every several years. to reflect  common practice because  shows  shows toll  Figure 2.13 tends  annual  toll  are often met by public opposition.  Toll  1—I—I—I—I—I—I—I—I—I—I—I—I—r  Figure 2.12 t o l l r a t e increase  toll  Year  (case-1)  increases  Chapter  2: Analytical  42  Model  Toll  n  I  I  I  I  F i g u r e 2.13 t o l l r a t e i n c r e a s e  r  Year  (case-2)  For b o t h c a s e s , t h e t o l l r a t e i s d e s c r i b e d a s :  tolli = a • tolh  (2.16)  where tolh and tolh are the toll rates in base year and year i respectively, and ai  is a toll growth parameter for year  i. Along with traffic growth parameters, a toll growth parameter is assigned to every year during the revenue phase as input data. It is not necessary that the parameter be constant because this parameter is also dependent on economic conditions, government policies, and so on.  a± are sometimes described as cd = {l + ay~^,  where a is average annual growth rate. ai for both cases looks like Figures 2.14 and 2.15. ai  "I—I—r I I r 1 I I r Figure 2.14 toll growth parameters  Year (case-l'  Chapter  2: Analytical  43  Model  ai  "1 I I I I I I I I r 1 I r t Figure 2.15 toll growth parameters (case-2)  When  toll  rates  increase,  traffic  volume  theoretically  decreases(Japan Highway Public Corporation, 1993; et al). No attempt is made to model this phenomenon here, however, because  of  a  lack  of  data  with  which  to  attempt  the  derivation of an empirical model.  In this model, input data for the distance proportional toll are:  proportional part of toll rate for ordinary motor vehicle,fixed part of toll rate (constant for all vehicle types); interchange pair distances; toll ratio between vehicle types; long distance discount information; and a toll growth parameter for every year during the revenue phase.  In this model, input data for the fixed toll are:  Chapter  •  2: Analytical  Model  44  every interchange pair toll for every vehicle type in base year for every revenue stream; and  •  a toll growth parameter for every year during the revenue phase.  2.5.5 General Form of Toll Revenue The constant dollar toll revenue is described as follows nrv rvd(i)mc(i)~l nic(0 nvt(i)  PTOLL  =2  Z  1=1 j=l  Z k=l  Z  ^Re-J->'•'•'")  l=k+l m=l  nrv n'd(_i)mc(_i)-l nic(_i) nvtiO  K  (2.17)  ~ Z Z Z Z Z!2(''*-'-'")'-r^"''('''*''-'")'^(''-'>^^6^ ,=1 J=l  t=l 7=*+l m=l  ^(M)  where PTOLL  ' constant dollar toll revenue of the project  j^fy  : the number of revenue streams  rvd(i)  • duration of RVS #i  nic(i)  • the number of interchanges for RVS #i  nvt(i)  • the number of vehicle types for RVS #i  R(i.j,k,i,m) • annual revenue interchanges #k and #1 for vehicle type #in in jth year for RVS #i Q(i.k.i,m) : daily traffic volume between interchanges #k and #1 for vehicle type #in in base year for RVS #i k^ij^  : traffic growth parameter of year j for RVS #i  fc(i^i)  : traffic growth parameter of base year for RVS #i  Chapter  r(i,k,i.m)  2: Analytical  Model  • toll between interchanges #k and #1 for vehicle type #m in base year for RVS #i  q(i,j)  : toll growth rate parameter in year j for RVS #i  A simple example is shown below. nrv rvd(i) rvd(2) mc(i) nic(2) nvt(i) nvt(2) Q(hkj.\) Qa,k,i,2) Q(2,k,l,l) Q(2,k.l,2) ^(1,1)  A:(i,2) ^(2,1)  k(2,2) k(2,3) r(i,k,i,i) r(l,k,l,2) r(2,k,l,l) r(2,k,l,2)  q(ui) g(.u2) q(2,i) ^(2,2) ^(2,3)  2 2 3 2 3 2 2 See Table 2. 7. See Table 2. 8. See Table 2.11. See Table 2.12. 5156 5350 5480 5610 5740 See Table 2. 9. See Table 2.10. See Table 2.13. See Table 2.14. 1.00 1.02 0 (1.02M 1.040 (1.02^) 1.061 (1.02') 1.082 (1.02*)  Table 2.7 Input Data for Toll Revenue (Example)  45  Chapter  2: Analytical  Model  46  I.e.#2 I.C.#1 8, 000 Table 2.8 Daily Traffic Volume (vehicles/day)  I.C.#1 Table 2.9 Daily Traffic Volume (vehicles/day)  Q(i,k,i,i)  Q(uk.i,2)  I.e.#2 i.e.tti 5 Table 2.10 Toll  I.e.#2 i.e.#i 7 Table 2.11 Toll ($  I.e.#2 12,000  ($)  r{l,k,l,2)  r(i,k,i,i)  I.e.#3 5, 000 14,000  I.e.#2 i.e.#i 10,000 Table 2.12 Daily Traffic Volume (vehicles/day)  I.e.#3 I.e.#2 7, 000 i.e.#i 14,000 15,000 Table 2.13 Daily Traffic Volume (vehicles/day)  Q(2,k,l,l)  Q(2.k,I,2)  I.e.#3 I.e.#2 3 i.e.#i 5 8 Table 2.14 Tolls ($  I.e.#3 I.e.#2 4 i.e.#i 7 10 Table 2.15 Tolls ($  r(2,k,I,l)  r(2,k,l,2)  According Tables  to  equation  (2.16) to  (2.18),  toll  revenues  are  shown  in  (2.26)  Revenue Stream #1:  I.e.#2 I.e.#l 14 . 60 Table 2.16 Annual Revenue $ million) R(l,l,k,l,l)  I.e.#2 i.e.#i 30 . 66 Table 2.17 Annual Revenue ($ million; R(l,l,k,l,2)  Chapter  2:  Analytical  Model  I.e.#2 I.C.#1 15 .45 Table 2.18 Annual Revenue ($ million) R{l,2,k,l,l)  47  I.e.#2 I.C.#1 32 .45 Table 2.19 Annual Revenue ($ million] R(l,2,k,I,2)  Revenue Stream #2  i.e.#i  I.e.#2 18 . 98  I.e.#3 5 .69 42 .52  i.e.#i  I.e.#2 37.20  I.e.#3 10.63 56 .94  Table 2.20 Annual Revenue ($ million)  Table 2.21 Annual Revenue ($ million)  R(2,l,k,I,l)  i?(2,i, *,;,2)  i.e.#i  I.e.#2 19 . 82  I.e.#3 5 .95 44 .40  i.e.#i  I.e.#2 38.85  I.e.#3 11. 10 59 .47  Table 2.22 Annual Revenue ($ million)  Table 2.23 Annual Revenue ($ million)  R(2,2,k,I,l)  R(2,2,k,l,2)  i.e.#i  I.e.#2 20.68  I.e.#3 6 .21 46 .33  i.e.#i  I.e.#2 40 .54  I.e.#3 11 .58 62 . 05  Table 2.24 Annual Revenue ($ million)  Table 2.25 Annual Revenue ($ million)  i?(2,3, *,/,!)  R(2,3.k,l,2)  Then, total revenues are: Total Revenue of RVS #1 Total Revenue of RVS #2 Total  $ 93 .16 million $ 538.94 million $ 632 .10 million  Table 2.26 Total Revenues for an Example  Chapter  2: Analytical  48  Model  2.6 Maintenance and Operation Cost Model Maintenance  and  structures,  toll  weather  operation  costs  collection  conditions,  are  dependent  systems,  organizational  on  traffic  structures,  road  volumes, and  other  factors. This  model  assumes  dependent  on  road  dependent  on  the  shown  in Tables  that  structure, others.  2.27  constant  in  constant  dollar  while  2.28.  costs  are  operation  Components  and  2.6.2 for more detail. written  maintenance  See  mainly  costs  are  each  group  are  sections  2.6.1  and  of  Maintenance and operation costs are dollar  maintenance  form. and  It  is  operation  assumed costs  that are  constant during the operation phase because the highway is maintained properly. The same inflation rate is used for all components, because of  the  difficulty  in  identifying  differences  inflation rates for each component.  road cleaning road maintenance road lighting bridge maintenance  bridge repair bridge repainting  tunnel maintenance snow and ice maintenance overlay others Table 2.27 Maintenance Costs  between  Chapter  2: Analytical  labor  costs  consignment  49  Model  o p e r a t i o n o f f i c e overhead o p e r a t i o n bureau overhead h e a d q u a r t e r s overhead toll collection t o l l c o l l e c t i o n machine maintenance b u i l d i n g and r e p a i r s r e l e v a n t e x p e n s e s of operation c o s t of machine and equipment others  costs  others  Table 2.28 O p e r a t i o n  costs  2.6.1 Maintenance Costs In  this  model,  maintenance  costs  are  calculated  basis of road length and the number of lanes.  on  Therefore,  this information should be input. 2 Lanes  4 lanes  6 lanes  Total  Bridge  IBI  1B t  IB6  IB  = IBI + IBA + IBS  Tunnel  IT.  ITA  IT 6  IT  = ht + ITA + IT 6  earthwork  IEI  IBA  IE6  IE = IE2 +  Total  h = IBZ + ITZ + IEI  h = IBA + IT A + IEA h =  Table 2.2 9 Road Length  IB6 + IT6 + IE6  the  IEA+IE6  I = IB + IT + IE 1= h+U+h  Chapter  2: Analytical  no ventilation  50  Model  j e t fan  others  total  hj hn ITO IT Table 2.3 0 Tunnel Length by Ventilation Methods  For example, if the road structure shown in Figure 2.16 is assumed. Tables 2.29 and 2.30 become Tables 2.31 and 2.32.  road length L  Legent: —  •  ):::(  . tunnel  earth work  bridge ^BSSnKKXKK  Figure 2.16 Road Structure (Example)  road direction  Chapter  2: Analytical  Model  51  Bridge Tunnel earthwork  2 Lanes 0 0 0  4 lanes bl tl+t2 e2+e3+e4  6 lanes 0 0 el  Total  0  bl+tl+t2+ e2+e3+e4  el  Total bl tl+t2 el+e2+e3+ e4 L  Table 2.31 Road Length (Example) no ventilation tl  jet fan  others  total  t2  0  tl+t2  Table 2.32 Tunnel Length by Ventilation Methods (Example)  Maintenance costs consist of nine factors. (1) Road Cleaning Costs Road cleaning costs are calculated on the basis of the road length and the number of lanes. Input data are as follows. the number of cost ($/km) lanes 2 Cc2 4 or more Cc4 Table 2.33 Road c2Leaning Costs  Road Cleaning Costs = Cci-xh + Cc^x^h + U)  (2.18)  (2) Road Maintenance Costs Road maintenance costs are calculated on the basis of the earth work length and the number of lanes.  These  Chapter  2: Analytical  include  Model  52  pavement  maintenance, e a r t h work  repair,  planting,  road  marking,  roadside  and s o o n .  length  = road length  - b r i d g e and t u n n e l l e n g t h  Input d a t a a r e as t h e number lanes  (2.19)  follows.  of  2 4 6  cost  ($/km)  Cmi Cm4 Cm6  Table 2.34 Road Maintenance Costs r o a d m a i n t e n a n c e c o s t s = Cmixls^ + CmAxlE^+Cm^xlEs  (2.20)  (3) Road Lighting Costs Road lighting costs are calculated on the basis of the earth work and bridge length and the number of lanes. Input data are as follows. the number of c o s t ($/km) lanes 1 or 2 Oi 4 or 6 Cf4 Table 2.35 Road Lighting Costs  road lighting costs = C;IX(/B2 + /B2)+C/4X {(/B4 + /B6)+(/E4 + /E6)}  (2.21)  (4) Bridge Maintenance (Repair) Costs Bridge repair costs are calculated on the basis of the bridge  length and the number of lanes.  These  costs  Chapter  2: Analytical  Model  53  include j o i n t repair,  shoe r e p a i r ,  handrail  repair,  and  so on. Input d a t a a r e as the number lanes  of  2 4 6  follows. cost ($/km) Cri Cr4  Cre  Table 2.3 6 Bridge Maintenance (Repairing)  Costs  b r i d g e r e p a i r c o s t s = CrixlB2+Cr4xlB4 + Cr6xlB6  (2.22)  (5) Bridge Maintenance (Repainting) Costs Bridge repainting costs are calculated on the basis of the bridge  length  and the number  of lanes.  Bridge  repainting is performed at intervals of specific years, which  depend  conditions,  on  etc.  the  owner's  standards,  weather  In this model, it is assumed  that  bridge repainting is performed every nl years (for this thesis, nl equals 7) . Input data are as follows. the number lanes 2 4 6  of  cost ($/km) Cp2 Cp4 Cp6  Table 2.37 Bridge Maintenance (Repainting) Costs  bridge repaint costs = CpixlBi+Cp4xlB4+CpexlB6  (2.23)  Chapter 2: Analytical  Model  54  (6) Tunnel Maintenance Costs Tunnel maintenance costs are calculated on the basis of tunnel  length  and  the  ventilation  methods.  They  include: •  cleaning costs of interior finish boards and lights,  •  replacement costs of light bulbs,  • maintenance  costs  of  independent  electric  power  plants and cables, •  repair  costs  of  tunnel  bodies,  interior  finish  boards, and inspection steps, •  electric fees,  •  traffic control costs, etc.  Input data are as follows. cost ($/km) ventilation methods  no ventilation Ch Ctj jet fan others Cto Table 2.38 Tunnel Maintenance Costs  tunnel maintenance =  2(chxlT„+ctjxlTj + cuxlT„)  (2.24)  (7) Snow and Ice Control Costs Snow and ice control costs are calculated on the basis of  the  road  length,  the  weather conditions. Input data are as follows.  number  of  lanes,  and  the  Chapter  2: Analytical  55  Model  weather condition cost ($/k:m/2lanes) area of heavy Csh snowfall (1) area of ordinary Cso snowfall (2) Table 2.39 Snow and I c e C o n t r o l C o s t s  snow and i c e c o n t r o l = c*»x(/2 + 2/4 + S/e) o r , C«<,x(/2+2/4 + 3/6)  (2.25)  8) Overlay Costs Overlay costs are calculated on the basis of the road length  and  the  number  scarification costs. of  specific  of  lanes.  years,  that  include  Overlay is performed at intervals which  depend  standards, weather conditions, etc.. is assumed  These  overlay  on  the  owner's  In this model, it  is performed  every n2 years  (for this thesis, n2 equals 12). Input data are as follows. the number of lanes 2 4 6  cost ($/km) Co 2 Coi  Cof,  Table 2.40 Overlay Costs  overlay :  hxcoi+UxcoA+hxcoe  (2.26;  Chapter 2: Analytical  Model  56  (9) Other Indirect Maintenance Costs Other Indirect Maintenance Costs {total of costs for (1) to (6)} x p  (2.27)  where j3  : parameter for other indirect maintenance costs  2.6.2 Operation Costs In this model, operation costs are mainly calculated on the basis of traffic volume and labour costs, and take the form of a step  function  as labour/equipment  must be added in  discrete units. Operation costs consist of six factors. that  toll  collection  work  and toll  This model assumes collection  machine  maintenance are performed by subcontractors.  (1) Labor Costs (Operation Office Overhead) These are labor costs for operation offices, and are calculated  on  the basis  of  traffic  volume,  collection method, and the number of toll gates. Input data are as follows.  toll  Chapter  2: Analytical  57  Model  t r a f f i c volume (vehicles/day) 0 to toi  A  B  C  D  E  sum  ai  bi  Cl  di  ei  Si  toi  to  t02  32  b2  C2  d2  e2  S2  t02 t03  to to  t03 t04  as  b3  C3  d3  es  S3  a4  b4  C4  d4  64  S4  t04  to  t05  a5  bs be  C5  ds de  65  S5  C6 66 Se as to5 or more Table 2.41 Manpower Required for O p e r a t i o n  Office  a. closed system Traffic volume is half of the total traffic volume that each toll gate deals with. b. open system Traffic volume is the total of traffic volume that each toll gate deals with.  cost A B C D E  director vice-director chief c l e r k or engineer worker  ($/person)  Cpa Cpb Cpc Cpj  Cpe  Table 2.42 Labour Cost for Operation Office  For example, if traffic volume is between to3 and to4, toll collection costs = a'ixCpa-\-bAXCpb + C4XCpc+d4XCpd-\-e4XCp,  (2.28)  Chapter 2: Analytical  Model  (2) Labor Costs  (Operation Bureau Overhead)  58  These are labor costs for operation bureaus. Operation Bureau Overhead = Rxaz  (2.29)  where ^2  : parameter for labor costs  (operation  bureau overhead)  (3) Labor Costs  (Headquarters Overhead)  These are labor costs for headquarters. Headquarters Overhead = Rxai  (2.30)  where QTj  : parameter for labour costs (headquarters overhead)  (4) Consignment Costs Consignments calculated  (Toll Collection)  costs on  for  the basis  toll of  collection traffic  work  volume,  collection method, and the number of toll gates. Input data are as follows.  ^^^  : labour cost ($/person)  ccs  • (closed system) parameter for consignment costs  ^g  (toll collection)  :(open system) parameter for consignment costs  (toll collection)  are toll  Chapter  2: Analytical  Model  closed system t r a f f i c volume (vehicles/day)  59  clerk  (per t o l l gate) open system t r a f f i c volume clerk (vehicles/day)  0 to til til to tl2  X2  0 to t31 t31 to t32  tl2  to  tl3  X3  t32  to  t33  tl3 tl4  to to  tl4 tl5  X4  tl5  to  tl6  X6  t33 t34 t35  to to to  t34 t35 t36  tl6  to  tl7  XI  t36  to  t37  tl7  to  tl8  X&  t37  to  t38  X9  t38  to  t39  y y% y^  XIO  t39  to  t40  710  xn xn xn xu  t40  to  t41  711  t41  to  t42  yn  t42  to  t43  yi3  t43  to  t44  yi4  X15  t44  to  t45  y^^  XI  X5  J'l  y^ y^ y^ y^ y6  tl8  to  tl9  tl9 t20  to to  t20 t21  t21  to  t22  t22  to  t23  t23 t24  to to  t24 t25  t25  to  t26  Xie  t45  to  t46  yi6  t26  to  t27  X\l  t46  to  t47  yn  t27  or more  Ai:i8  t47  to  t48  yis  t48 or more Table 2.43 Manpower Required for Toll Collection  yi9  a. closed system Consignment Costs (Toll Collection) = {S(the number of clerks) x cto} x as  (2.31)  b. open system Consignment Costs (Toll Collection) = {Z(the number of clerks) x Cto} x ae  (2.32)  Chapter 2: Analytical  Model  (5) Consignment Costs  60  (Toll Collection Machine  Maintenance) Consignment maintenance costs  costs  of  toll  collection  machine  are calculated on the basis of consignment  of toll  collection  work  and, toll  collection  method. (closed system) Consignment Costs  (Toll Collection Machine Maintenance)  = Consignment Costs  (Toll Collection) x a?  (2.33)  (open system) Consignment Costs  (Toll Collection Machine Maintenance)  = Consignment Costs  (Toll Collection) x as  where ^7  : (closed system) parameter for consignment  costs  (toll collection machine maintenance) CCS  : (open system) parameter for consignment costs (toll collection machine maintenance)  (6) Other Operation Costs These include:  • building and repair expenses, •  operational expenses,  •  cost for machine and equipment, and  • others.  (2.34)  Chapter  2: Analytical  Model  61  The total of (6) to (9) = {cop X (os + U) + Co/}  (2.35)  where OB  : the number of operation office personnel  ts  : the number of toll collection clerks  Cop  : parameter for other operation costs  Cof  : parameter for other operation costs  In addition, inflation rates for maintenance and operation costs are required.  2.6.4 General Form of Maintenance and Operation Costs The  constant  dollar  maintenance  and  operation  costs  are  described as follows. nrv nm no  PMs.o = Y,TalLi^^''J^ + Oii,k))  (2.36)  ,=1 j=i t=i  where PMSCO  '• constant dollar maintenance and operation costs  nrv  : the number of revenue streams  nm  : the number of items required for maintenance cost estimates (= 9 in this model)  no  : the number of items required for operation cost estimates (= 6 in this model)  M(i,j)  • maintenance cost of item #j for RVS #i  0{ij)  '• operation cost of item #j for RVS #i  Chapter 3 Application 3.1 General This chapter applies the analytical model described in Chapter 2 to an actual deterministic feasibility study for a large toll highway project.  Section two describes the sample project, and  sections three and four present results from a sensitivity and risk analysis.  The  data  for  this  example  were  obtained  from  an  actual  deterministic feasibility analysis conducted for a toll highway in Japan.  62  Chapter  3:  63  Application  3.2 Sample Project 3.2.1 Sample Project General Information This toll highway is being constructed in northern Japan as a  bypass  urban  road  area.  intended Because  to ease this  traffic  highway  congestion  passes  near  an  in  an  urban  area, high construction costs and large traffic volumes are expected. The general details are shown in Table 3.1.  Road Length Road Structure Earth Work Bridge and Viaduct Tunnel Number of Lanes Number of Interchanges Toll Collection System Number of Vehicle Types Toll Rate  2 0.8 Km 16.8 Km 4 . 0 Km -  2 and 4 6 Closed System (Manual Collection) 5 34 cents/Km (Ordinary Motor Vehicle)  (toll ratio) Light motor vehicle 0.80 Ordinary motor vehicle 1. 00 Medium-sized motor vehicle 1.06 Large-sized motor vehicle 1 .55 Special large-sized motor vehicle 2 .75 Construction Period 10.5 years Operation Period 30 years Construction Costs $753 million Rest Facility Table 3.1 General Features of t tie Sample Project  Chapter  3: Application  64  This highway project is divided into three sections, each with a different opening date.  However, to simplify the  model, amortization of financing is assumed to start when the last segment opens.  For  illustrative  expenditure  purposes,  profiles  for  uniform  work  package  constant  dollar  costs,  uniform  constant dollar annual expenditure profiles for operating costs, and uniform constant dollar annual revenue profiles for revenue streams are assumed. I W.P.#i  ,  See Figures 3.1 and 3.2.  W.P.#i+1  T  1  r  T  r  Year  Figure 3.1 Expenditure Profiles for the Construction Phase RVS#i  RVS#I+1  toll revenue  -|  r  1  r  T  r  Year  operation cost  Figure 3.2 Expenditure and Revenue Profiles for the Revenue Phase  Chapter 3: Application  In  addition,  65  constant  interest  and inflation  rates are  The values assumed for the inflation rateidc  assumed.  and  6^) , the interest rate (r) , the discount rate (y) , and the equity  fraction  (f) are shown  construction work packages  in Table  are assumed  3.2.  to have  All  identical  inflation rates.  a  6k  Mean  a  4 .311% 4 .311% 6 .500% 6 .500% 0.000  1.093% 1.093% 0 .163%  ^  #  9 .4  2 .0 2 .0 0.1  r y f Table 3.2 Statistical Data for Inflation, Interest, Discount Rates, and Equity Fraction  9 .4 5.9 -  •^//ft and >& are the moments ratios that describe the Pearson family of distributions.  This analysis 1.1  follows the procedures  described  in Figure  and assumes that the Pearson family of distributions  will provide a good fit to most "real life" distributions (Ranasinghe, 1990). variables  Therefore, all probabilistic  and derived  variables  here  primary  are assumed  to  approximate to the Pearson family of distributions.  Figure 3.3 shows a time line for the sample project. For the  base  years  of revenue  streams  #1, #2, and #5, the  highway is assumed to open in stages, and in the other base years,  changes  predicted.  to  conditions  on  related  roads are  Chapter  3:  66  Application  ^^ M I I I I I I I I I I I  RVS#9  ^TTl  RVS#8  M-m  RVS#7 RVS#6 RVS#5 RVS#4 RVS#3  : base years  RVS#2 RVS#1 W.P.s 10  20  30  40  Year  Figure 3.3 Time Line for a Sample Project  For the purpose of this thesis, the project's net present value  (NPV)  is dealt  with  as a derived  variable  at  the  decision level.  3.2.2 Work Packages The starting point for the analysis is at the work package level. The original construction program has been modified into that described in Figure 3.4 and Table 3.5.  According to Table 3.5,  work package durations and work package costs seem not to be correlated.  This often happens because each work package does  not have the same technical complexity.  Chapter 3: Application  67  The analytical model requires the five percentile estimates for every  probabilistic  primary  variable,  and allows  package to have a different distribution. the  analysis  classified  for this  into  sample  categories  project,  each work  However, to simplify work  packages are  and the five percentile  estimate  parameters for a quasi normalized distribution are assigned to each category.  The shapes of the distribution function for all  of the work packages in one category are assumed to be identical. Such an assumption  should not be made when modeling actual  projects, as there can be significant differences in technical complexity amongst work packages in the same category.  For  example, for the category survey and design, there are 6 work packages (W.P.#2 to W.P.#7), and they have the same distribution function.  The normalized distributions correspond to the Pearson  family of distributions.  Table 3.3 shows the five percentile estimate parameters for W.P. duration.  Land acquisition has high uncertainty and is skewed to  the right because of probable difficulties in negotiating with land  owners  and residents.  Earth  work,  Interchange, and  appurtenant work also have higher uncertainty than survey and design, bridge, and others because of the greater possibility of external intervention and the complicated nature of the work.  For example, if deterministic W.P. duration for one paving job is 1  year,  the estimates  for 2.5,  5.0, 50.0, 95.0, and  97.5  percentiles are 0.90, 0.91, 1.00, 1.09, 1.10 years respectively.  Chapter 3:  68  Application  categorysurvey & design land acquisition earth work bridge pavement IC  ancillary facilities appurtenant work building & repairing overhead revenue  2.5%  5.0%  50.0%  95.0%  97.5%  VA  0.900 0.900 0.850 0.900 0.900 0.850 0.900 0.900 0.900 0.900 0.900  0.910 0.910 0.870 0.910 0.910 0.870 0.910 0.910 0.910 0.910 0.910  1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000  1.180 1.500 1.450 1.180 1.090 1.450 1.090 1.450 1.090 1.180 1.090  1.200 1.650 1.500 1.200 1.100 1.500 1.100 1.500 1.100 1.200 1.100  0.6 2.0 0.9 0.6 0.0 0.9 0.0 1.1 0.0 0.6 0.0  >& 2.4 8.0 2.8 2.4 2.2 2.8 2.2 3.2 2.2 2.4 2.2  Table 3.3 Five Percentile Estimate Parameters for W.P. Duration  There are also the five percentile estimate parameters for W.P. costs.  Table 3.4 shows the five percentile estimate parameters  for W.P. cost.  These parameters have similar shape to those of  W.P. duration.  In addition, the inflation rate is expected to be  highly uncertain. category survey & design land acquisition earth work bridge pavement IC ancillary facilities appurtenant work building & repairing overhead interest rate inflation rate  2.5%  5.0%  50.0%  95.0%  97.5%  VA  Pz  0.950 0.920 0.900 0.920 0.920 0.900 0.850 0.850 0.800 0.700 0.950 0.800  0.952 0.930 0.920 0.930 0.930 0.910 0.870 0.860 0.810 0.710 0.960 0.820  1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000  1.350 1.500 1.550 1.250 1.250 1.500 1.250 1.650 1.180 1.580 1.040 1.300  1.410 1.650 1.700 1.300 1.300 1.560 1.300 1.850 1.200 1.600 1.050 1.400  1.6 2.0 2.0 1.2 1.2 1.2 0.8 2.0 0.0 0.5 0.0 1.4  5.2 7.6 7.8 4.0 4.0 3.6 3.3 8.3 2.1 2.1 5.6 1.1  Table 3.4 Five Percentile Estimate Parameters for W.P. Costs  Once again, these parameters are used to simplify the example. In  actual  practice,  however,  it  component be estimated independently.  is  recommended  that  each  Chapter 3: Application  69  Tables 3.5, and 3.6 show statistics for work package durations and constant dollar costs used for the original deterministic feasibility analysis respectively, and Table 3.7 shows discounted work package costs based on them.  Chapter  3:  Application  Figure 3.4 Precedence Network for the Sample Project  70  Chapter  WP# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33  3:  71  Application  Work Package description  Duration (year)  Cost  Start Work Package Survey and design (1) Survey and design (2) Survey and design (3) Survey and design (4) Survey and design (5) Survey and design (6) Land Acquisition (1) Land Acquisition (2) Land Acquisition (3) Earth Work (1) Earth Work (2) Earth Work (3) Bridge (1) Bridge (2) Pavement (1) Pavement (2) Pavement (3) Interchange (1) Interchange (2) Interchange (3) Interchange (4) Ancillary Facility (1) Ancillary Facility (2) Ancillary Facility (3) Ancillary Facility (4) Appurtenant Work (1) Appurtenant Work (2) Building and Repairs (1) Building and Repairs (2) Building and Repairs (3) Overhead Finish Work Package (Revenue Phase) Total Base Estimate  -  -  ($)  1.0 0.5 2.0 2.0 1.0 2.5 0.5 2.0 2.0 0.5 3.0 1.5 3.0 1.5 1.0 1.5 1.5 2.5 3.0 1.5 1.5 0.5 1.0 1.5 1.5 2.5 3.0 1.0 1.5 1.5 10.5 26.0  2,325,600 1,162,800 3,488,400 6,201,600 3,876,000 2,325,600 6,866,100 143,043,750 78,960,150 1,256,500 57,172,200 67,224,400 46,589,500 82,825,900 30,064,700 6,906,700 3,656,500 17,600,300 34,435,400 15,304,600 9,182,800 8,570,100 16,767,700 7,452,300 4,471,400 18,373,100 22,456,000 15,347,600 4,514,000 2,708,400 32,099,500  10.5  753,229,600  ~  Table 3.5 Deterministic Values for Work Package Durations and Costs  Chapter  WP#  3:  Duration E [WPD]  1  72  Application  (year)  Constant  Dollar  GWPD  4P^  p.  E[Co]  OWPD  -  -  -  -  -  Cost  ($)  4P^ A -  -  300,516  1.6  5.2  150,258  1.6  5.2  2  1.017  0.085  0.6  2.4  2,455,530  3  0.508  0.042  0.6  2.4  1,227,770  4  2.033  0.170  0.6  2.4  3,683,300  450,774  1.6  5.2  5  2.033  0.170  0.6  2.4  6,548,080  801,376  1.6  5.2  6  1.017  0.085  0.6  2.4  4,092,550  500,860  1.6  5.2  7  2.543  0.211  0.6  2.5  2,455,530  300,516  1.6  5.2  8  0.539  0.104  2.0  8.0  7,412,300  1,369,470  2.0  7.6  9  2.152  0.410  2.0  8.0  154,423,000  28,530,600  2.0  7.6  10 11  2.152  0.410 0.094  2.0  8.0  85,241,400  15,748,900  2.0  7.6  0.530  0.9  2.8  1,365,790  274,652  2.0  7.8  12  3.178  0.565  0.9  2.8  62,143,300  12,496,600  2.0  7.8  13  1.591  0.282  0.9  2.8  73,069,600  14,693,900  2.0  7.8  14  3.050  0.255  0.6  2.4  48,141,000  4,840,470  1.2  4.0  15  1.526  0.126  0.6  2.4  85,584,000  8,605,280  1.2  4.0  16  1.000  0.055  0.0  2 .2  3,123,600  1.2  4.0  17  1.502  0.082  0.0  2.2  7,136,740  717,584  1.2  4.0  18  1.502  0.082  0.0  2.2  3,778,280  379,898  1.2  4.0  31,065,800  19  2.650  0.471  0.9  2 .8  18,935,300  3,371,490  1.2  3.6  20  3.178  0.565  0.9  2.8  37,047,300  6,596,390  1.2  3.6  21  1.591  0.282  0.9  2.8  16,465,500  2,931,730  1.2  3.6  22  0.282  0.9  2.8  9,879,280  1,759,040  1.2  3.6  23  1.591 0.500  0.027  0.0  2.2  8,760,390  1,021,340  0.8  3.3  24  1.000  0.055  0.0  2.2  17,139,900  1,998,280  0.8  3.3  25  1.502  0.082  0.0  2.2  7,617,730  888,125  0.8  3.3  26  1.502  0.082  0.0  2.2  4,570,640  532,875  0.8  3.3  27  2.668  0.438  1.1  3.2  20,106,600  5,019,960  2.0  8.3  28  3.200  0.526  1.1  3.2  24,574,700  6,135,510  2.0  8.3  29  1.000  0.055  0.0  2.2  15,319,200  1,726,440  0.0  2.1  30  1.502  0.082  0.0  2.2  4,505,650  507,775  0.0  2.1  31  1.502  0.082  0.0  2.2  2,703,390  304,665  0.0  2.1  32  10.676  0.891  0.6  2.4  33,821,600  8,787,020  0.5  2.1  33  26.000  1.422  0.0  2.2  801,271,150  -  -  -  Table 3.6 Statistics for Work Package Durations and Costs  Chapter  3:  73  Application  WP# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Total  Discounted W.P. cost ($) -  2,296,771 1,127,032 3,277,390 5,542,311 3,336,191 1,916,290 6,654,896 134,391,152 70,565,928 1,217,880 53,053,544 58,959,172 43,233,280 72,642,408 25,556,122 5,690,555 2,865,718 16,640,328 30,396,242 12,768,268 7,196,808 7,610,584 14,432,428 6,217,264 3,504,348 17,370,926 19,332,550 13,210,146 3,765,920 2,122,653 28,232,106 -  675,127,211  Table 3.7 Discounted Work Package Costs  Chapter  3:  Application  74  3.2.3 Revenue Streams In  this  example,  revenue  streams,  like  work  packages, are  calculated using the five percentile estimate parameters.  Table  3.8 shows the five percentile estimate parameters for revenue streams.  Traffic volumes and inflation rates are assigned high  uncertainty because of the difficulty in forecasting them.  In  contrast, toll growth rates involve less uncertainty than other factors because they can be controlled by the highway operators to a certain extent. category-  2.5%  5.0%  50.0%  95.0%  97.5%  yfF^  ^  traffic volume RVS duration toll toll growth rate traffic growth rate road length inflation rate (maintenance cost) maintenance unit costs cost parameter (operation cost) labour cost traffic range number of workers cost parameter  0.350 0.900 0.900 0.800 0.700 0.920 0.800  0.500 0.910 0.910 0.850 0.750 0.930 0.820  1.000 1.000 1.000 1.000 1.000 1.000 1.000  1.350 1.090 1.180 1.050 1.090 1.070 1.300  1.400 1.100 1.200 1.060 1.100 1.080 1.400  -1.0 0.0 0.6 -2.0 -1.0 0.0 1.40  5.9 2.2 2.4 10.2 3.4 2.4 7.7  0.92 0 0.900  0.930 0.910  1.000 1.000  1.250 1.250  1.300 1.300  1.2 1.0  4.0 3.4  0.900 0.900 0.900 0.900  0.910 0.910 1.910 0.910  1.000 1.000 1.000 1.000  1.250 1.250 1.090 1.250  1.300 1.300 1.100 1.300  1.0 1.0 0.0 1.0  3.4 3.4 2.2 3.4  Table 3.8 Five Percentile Estimate Parameters for Revenue Streams  In  this  example,  categories:  vehicles  are  classified  light motor vehicle, ordinary  into  five  motor vehicle,  medium-sized motor vehicle, large-sized motor vehicle, and special  large-sized  motor  vehicle.  Deterministic  ratios between vehicle types are shown in Table 3.1.  toll It is  Chapter 3: Application  75  assumed that the numbers for all vehicle types grow at the same rate, and have the same distribution.  In real life,  for example, when a big industrial area is developed, the number  of trucks  vehicle  types.  difference  may increase However,  more  in this  than  example,  that this  is not considered because, at least  differential  traffic  volume  increases  due  of other possible in Japan, to  local  development are not considered for feasibility analyses for regional highways, in order to avoid overestimating future traffic volumes However,  (Japan Highway Public Corporation,  in the model,  it is possible  1983).  to set different  growth rates and distributions for each vehicle type.  Interchange  distances  are shown  in Table  each vehicle type are shown in Tables  3.9; tolls for  3.10 to 3.14; and  spot traffic volumes are shown in Tables 3.15 to 3.19 and Figures 3.5 to 3.9 (A indicates base years). (Unit : km)  I . e . #4 I . e . #3 6. 7 I . e . #2 3 .3 10 . 0 I . e . #1 3 .4 6. 7 13 .4 T a b l e 3 . 9 I n t e r c ]biange DisS t a n c e s  I . e . #5 3 .0 9. 7 13 .0 16 .4  Dollar) I . e . #6 I . e . #5 1. 0 I . e . #4 2. 0 1. 0 2. 0 2 .5 I . e . #3 3 .5 1. 0 2 .5 3 .5 4 .5 2. 0 4 .5 5 .5 3 .5 f o r L i g h t: M o t o r \V e h i c l e (Unit  I . e . #2 I . e . #1 1. 0 T a b l e 3 . 10 T o l l  I . e . #6 4 .4 7 .4 14 . 1 17 .4 20 . 8  :  Chapter  3:  76  Application (Unit  I.e. #4 I.e. #3 1. 0  2 .5 3 .5 4 .5  : Dollar)  I.e. #5 1. 0 3 .5 4 .5 5 .5  I.e. #2 I.e. #1 1 .5 2 .5 T a b l e 3. 11 Toll for O r d i n a r y M o t o r  I.e. #6 1.5 2 .5 5 .0 6. 0  7.0  Vehicl e  (Unit  I.e. 2 3 5  #4 .5 .5 .0  I.e. 1 3 4 6  : ]Dollar) I.e. #6 1 .5 #5 .0 2 .5 .5 5 .0 .5 6 .0 .0 7.5  I.e. #3 I.e. #2 1.0 I.e. #1 1 .5 2 .5 T a b l e 3. 12 Toll for M e d i u m - s i z e d M o t o r  Ve h i d e  (Unit  : ]Dollar) I.e. #6 I.e. #5 2 .5 1. 5 4 .0 5 .0 7.5  I.e. #2 2 . 0 I.e. #1 T a b l e 3. 13 T o l l  I.e. #4 I.e. #3 3 .5 1 .5 5 .0 6.5 9.0 3 .5 7.0 8 .5 11 . 0 f o r L a r g €; - s i z e d M o t o r V e h icle  (Unit : ]Dollar) I.e. #5 I.e. #4 I.e. #3 I.e. #2 I.e. #1 T a b l e 3. 14  3 . 0 6 .0  3 .0  Toll  6 . 0 9 .0 12 . 0  3 . 0  9.0 12 . 0 15 . 0  I.e. #6 4 .0  7.0 13 . 0 16 . 0 19 . 0  for Spec:lal Large'-sized M otor  Veh icle  The toll rate is assumed to increase every three years in proportion  to one half  of the inflation  increase of approximately 2% per year.  rate, giving an  Chapter  3:  Application  Year  RVS # Daily Traffic Volume (vehicles/day) 1 1 0 2 2 0 3 0 3 4 4 0 5 5 11,266 6 11,419 7 12,084 6 8 12,340 7 9 15,246 10 15,556 11 15,844 12 16,179 13 8 31,337 14 31,912 15 32,429 16 33,Oil 17 9 33,090 18 33,510 19 33,884 20 34,362 21 34,786 22 35,167 23 35,590 24 36,010 25 36,442 26 36,862 27 37,284 28 37,666 29 38,082 30 38,559 Table 3.15 Spot Traffic Volume between Interchange #1 and #2  77  Chapter  3:  Application  Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  RVS # Daily Traffic Volume (vehicles/day) 1 0 2 12,200 3 18,769 4 20,512 26,247 5 26,601 6 27,985 28,583 7 31,293 31,936 32,536 33,232 8 46,416 47,274 48,064 48,933 9 49,717 50,363 50,938 51,668 52,324 52,908 53,558 54,205 54,857 55,509 56,156 56,741 57,381 58,112  Table 3.16 Spot Traffic Volume between Interchange #2 and #3  78  Chap ter  3: Appl i cat ion  Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  RVS # Daily Traffic Volume (vehicles/day) 1 17,462 2 20,271 24,307 3 4 26,114 5 30,098 30,500 32,233 6 32,928 7 35,348 36,076 36,760 37,545 8 49,423 50,342 51,185 52,110 9 52,385 53,068 53,686 54,457 55,146 55,772 56,456 57,146 57,837 58,534 59,217 59,838 60,519 61,293  Table 3.17 Spot Traffic Volume between Interchange #3 and #4  79  Chapter  3:  Application  Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  RVS # Daily Traffic Volume (vehicles/day) 1 22,212 2 24,960 28,421 3 4 30,591 5 32,386 32,819 34,763 6 35,518 7 39,651 40,475 41,251 42,137 8 53,704 54,712 55,640 56,647 9 57,008 57,768 58,441 59,290 60,052 60,733 61,487 62,246 63,007 63,775 64,530 65,215 65,964 66,808  Table 3.18 Spot Traffic Volume between Interchange #4 and #5  80  Chapter  3:  Application  Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  RVS # Daily Traffic Volume (vehicles/day) 1 22,943 2 24,572 3 28,740 4 31,723 5 33,716 34,174 6 35,470 36,213 7 44,827 45,731 46,571 47,546 8 56,263 57,298 58,241 59,276 9 60,356 61,127 61,812 62,681 63,451 64,148 64,916 65,679 66,475 67,246 68,010 68,708 69,471 70,338  Table 3.19 Spot Traffic Volume between Interchange #5 and #6  81  Chapter  3:  82  Application  80000 70000 0)  60000  o & 50000 § I 40000 d u h 1 30000 >^ > '5 ^ 20000 G 10000 0  H  f-  A  I ^ I ^ I—I—I 4  I—^—1—4"  H  1 1 1 H  H  1 1  1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930 Year F i g u r e 3.5  Spot T r a f f i c V o l u m e b e t w e e n #1 and #2  Interchange  80000 70000 I  60000  o 5* 50000 i= »• 40000 h » 30000 (5 Q  20000 10000 H 1 1 1 1 1H 1 1 ! 1A 4 4 A ' A I 4 I I iH^ 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930  Year F i g u r e 3.6  Spot T r a f f i c V o l u m e b e t w e e n #2 and #3  Interchange  Chapter  3:  83  Application  80000 70000  I  60000  0 O 50000  > S  1 £ 40000 d u H ^ 30000 >• > (5 "^ 20000 G 10000 O A f 4 ^ 4 I 4 I A H 1 h 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930 Year  F i g u r e 3.7 Spot T r a f f i c Volume between #3 and #4  Interchange  80000 ^ 70000 0)  60000  0 S" 50000 > TO  1 S 40000 Id u  h S 30000 ^ " ^ 20000 G 10000  QIAAAAI A I A  I  A  I — I — I — I — I — I — I — I — I -  H  \  1  1 2 3 4 5 6 7 8 91011121314151617181920212223242526272829X Year  Figure 3.8 Spot Traffic Volume between Interchange #4 and #5  Chapter  3:  84  Application  80000 70000  I  60000  o e 50000 > £ d H  ^ £ 40000 u ^ 30000  •g Q  20000 10000 H 1 1 1 1 1 1 1 O^AAAA I A I 4 I I I 4 I I I 4 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930  Year  Figure 3.9 Spot Traffic Volume between Interchange #5 and #6  Appendix  C contains  interchange  pair  traffic  volumes in  base years, traffic volume growth parameters, and toll rate growth parameters.  Appendix B contains other more detailed  input data.  Table  3.20  shows  deterministic  annual  revenues  maintenance and operating costs (constant dollar).  and  annual  A total of  nine revenue streams corresponding to nine different base years are used to describe the project.  Each revenue stream includes  all vehicle types and all increases in traffic volumes and toll rates for that revenue stream's duration.  Table 3.21 shows the  deterministic  form  discounted  revenues  which  parts  of the  Chapter 3: Application  conventional analysis.  85  They will be used later to compare with  the probabilistic results.  RVS # year  annual revenues($)  annual operation costs ($)  1 2 3 4 5  1 1 1 1 1 2 1 2 1 2 3 4 1 2 3 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14  36,241,000 6,908,380 45,332,800 8,Oil,250 54,980,500 9,091,350 62,667,200 9,370,250 74,931,300 10,534,000 75,820,300 10,549,100 6 84,904,900 11,049,400 86,729,300 16,780,200 7 98,677,500 12,799,500 13,087,200 106,880,000 108,875,000 13,121,100 111,036,000 16,405,300 8 162,106,000 15,211,800 164,962,000 15, 556,800 168,057,000 15,905,900 181,374,000 22,029,700 9 182,462,000 16,546,000 184,958,000 16,786,100 198,918,000 17,023,400 201,567,000 17,068,500 203,951,000 17,109,000 219,245,000 17,698,200 222,056,000 18,042,400 224,866,000 27,284,400 241,621,000 19,017,300 244,604,000 19,068,000 247,587,000 19,118,700 265,904,000 19,430,100 268,753,000 19,478,500 271,918,000 19,532,400 Total 4,801,984,800 469,614,230 Table 3.20 Deterministic Annual Revenues and Annual Maintenance and Operating Costs (Constant Dollar)  Chapter  3:  Application  RVS # Discounted Revenues ($) 1 17,197,658 2 20,396,808 3 23,375,566 4 25,423,164 55,608,140 5 6 51,585,960 7 108,936,328 137,441,792 8 9 341,720,064 781,685,480 Total Table 3.21 Discounted Revenues for the Original Feasibility Analysis  86  Chapter  3:  87  Application  3.2 4 Calculation Results T a b l e s 3.22 t o 3.24 show t h e s t a t i s t i c s anal y t i c a l  approach •  WP# E[Cost] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33  e v a l u a t e d from t h e  2,426,922 1,191,287 3,466,470 5,868,715 3,536,048 2,033,763 7,189,650 145,033,968 75,812,112 1,324,929 57,561,288 63,972,888 44,655,704 74,626,536 26,237,010 5,850,180 2,967,196 17,908,290 32,546,888 13,645,265 7,766,000 7,775,125 14,761,998 6,365,913 3,606,331 19,014,506 2,111,917 13,193,518 3,731,328 2,128,250 29,856,906 -  Discounted Work Package Costs ($) OtVPD skewness 307,731 1 .441 150,934 1.445 440,294 1.436 754,482 1.397 461,781 1.356 272,631 1.302 1,348,819 1 .909 27,284,032 1.895 14,369,514 1.856 269,923 1.923 11,775,636 1.898 13,181,744 1.862 4,762,571 1.019 8,225,747 0.966 2,963,008 0 . 949 678,961 0 .941 359,682 0.953 1 .132 3,250,705 5,980,267 1.099 2,546,414 1. 070 1,478,051 1 . 046 0 .687 965,464 1,853,530 0 .691 814,869 0.691 483,579 0 . 712 1 .944 4,794,670 5,374,707 1. 890 0 . 057 1,609,108 469,362 0.108 278,937 0 .208 7,878,655 0 .479 -  Table 3.22 S t a t i s t i c s for Discounted Work Package Costs  kuTtosis 4 .531 4 .542 4 .492 4 .343 4.207 4.035 7.139 7.057 6.844 7.392 7 .265 7.055 3 .246 3 .121 3 .080 3 .062 3 .090 3 .537 3 .450 3 .375 3 .314 2 .596 2 .573 2 .572 2 .609 7.957 7.655 2 .004 2 . 014 2 .052 2 .275 -  Chapter  3:  88  Application  Discounted Revenues ($) OtFPD skewness 3,070,476 -0 .579 3,085,872 -0.576 3,676,449 -0.565 -0.557 3,901,506 8,278,854 -0.111 8,457,769 -0.106 18,919,314 0 .252 23,890,288 0.210 69,715,768 0.246  RS# 1 2 3 4 5 6 7 8 9  E[Revenue] 16,309,014 19,234,812 22,230,906 23,743,590 50,141,572 46,100,320 98,181,080 124,448,704 305,117,600  kurtosis 2 .402 2 .398 2 .384 2 .372 2 . 015 2 .013 2 .076 2 . 053 2 .073  Table 3.23 S t a t i s t i c s for Discounted Revenues  Project (month) Project ($) Project ($) NPV($)  Mean 135.77  Duration  OtfTD  7 .21  skewness 0 .700  kurtosis 3 .600  Cost  717,174,144  39,283,612  0.876  4.100  Revenue  705,507,584  77,309,352  0.190  1.411  -11,666,560  86,717,576  0 . 053  2 .043  Table 3.24 S t a t i s t i c s Project Cost, P r o j e c t Value(NPV)  for Project Duration, Discounted Revenue, and P r o j e c t Net P r e s e n t  Cumulative  of  probabilities  derived  variables  at  the  project  performance l e v e l and the p r o j e c t decision l e v e l are described below.  (1) P r o j e c t  Table  3.25  Duration  and  Figure  p r o b a b i l i t y of t h e p r o j e c t  3.10  present  duration.  the  cumulative  Chapter 3: Application  According  89  to the original  deterministic  project duration was 126 months. model  indicates  that  estimate, the  However, this analytical  the expected  project  duration is  135.77 months, and the standard deviation is 7.21 months. The project  duration  longer  was indicated  than  is projected  to be about  by the original  10 months  deterministic  feasibility analysis. Cumulative Probability(%) 0.25 0.50 1.00 2.50 5 .00 10 . 00 25 .00 50 .00 75 .00 90.00 95 .00 97.50 99 .00 99.50 99 .75  Project Duration (month) 121.69 122 .31 123.05 124 .32 125 .57 127 .22 130.49 134.89 140.11 145 .47 148 .97 152 .16 156.04 158.77 161.38  Table 3.25 Cumulative Probability of Project Duration  Chapter  3:  90  Application  Figure 3.10 Cumulative Probability of Project Duration  (2) Project Costs Table  3.26  and  Figure  3.11  present  the  cumulative  probability of the project cost. According  to  the  original  deterministic  discounted project  cost was  $675,127,211.  estimate,  the  However, this  analytical model indicates that the expected project cost is $717,174,144, and the standard deviation is $39,283,612. The project cost is projected to be about $42,000,000 more than  was  indicated  feasibility analysis.  by  the  original  deterministic  Chapter  3:  91  Application  Cumulative Project Cost ($) Probability{%) 0 .25 606905024.00 0.50 615987392.00 1.00 625788672.00 2 .50 640178240.00 5.00 652556544.00 10.00 666828288.00 25 .00 690677376.00 717174144.00 50.00 75 . 00 743670912.00 90.00 767520000.00 781791744.00 95 .00 97 .50 794170048.00 99.00 808559616 . 00 99 .50 818360896.00 99 . 75 827443264.00  Table 3.26 Cumulative P r o b a b i l i t y of P r o j e c t Cost  600 620 640 660 680 700 720 740 760 780 800 820 840  project cost ($,000,000) Figure 3.11 Cumulative Probability of Project Cost  (3) Project Revenue Table  3.27  and  Figure  3.12  present  probability of the project revenue.  the  cumulative  Chapter 3: Application  According  92  to the original  deterministic  discounted project revenue was $781,685,480. analytical revenue  model  indicates  is $705,507,584,  that  estimate, the However, this  the expected  and the standard  project  deviation is  $77,309,352. The project less  than  revenue  is projected  was indicated  to be about  by the original  $76,000,000  deterministic  feasibility analysis. Cumulative Project Revenue ($) Probability(%) 0 .25 488500224 .00 0.50 506374144.00 1 .00 525662848.00 2 .50 553981248.00 5.00 578341440 .00 10 .00 606427904 .00 25.00 653362432.00 50.00 705507584.00 75 . 00 757652736 .00 90 .00 804587264 .00 95.00 832673728 .00 97.50 857033920.00 99.00 885352320.00 99.50 904641024.00 99.75 922514944.00  Table 3.27 Cumulative Probability of Project Revenue  Chapter  3:  93  Application  1.00  y--^^^  .80 /  ,60  7 --A ^ - 1 : :  ,40 0.20 0.00  - »-i».HahrH^r^  i  •1 i  ^  i  : -  ,1  y  \  i  --I  1  - )  450 500 550 600 650 700 750 800 850 900 950 project re venue ($,000,000) Figure 3.12 Cumulative Probability of Project Revenue  (4) Net Present Value Table  3.28  and  Figure  3.13  present  the  probability of the Project Net Present Value According  to the original  was $106,558,269. that  the  expected  deterministic  cumulative  (NPV).  estimate,  However, this analytical model NPV  is  -$11,666,560,  and  the  the NPV indicates standard  deviation is $86,717,576. The NPV is projected to be about $118,000,000 less than was indicated analysis.  by  the  original  deterministic  feasibility  Chapter  3:  94  Application  Cumulative Probability(%)  NPV  ($)  0.25 -255082800.00 0.50 -235033696.00 1.00 -213397664.00 2 .50 -181633008.00 5 .00 -154308304.00 10.00 -122803808.00 25 .00 -70157568.00 50 .00 -11666560 .00 46824444 .00 75 .00 90.00 99470688.00 95 .00 130975184.00 97 .50 158299888.00 99 .00 190064544.00 99.50 211700576.00 231749680.00 99 . 75 Table 3.28 Cumulative Probability of Project Net Present Value  1.00^  a o 0)  >  E U  -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 NPV{$,000.000) Figure 3.13 Cumulative Probability of Project Net Present Value  Chapter  3: Application  95  3.3 Sensitivity Analysis 3.3.1 Results This section describes the sensitivity analysis for the sample project.  The analytical model requires subjective estimates of  primary variables whose accuracy can affect the entire analysis. Therefore, it is important to identify the sensitivity of each primary variable, and to be very careful when highly sensitive variables are estimated.  The purpose of sensitivity analysis is  to identify how much a change in a primary variable affects the derived variable.  In this section, the focus is on revenue  streams. The sensitivity of a primary variable is measured by the total sensitivity coefficient for that variable.  The general idea of  sensitivity analysis is as follows. The sensitivity of the derived variable whose functional form is given by Y = g{X) is described as (Russell, 1992), AY  where  AY  —  AXi  ^^  AXi  and  I  are  the  percent  changes  m  /  and  Xi  JCi  respectively, and ^i is the total sensitivity coefficient, which is defined as (Russell, 1992), o.  ^  Xi  ^ i  Y  Si=  3.2  Chapter  3: Application  where  96  i s the s e n s i t i v i t y c o e f f i c i e n t  of /  with respect  to  Xi.  Because moment analysis is based on the truncated Taylor series expansion  g{X),  of  the partial  primary variables are evaluated.  derivatives  with  respect  However, since the analytical  method transforms the primary variables X to Z and g{X) prior to using coefficients  the Taylor  are  evaluated  to  to G{Z)  series expansion,  the  sensitivity  with  the  transformed  respect  to  variables.  ^.2^,^ Y  ^  (3.3,  Zi  Si=  (3.4) cZiY  In this  section,  variables.  revenue  streams  are  considered  as derived  Highly sensitive primary variables for each derived  variable are shown in Tables 3.29 to 3.37.  Chapter  3:  Application  97  (Deterministic Duration Estimate : 1 year) Ranking 1 2 3 3 5 6 7 7 9 9 11  Primary Variable parameter (toll rate growth) RVS early start time toll(Ic#3-#6, vehicle-2) traffic volume (Ic#3-#6, vehicle-2) parameter (consignment cost of toll collection) labor cost (toll collection) toll(Ic#3-#5, vehicle-2) traffic volume (Ic#3-#5, vehicle-2) toll(Ic#3-#6, vehicle-l) toll(Ic#3-#6, vehicle-l) inflation rate  Si  1.32811 -0.526802 0.453709 0.453709 -0.185005 -0.185002 0.135406 0.135406 0.106513 0.106513 -0.104595  Table 3.29 Total sensitivity Coefficients for RVS #1  (Deterministic Duration Estimate : 1 year) Ranking 1 2 3 3 5 5 7 7 9 10 11 11  Primary Variable parameter (toll rate growth) RVS early start time toll (Ic#2-#6, vehicle-2) traffic volume (Ic#2-#6, vehicle-2) labor cost (toll collection) parameter (consignment cost of toll collection) toll(Ic#3-#6, vehicle-2) traffic volume (lc#3-#6, vehicle-2) inflation rate the number of toll collection clerks toll(Ic#2-#5, vehicle-2) traffic volume (Ic#2-#5, vehicle-2)  Si  1.32186 -0.606351 0.274935 0.274935 -0.180724 -0.180724 0.172023 0.172023 -0.117903 -0.114262 0.108815 0.108815  Table 3.30 Total sensitivity Coefficients for RVS #2  Chapter  3:  98  Application  (Deterministic Duration Estimate : 1 year) Ranking 1 2 3 3 5 5 7 7 9 9 11  Primary Variable parameter (toll rate growth) RVS early start time toll (Ic#2-#6, vehicle-2) traffic volume (Ic#2-#6, vehicle-2) labor cost (toll collection) parameter (consignment cost of toll collection) toll (Ic#2-#5, vehicle-2) traffic volume (Ic#2-#5, vehicle-2) toll (Ic#3-#6, vehicle-2) traffic volume toll (Ic#3-#6, vehicle-2) inflation rate  Si  1.28879 -0.675688 0.325839 0.325839 -0.166774 -0.166774 0.125868 0.125868 0.123317 0.123317 -0.120515  Table 3.31 Total sensitivity Coefficients for RVS #3  (Deterministic Duration Estimate : 1 year) Ranking 1 2 3 3 5 5 7 8 8 10 10  Primary Variable parameter (toll rate growth) RVS early start time toll (Ic#2-#6, vehicle-2) traffic volume (Ic#2-#6, vehicle-2) labor cost (toll collection) parameter (consignment cost of toll collection) inflation rate toll (Ic#2-#5, vehicle-2) traffic volume (Ic#2-#5, vehicle-2) toll (Ic#3-#6, vehicle-2) traffic volume (Ic#3-#6, vehicle-2)  St  1.28737 -0.755225 0.313043 0.313043 -0.169169 -0.169169 -0.133920 0.125191 0.125191 0.105923 0.105923  Table 3.32 Total sensitivity Coefficients for RVS #4  Chapter  3:  Application  99  (Deterministic Duration Estimate : 2 year) Ranking 1 2 3 4 5 6 7 8 9 10 11 11  Primary Variable RVS early start time parameter (toll rate growth) the first year parameter (traffic growth) the first year parameter (toll rate growth) the second year parameter (traffic growth) the second year traffic volume (Ic#2-#6, vehicle-2) toll (Ic#2-#6, vehicle-2) parameter (consignment cost of toll collection) labor cost (toll collection) inflation rate toll (Ic#l-#6, vehicle-2) traffic volume (Ic#l-#6, vehicle-2)  Si  -0.884902 0.659903 -0.624994 0.624937 0.624933 0.228876 0.228872 -0.168755 -0.168751 -0.162603 0.117991 0.117991  Table 3.33 Total sensitivity Coefficients for RVS #5  Chapter  3:  100  Application  (Deterministic Duration Estimate : 2 year) Ranking 1 2 3 4 5 6 7 8 9 10 11 12  Primary Variable RVS early start time parameter (toll rate growth) the first year parameter (traffic growth) the first year parameter (toll rate growth) the second year parameter (traffic growth) the second year inflation rate traffic volume (Ic#2-#6, vehicle-2) toll (Ic#2-#6, vehicle-2) parameter (consignment cost of toll collection) labor cost (toll collection) toll(Ic#l-#6, vehicle-2) traffic volume (Ic#l-#6, vehicle-2)  Si  -1.10177 0.710231 -0.679008 0.678934 0.678929 -0.255841 0.237182 0.237177 -0.179586 -0.179581 0.124552 0.124552  Table 3.34 Total sensitivity Coefficients for RVS #6  Chapter  3:  Application  101  (Deterministic Duration Estimate : 4 year) Ranking 1 2 3 4 5 6 7 8 8 10 11 12 13 13 15 15  Primary Variable RVS early start time parameter (traffic growth) the first year parameter (traffic growth) the second year parameter (toll rate growth) the second year parameter (toll rate growth) the first year parameter (traffic growth) the third year parameter (toll rate growth) the third year parameter (toll rate growth) the fourth year parameter (traffic growth) the fourth year inflation rate traffic volume (Ic#2-#6, vehicle-2) toll (Ic#2-#6, vehicle-2) labor cost (toll collection) parameter (consignment cost of toll collection) toll (Ic#l-#6, vehicle-2) traffic volume (Ic#l-#6, vehicle-2)  Si  -1.23521 -0.992122 0.346556 0.346552 0.341947 0.330304 0.330300 0.315163 0.315163 -0.272465 0.203149 0.203153 -0.192027 -0.192027 0.136613 0.136613  Table 3.35 Total sensitivity Coefficients for RVS #7  Chapter  3:  Ranking 1 2 3 4 4 6 7 8 9 10 11 12 13 13 15 15 17 17  Application  (Deterministic Duration Estimate : 4 year) Primary Variable Si RVS early start time -1.52193 parameter (traffic growth) -0.942056 the first year parameter (toll rate growth) 0.339475 the first year parameter (toll rate growth) 0.323165 the second year parameter (traffic growth) 0.323165 the second year parameter (traffic growth) 0.310871 the fourth year parameter (toll rate growth) 0.310868 the fourth year parameter (traffic growth) 0.307962 the third year parameter (toll rate growth) 0.307955 the third year inflation rate -0.295489 traffic volume 0.179443 (Ic#l-#6, vehicle-2) toll (Ic#l-#6, vehicle-2) 0.179440 labor cost (toll collection) -0.162416 parameter (consignment cost -0.162416 of toll collection) toll (Ic#2-#6, vehicle-2) 0.126082 traffic volume 0.126082 (Ic#2-#6, vehicle-2) toll (Ic#l-#6, vehicle-4) 0.126033 traffic volume 0.126033 (Ic#l-#6, vehicle-4)  Table 3.36 Total sensitivity Coefficients for RVS #8  102  Chapter  3:  Application  (Deterministic Duration Estimate : 14 year) Ranking Primary Variable Si 1 RVS early start time -1.91796 2 parameter (traffic growth) -1.21835 the first year inflation rate -0.520859 3 4 labor cost (toll collection) -0.210106 4 parameter (consignment cost -0.210106 of toll collection) traffic volume 0.181898 6 (Ic#l-#6, vehicle-2) 6 toll (Ic#l-#6, vehicle-2) 0.181898 toll (Ic#2-#6, vehicle-2) 0.133843 8 traffic volume 0.133843 8 (Ic#2-#6, vehicle-2) 10 toll (Ic#l-#6, vehicle-4) 0.122000 10 traffic (Ic#l-#6, vehicle-4) 0.122000 12 parameter (toll rate growth) 0.118742 the first year 13 parameter (toll rate growth) 0.112559 the second year 13 parameter (traffic growth) 0.112559 the second year 15 parameter (toll rate growth) 0.113193 the third year 15 parameter (traffic growth) 0.113193 the third year 17 parameter (toll rate growth) 0.107248 the fourth year 17 parameter (traffic growth) 0.107248 the fourth year 19 toll (Ic#l-#5, vehicle-4) 0.102694 traffic volume 0.102694 19 (Ic#l-#5, vehicle-4) 21 parameter (toll rate growth) 0.101456 the fifth year 21 parameter (traffic growth) 0.101456 the fifth year parameter (toll rate growth) 0.101953 23 the sixth year parameter (traffic growth) 23 0.101953 the sixth year  Table 3.37 Total sensitivity Coefficients for RVS #9  103  Chapter  3: Application  104  3.3.2 Summary of Sensitivity Analysis Although there are some differences between the revenue streams, it can be  said  that  the following  factors demonstrate  high  sensitivity in most cases: revenue stream early start time; toll rate growth parameter; traffic volume growth parameter; tolls and traffic volume; inflation rate; and parameter for consignment cost of toll collection.  In addition to the above, revenue stream durations affect the sensitivity coefficients of toll rate growth and traffic volume growth parameters.  Chapter  3: Application  105  3.4 Summary This  chapter  deterministic project.  applied  the  feasibility  The project  analytical study  NPV  of  model  for a large the original  to toll  a  real  highway  deterministic  feasibility study indicated that this project was feasible. However, the analytical model indicates the likelihood of delay  and  cost  overrun,  and  shows  negative  NPV.  This  project should be reexamined and reconsidered. Because this model has the capacity to measure uncertainty, and  to  investigate  performance  to  changes  the  sensitivity  in primary  of  variables  the for  project a  toll  highway project, it is useful for feasibility analyses both in the preliminary and detailed stages of analysis.  Chapter 4 Risk Management 4.1 General This chapter examines strategies for risk management and explores their impact on overall project risks. it  is  important  corporations  for  the private  to negotiate  risk  In order to manage risks,  sector  sharing  and/or  with  quasi-public  the government.  Beesley and Hensher (1990) describe some of risks that should be considered. They are: •  termination risks that involve negotiating the residual value and takeback date when the project  is handed over to the  government; • regulation  risks  that  primarily  involve  consideration  of  possible changes such as ones in existing regulations and the political  ideology  of  the  government  which  affects  price  control; •  construction risks which include the usual engineering risks associated with construction; and 106  Chapter 4: Risk Management  •  107  information risks that concern  the reliability  of traffic  forecasts. Among these risks, only economic risks are addressed here, and the focus is on risk management for the revenue phase. Uncertainty  surrounding  estimates  for the revenue  phase is  related to: • time estimates for work packages and revenue streams (e.g. productivity and quantity); • revenue estimates  (e.g. interchange pair traffic volume for  different vehicle types, toll rate, and operating costs); and • prediction  of economic  factors  (e.g. inflation  rate and  interest rate).  Section two presents possible ways of reducing the uncertainty; section three attempts to quantify their effects; and section four presents conclusions.  4.2 Strategies for Risk Management One of the most effective ways of decreasing risk seems to be to reduce the uncertainty of variables that performance present value) is highly sensitive to.  According to the results  of the sensitivity analysis in chapter 3, they are: (1)revenue stream early start time; (2)toll rate growth parameters; (3)traffic volume growth parameters;  (e.g. net  Chapter 4: Risk Management  108  (4)tolls;  (5)traffic volume; (6)inflation rate; and (7)parameter for consignment cost of toll collection.  In this section, strategies for tightening distributions for the above  variables  are  discussed,  and  the  effects  distributions on overall project risks are examined. of each distribution is decreased by half.  of  tighter  The range  As mentioned in  chapter 3, the five percentile estimate parameters are used for this sample project.  Therefore, the range of each distribution  is indicated by the parameters.  For convenience, the original  sample project is called case-1.  In each case except case-9, the  distribution of variables changes in one category only in order to examine an individual  effect. Cumulative  effects are not  considered until case-9.  4.2.1 Revenue Stream Early Start Time (case-2) A tightening of the distribution describing revenue stream early start  time  is considered  here.  The  following  are possible  strategies for tightening the distributions for revenue stream early start time: •  to use modern construction management techniques for better time management of the design and construction phase; and  Chapter 4: Risk Management  109  • to add clauses such as penalty clauses for delays, in order to encourage contractors to meet deadlines in contracts. Table 4.1 shows the parameters for case-1, and Table 4.2 shows ones for case-2. categorysurvey & design land acquisition earth work bridge pavement IC ancillary facilities appurtenant work building & repairing overhead revenue phase duration  2.5% 0.900 0.900 0.850 0.900 0.900 0.850 0.900 0.900 0.900 0.900 0.900  5.0% 0.910 0.910 0.870 0.910 0.910 0.870 0.910 0.910 0.910 0.910 0.910  50.0% 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000  95.0%  97.5%  1.180 1.500 1.450 1.180 1.090 1.450 1.090 1.450 1.090 1.180 1.090  1.200 1.650 1.500 1.200 1.100 1.500 1.100 1.500 1.100 1.200 1.100  >/A  /fe  0.6 2.0 0.9 0.6 0.0 0.9 0.0 1.1 0.0 0.6 0.0  2.4 8.0 2.8 2.4 2.2 2.8 2.2 3.2 2.2 2.4 2.2  Table 4.1 Five Percentile Estimate Parameters for W.P, Durations (case- 1) category survey & design land acquisition earth work bridge pavement IC ancillary facilities appurtenant work building & repairing overhead revenue phase duration  2.5%  5.0%  50.0%  95.0%  97.5%  >/A  A  0.950 0.950 0.925 0.950 0.950 0.925 0.950 0.950 0.950 0.950 0.950  0.955 0.955 0.930 0.955 0.955 0.930 0.955 0.960 0.955 0.955 0.955  1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000  1.090 1.280 1.200 1.090 1.045 1.200 1.045 1.200 1.045 1.090 1.045  1.100 1.325 1.250 1.100 1.050 1.250 1.050 1.250 1.050 1.10 1.050  0.6 1.5 1.4 0.6 0.0 1.4 0.0 1.7 0.0 0.6 0.0  2.4 4.8 5.3 2.4 2.2 5.3 2.2 6.3 2.2 2.4 2.2  Table 4.2 Five Percentile Estimate Parameters for W.P, Durations (case- 2)  Tables 4.3, 4.4, and Figure 4.1 show the comparison between the two cases in terms of the project revenue, and Tables 4.5, 4.6, and Figure 4.2 show the comparison between the two cases in terms of the project NPV.  Mean value and standard deviation of the  Chapter 4: Risk Management  110  early start time of the first revenue for case-1 are 7.56 years and 0.523 years respectively, and those for case-2 are 7.25 years and 0.258 years respectively. case mean skewness a 1 705,507,584 77,309,352 0.190 2 0.241 729,199,360 74,547,520 Table 4.3 Comparison of the Project Revenue (case-1 and case-2)  kurtosis 1.411 1.495  cumulative Case 1 Case 2 probability(%) ($,000,000) ($,000,000) 0.25 488.5 519.9 537.2 0.50 506.4 525.7 1.00 555.8 2.50 583.1 554.0 5.00 578.3 606.6 10.00 606.4 633.7 25.00 653.4 678.9 50.00 729.2 705.5 75.00 757.7 779.5 90.00 804.9 824.7 832.7 95.00 851.8 97.50 857.0 875.3 99.00 885.4 902.6 99.50 904.6 921.2 99.75 922.5 938.5 Table 4.4 Cumulative Probability of the Project Revenue (case-1 and case-2)  Chapter  4: Risk  Management  111  inn  ^  •£  sn  0  .Q  o  en  S^  40  > ^  S Id  20  3  E  460  560  660  760  860  960  project revenue ($,000,000)  Figure 4.1 Cumulative Probability of the Project Revenue (case-1 and case-2) case  mean a -11,666,560 86,717,576 9,563,840 84,254,624 Table 4.5 Comparison of the Project NPV (case-1 and case-2) 1 2  skewness 0.053 0.078  Cumulative Case 1 Case 2 P r o b a b i l i t y (%) ($,000,000) ($,000,000) 0.25 -255.1 -226.9 0.50 -235.0 -207.5 1.00 -213.4 -186.4 2.50 -181.6 -155.6 5.00 -154.3 -129.0 10.00 -122.8 -98.4 25.00 -70.2 -47.3 9.6 50.00 -11.7 75.00 46.8 66.4 90.00 99.5 117.5 95.00 131.0 148.2 97.50 158.3 174.7 99.00 190.1 205.6 99.50 211.7 226.6 99.75 231.7 246.1 Table 4.6 Cumulative Probability of the Project NPV (case-1 and case-2)  kurtosis 2.043 2.131  Chapter  4: Risk  Management  112  n o  case-1 s  >  case-2  a  £  u -280  -180  -80  20  120  220  net pre sent value ($,000,000)  Figure 4.2 Cumulative Probability of the Project NPV (case-1 and case-2)  A tightening of the distribution describing revenue stream early start time improves expected project revenue and net present value  significantly  but does  measured by cr, by much.  not reduce  the uncertainty as  Clearly, efforts to fast track or  accelerate a project can have a significant effect on expected NPV, although possibly at the price of increased risk.  4.2.2 Toll Rate Growth Parameters (case-3) A tightening up of the distribution describing toll rate growth parameters, described by ca in 2.5.4, is considered here.  Toll  rate growth parameters can be controlled by road operators even though  they  are affected  by inflation.  The following are  possible strategies for reducing the uncertainty: •  to negotiate a long-term pricing policy; and  Chapter 4: Risk Management  113  • to require that the project be feasible without increases in toll rate. Tables 4.7 and 4.8 describe the parameters for case-1 and case-3 2.5% 0.800 0.900  case-1 case-3  5.0% 0.850 0.910  50.0% 1.000 1.000  95.0% 1.050 1.028  97.5% 1.060 1.030  Table 4.7 Five Percentile Estimate Parameters for Toll Rate Growth Parameters  case-1 case-3  Mean 0.9815 0.9885  Standard Deviation 0.0703 0.0383  ^|F^ -2.0 -0.9  /&  10.2 2.8  Table 4.8 Statistics Information of Five Percentile Estimate Parameters for Toll Rate Growth Parameters  Tables 4.9, 4.10, and Figure 4.3 show the comparison between case-1 and case-3 in terms of the project revenue, and Tables 4.11, 4.12, and Figure 4.4 show the comparison between the two cases in terms of the project NPV. case 1 3  mean 705,507,584 715,485,760  a 77,309,352 77,054,544  skewness 0.190 0.200  Table 4.9 Comparison of the Project Revenue (case-1 and case-3)  kurtosis 1.411 1.396  Chapter  4: Risk  Management  114  cumulative Case 1 Case 3 probability(%) ($,000,000) ($,000,000) 0.25 499.2 488.5 0.50 506.4 517.0 1.00 525.7 536.2 2.50 554.0 564.5 5.00 578.3 588.7 10.00 606.4 616.7 25.00 653.4 663.5 50.00 705.5 715.5 75.00 757.7 767.5 90.00 814.2 804.9 95.00 832.7 842.2 97.50 857.0 866.5 99.00 885.4 894.7 99.50 904.6 914.0 99.75 922.5 931.8 Table 4.10 Cumulative Probability of the Project Revenue (case-1 and case-3)  460  560  660  760  860  960  project revenue ($,000,000)  Figure 4.3 Cumulative Probability of the Project Revenue (case-1 and case-3) mean case skewness a 1 -11,666,560 86,717,576 0.053 -1,688,384 86,490,488 3 0.060 Table 4.11 Comparison of the Project NPV (case-1 and case-3)  kurtosis 2.043 2.036  Chapter  4: Risk  Management  Cumulative Probability (%) 0.25 0.50 1.00 2.50 5.00 10.00 25.00 50.00 75.00 90.00 95.00 97.50 99.00 99.50 99.75  115 Case 1 ($,000,000) -255.1 -235.0 -213.4 -181.6 -154.3 -122.8 -70.2 -11.7 46.8 99.5 131.0 158.3 190.1 211.7 231.7  Case 3 ($,000,000) -244.5 -224.5 -202.9 -171.2 -144.0 -112.5 -60.0 -1.7 56.6 109.2 140.6 167.8 199.5 221.1 241.1  Table 4.12 Cumulative Probability of the Project NPV (case-1 and case-3)  .£3  o  case-1 s  >  case-3  1 £ o -280  -180  -80  20  120  220  net present value ($,000,000)  Figure 4.4 Cumulative Probability of the Project NPV (case-1 and case-3)  A tightening of the distribution describing toll rate growth parameters shifts project revenue and net present value in a positive direction, but it does little to reduce uncertainty.  Chapter  4: Risk  Management  116  4.2.3 Traffic Volume Growth Parameters (case-4) A tightening of the distribution describing traffic volume growth parameters, described as k in section  2.1, is considered here.  It is very difficult to control the distribution for traffic volume growth parameters.  A possible way is to review past data  of similar highway projects, and to analyze information about development plans, road capacity, economic condition, and so on. Tables 4.13 and 4.14 describe the parameters for case-1 and case-4 2.5% 0.700 0.850  case-1 case-4  5.0% 0.750 0.870  50.0% 1.000 1.000  95.0% 1.090 1.045  97.5% 1.100 1.050  Table 4.13 Five Percentile Estimate Parameters for traffic volume growth parameters  case-1 case-4  Mean 0.9704 0.9843  Standard Deviation 0.1104 0.0568  V^  /32  -1.0 -0.9  3.4 2.9  Table 4.14 Statistics Information of Five Percentile Estimate Parameters for Traffic Volume Growth Parameters  Tables 4.15, 4.16, and Figure 4.5 show the comparison between case-1 and case-4 in terms of the project revenue, and Tables 4.17, 4.18, and Figure 4.6 show the comparison between the two cases in terms of the project NPV. case 1 4  mean 705,507,584 702,523,968  a 77,309,352 61,274,760  skewness 0.190 -0.170  Table 4.15 Comparison of the Project Revenue (case-1 and case-4)  kurtosis 1.411 1.383  Chapter  4: Risk  111  Management  cumulative probability(%) 0.25 0.50 1.00 2.50 5.00 10.00 25.00 50.00 75.00 90.00 95.00 97.50 99.00 99.50 99.75  Case 1 ($,000,000) 488.5 506.4 525.7 554.0 578.3 606.4 653.4 705.5 757.7 804.9 832.7 857.0 885.4 904.6 922.5  Case 4 ($,000,000) 530.5 544.7 560.0 582.4 601.7 624.0 661.2 702.5 743.9 781.1 803.3 822.6 845.1 860.4 874.5  Table 4.16 Cumulative P r o b a b i l i t y of the Project Revenue (case-1 and case-4)  case-1 case-4  460  560  660  760  860  960  project revenue ($,000,000)  Figure 4.5 Cumulative Probability of the Project Revenue (case-1 and case-4) case mean skewness a 1 -11,666,560 86,717,576 0.053 4 -14,650,176 72,785,976 -0.239 Table 4.17 Comparison of the Project NPV (case-1 and case-4)  kurtosis 2.043 2.281  Chapter  4: Risk  Management  Cumulative Probability (%) 0.25 0.50 1.00 2.50 5.00 10.00 25.00 50.00 75.00 90.00 95.00 97.50 99.00 99.50 99.75  118 Case 1 ($,000,000) -255.1 -235.0 -213.4 -181.6 -154.3 -122.8 -70.2 -11.7 46.8 99.5 131.0 158.3 190.1 211.7 231.7  Case 4 ($,000,000) -219.0 -202.1 -184.0 -157.3 -134.4 -107.9 -63.7 -14.7 34.4 78.6 105.1 128.0 154.7 172.8 189.7  Table 4.18 Cumulative Probability of the Project NPV (case-1 and case-4)  X)  o  case-1  >  case-4  1 s E 3  -280  -180  -80  20  120  220  net present value ($,000,000)  Figure 4.6 Cumulative Probability of the Project NPV (case-1 and case-4) A tightening of the distribution describing traffic volume growth parameters significantly reduces the uncertainty of an overall project; mean values of project revenue and net present value, however, are decreased.  Chapter  4: Risk  119  Management  4.2.4 Tolls (case-5)  The effects of tightening the distribution of base toll rates are considered in this section.  In general, toll rates are decided  on the basis of benefit-cost principles, in which the tolls charged to the various road users should not exceed the benefit normally received by them for using the highway.  Practically,  the uncertainty surrounding base tolls disappears near the end of the construction phase, or earlier, if the concession structure dictates the base toll rate. An example of where the uncertainty in the toll rate persists to the commissioning phase of a project is the recently completed English Chunnel project. Tables 4.19 and 4.20 describe the parameters for case-1 and case-5. 2.5% 0.900 0.950  case-1 case-5  5.0% 0.910 0.955  50.0% 1.000 1.000  95.0% 1.180 1.09  97.5% 1.200 1.100  Table 4.19 Five Percentile Estimate Parameters for Tolls  case-1 case-5  Mean 1.0167 1.0083  Standard Deviation 0.0850 0.0425  V^  /&  0.6 0.6  2.4 2.4  Table 4.20 Statistics Information of Five Percentile Estimate Parameters for Tolls  Tables 4.21, 4.22, and Figure 4.7 show the comparison between case-1 and case-5 in terms of the project revenue, and Tables 4.23, 4.24, and Figure 4.8 show the comparison between the two cases in terms of the project NPV.  Chapter  4: Risk  120  Management  mean skewness case a 1 705,507,584 77,309,352 0.190 699,348,992 0.192 5 76,269,088 Table 4.21 Comparison of the Project Revenue (case-1 and case-5)  kurtosis 1.411 1.419  Case 1 Case 5 cumulative probability(%) ($,000,000) ($,000,000) 488.5 485.3 0.25 506.4 0.50 502.9 525.7 1.00 521.9 2.50 554.0 549.9 578.3 5.00 573.9 606.4 10.00 601.6 653.4 25.00 647.9 705.5 50.00 699.3 75.00 757.7 750.8 90.00 804.9 797.1 832.7 95.00 824.8 97.50 857.0 848.8 885.4 99.00 876.8 99.50 904.6 895.8 99.75 922.5 913.4 Table 4.22 Cumulative Probability of the Project Revenue (case-1 and case-5)  Chapter  4: Risk  Management  121  100-  is  ™^^^H®*'™*™®  80-  Si  S  60.  g ^  40.  — • — case-1 a  case-5  1 •3 E  20-  3  04i30  560  660  760  860  960  project revenue ($,000,000)  Figure 4.7 Cumulative Probability of the Project Revenue (case-1 and case-5) case  mean skewness a 1 -11,666,560 86,717,576 0.053 5 -17,825,152 85,791,464 0.051 Table 4.23 Comparison of the Project NPV (case-1 and case-5) Cumulative Case 1 Case 5 P r o b a b i l i t y (%) ($,000,000) ($,000,000) 0.25 -255.1 -258.6 0.50 -235.0 -238/.8 1.00 -213.4 -217.4 2.50 -181.6 -186.0 5.00 -154.3 -158.9 10.00 -122 . 8 -127.8 25.00 -70.2 -75.7 50.00 -11.7 -17.8 75.00 46.8 40.0 90.00 99.5 92.1 95.00 131.0 123.3 97.50 158.3 150.3 99.00 190.1 181.8 99.50 211.7 203.2 99.75 231.7 223.0 Table 4.24 Cumulative Probability of the Project NPV (case-1 and case-5)  kurtosis 2.043 2.061  Chapter  4: Risk  122  Management  r  case-1 s  case-5  E  s  -280  -180  -80  20  120  220  net present value ($.000,000)  Figure 4.8 Cumulative Probability of the Project NPV (case-1 and case-5)  A tightening of the distribution describing base toll rates does not significantly reduce overall uncertainty.  A small negative  impact on the expected value is observed.  4.2.5 Traffic Volume (case-6) A  tightening  of the distribution  considered here.  of base  traffic volume is  It is also difficult to achieve in practice.  It may be obtained, in part, through detailed traffic surveys, and more detailed  traffic  forecasts.  describe the parameters for case-1 and case-6  Tables  4.25 and 4.26  Chapter  4: Risk  123  Management  2.5% 0.350 0.675  case-1 case-6  5.0% 0.500 0.700  50.0% 1.000 1.000  95.0% 1.350 1.180  97.5% 1.400 1.200  Table 4.25 Five Percentile Estimate Parameters for Traffic Volume  case-1 case-6  Mean 0.9723 0.9778  Standard Deviation 0.2667 0.1488  >/^  y&  -1.0 -0.4  5.9 2.2  Table 4.26 Statistics Information of Five Percentile Estimate Parameters for Traffic Volume  Tables 4.27, 4.28, and Figure 4.9 show the comparison between case-1 and case-6 in terms of the project revenue, and Tables 4.29, 4.30, and Figure 4.10 show the comparison between the two cases in terms of the project NPV. case 1 6  mean 705,507,584 712,278,592  a 77,309,352 73,196,800  skewness 0.190 0.249  Table 4.27 Comparison of the Project Revenue (case-1 and case-6)  kurtosis 1.411 1.472  Chapter  4: Risk  124  Management  Case 6 cumulative Case 1 ($,000,000) ($,000,000) probability(%) 488.5 506.8 0.25 506.4 523.7 0.50 525.7 542.0 1.00 568.8 2.50 554.0 5.00 578.3 591.9 606.4 10.00 618.5 25.00 653.4 662.9 50.00 705.5 712.3 75.00 757.7 761.6 90.00 804.9 806.1 95.00 832.7 832.7 97.50 855.7 857.0 99.00 885.4 882.6 99.50 904.6 900.8 99.75 922.5 917.7 Table 4.28 Cumulative Probability of the Project Revenue (case-1 and case-6)  case-1 case-6  460  560  660  760  860  960  project revenue ($,000,000)  Figure 4.9 Cumulative Probability of the Project Revenue (case-1 and case-6) case mean skewness a 1 -11,666,560 8,6717,576 0.053 -4,895,552 7,3196,800 6 0.249 Table 4.2 9 Comparison of the Project NPV (case-1 and case-6;  kurtosis 2.043 1.472  Chapter  4: Risk  Management  Cumulative Probability (%) 0.25 0.50 1.00 2.50 5.00 10.00 25.00 50.00 75.00 90.00 95.00 97.50 99.00 99.50 99.75  125 Case 6 ($,000,000) -238.1 -218.9 -198.1 -167.7 -141.5 -111.4 -60.9 -4.9 51.1 101.6 131.7 157.9 188.4 209.1 228.3  Case 1 ($,000,000) -255.1 -235.0 -213.4 -181.6 -154.3 -122.8 -70.2 -11.7 46.8 99.5 131.0 158.3 190.1 211.7 231.7  Table 4.30 Cumulative Probability of the Project NPV (case-1 and case-6)  .£3  a o  case-1  r  E  case-6  S  3  i — • •  -280  -180  -80  20  120  220  net pre sent value ($.000,000)  Figure 4.10 Cumulative Probability of the Project NPV (case-1 and case-6)  This  tightening  has  no  significant  uncertainty of an overall project.  effect  on  reducing  the  Chapter  4: Risk  126  Management  4.2.6 Inflation Rate (case-7) A tightening of the distribution for the inflation rate that applies to operating costs only is considered here.  It cannot be  controlled by road operators although it is necessary to observe economic conditions and to forecast its trend carefully to reduce the uncertainty. Tables 4.31 and 4.32 describe the parameters for case-1 and case-7. 2.5% 0.800 0.900  case-1 case-7  5.0% 0.820 0.910  50.0% 1.000 1.000  95.0% 1.300 1.180  97.5% 1.400 1.200  Table 4.31 Five Percentile Estimate Parameters for Inflation Rate  case-1 case-7  Mean 1.0222 1.0167  Standard Deviation 0.1540 0.0850  >/A 1.4 0.6  ;&  7.7 2.4  Table 4.32 Statistics Information of Five Percentile Estimate Parameters for Inflation Rate  Tables 4.33, 4.34, and Figure 4.11 show the comparison between case-1 and case-7 in terms of the project revenue, and Tables 4.35, 4.36, and Figure 4.12 show the comparison between the two cases in terms of the project NPV. case 1 7  mean 705,507,584 709,877,120  a 77,309,352 73,241,816  skewness 0.190 0.334  Table 4.33 Comparison of the Project Revenue (case-1 and case-7)  kurtosis 1.411 1.491  Chapter  4: Risk  127  Management  cumulative probability(%) 0.25 0.50 1.00 2.50 5.00 10.00 25.00 50.00 75.00 90.00 95.00 97.50 99.00 99.50 99.75  Case 1 ($,000,000) 488.5 506.4 525.7 554.0 578.3 606.4 653.4 705.5 757.7 804.9 832.7 857.0 885.4 904.6 922.5  Case 7 ($,000,000) 504.3 521.2 539.5 566.3 589.4 616.0 660.5 709.9 759.3 803.7 830.4 853.4 880.3 898.5 915.5  Table 4.34 Cumulative P r o b a b i l i t y of the Project Revenue (case-1 and case-7)  case-1 case-7  460  560  660  760  860  960  project revenue ($,000,000)  Figure 4.11 Cumulative Probability of the Project Revenue (case-1 and case-7) mean case skewness a 1 -11,666,560 86,717,576 0.053 7 0.137 -6,317,120 82,959,512 Table 4.35 Comparison of the Project NPV (case-1 and case-7)  kurtosis 2.043 2.139  Chapter  4: Risk  128  Management  Cumulative Probability (%) 0.25 0.50 1.00 2.50 5.00 10.00 25.00 50.00 75.00 90.00 95.00 97.50 99.00 99.50 99.75  Case 7 ($,000,000) -239.2 -220.0 -199.3 -168.9 -142.8 -112.6 -62.3 -6.3 49.6 100.0 130.1 156.3 186.7 207.4 226.6  Case 1 ($,000,000) -255.1 -235.0 -213.4 -181.6 -154.3 -122.8 -70.2 -11.7 46.8 99.5 131.0 158.3 190.1 211.7 231.7  Table 4.36 Cumulative Probability of the Project NPV (case-1 and case-7)  XI  o  - • — case-1  09 ^ > s E u  s  -280  -180  -80  20  120  case-7  220  net present value ($,000,000)  Figure 4.12 Cumulative Probability of the Project NPV (case-1 and case-7)  This  tightening  has  no  significant  uncertainty for the overall project.  effect  on  reducing  the  Chapter  4: Risk  129  Management  4.2.7 Parameter for Consignment Cost of Toll Collection (case-8) A  tightening  of  the  distribution  of  the  parameter  consignment cost of toll collection is examined here.  for the This can  be controlled, in part, by road operators. Tables 4.37 and 4.3 8 describe the parameters for case-1 and case-8. 2.5% 0.900 0.950  case-l case-8  5.0% 0.910 0.955  50.0% 1.000 1.000  95.0% 1.250 1.120  97.5% 1.300 1.150  Table 4.37 Five Percentile Estimate Parameters for Parameter for Consignment Cost of Toll Collection  case-1 case-7  Mean 1.0296 1.0139  Standard Deviation 0.1104 0.0539  VA  A  1.0 1.4  3.4 5.6  Table 4.38 Statistics Information of Five Percentile Estimate Parameters for Parameter for Consignment Cost of Toll Collection  Tables 4.39, 4.40, and Figure 4.13 show the comparison between case-1 and case-8 in terms of the project revenue, and Tables 4.41, 4.42, and Figure 4.14 show the comparison between the two cases in terms of the project NPV. case 1 8  mean 705,507,584 708,981,504  a 77,309,352 76,916,008  skewness 0.190 0.197  Table (4.39) Comparison of the Project Revenue (case-1 and case-8)  kurtosis 1.411 1.420  Chapter  4: Risk  Management  130  cumulative Case 1 Case 8 probability(%) ($,000,000) ($,000,000) 0.25 488.5 493.1 0.50 506.4 510.9 1.00 525.7 530.1 2.50 554.0 558.2 5.00 578.3 582.5 606.4 10.00 610.4 25.00 653.4 657.1 50.00 705.5 709.0 75.00 757.7 760.9 90.00 804.9 807.6 95.00 832.7 835.5 97.50 859.7 857.0 99.00 885.4 887.9 99.50 907.1 904.6 99.75 922.5 924.9 Table 4.40 Cumulative Probability of the Project Revenue (case-1 and case-8)  460  560  660  760  860  960  project re venue ($,000,000)  Figure 4.13 Cumulative Probability of the Project Revenue (case-1 and case-8) mean case skewness (7 1 0.053 -11,666,560 86,717,576 8 -8,192,640 86,367,096 0.056 Table 4.41 Comparison of the Project NPV (case-1 and case-8)  kurtosis 2.043 2.053  Chapter  4: Risk  Management  Cumulative Probability (%) 0.25 0.50 1.00 2.50 5.00 10.00 25.00 50.00 75.00 90.00 95.00 97.50 99.00 99.50 99.75  131 Case 1 ($,000,000) -255.1 -235.0 -213.4 -181.6 -154.3 -122.8 -70.2 -11.7 46.8 99.5 131.0 158.3 190.1 211.7 231.7  Case 8 ($,000,000) -250.6 -230.7 -209.1 -177.5 -150.3 -118.9 -66.4 -8.2 50.1 102.5 133.9 161.1 192.7 214.3 234.2  Table 4.42 Cumulative Probability of the Project NPV (case-1 and case-8)  O  >  -•  case-1  s  case-8  E  3 U  -280  -180  -80  20  120  220  net present value ($.000,000)  Figure 4.14 Cumulative Probability of the Project NPV (case-1 and case-8)  This  tightening  has  no  significant  uncertainty for the overall project.  effect  on  reducing  the  Chapter  4: Risk  Management  132  4.2.8 Combination of Case-2 to Case-8 (case-9) The total effect of all the distribution tightenings described in case-2 to case-8 is considered here.  Tables 4.43, 4.44, and Figure 4.15 show the comparison between case-1 and case-9 in terms of the project revenue, and Tables 4.45, 4.46, and Figure 4.16 show the comparison between the two cases in terms of the project NPV. case 1 8  mean 705,507,584 733,059,648  a 77,309,352 40,677,744  skewness 0.190 0.161  kurtosis 1.411 1.355  Table 4.43 Comparison of the Project Revenue (case-l and case-9) cumulative probability{%) 0.25 0.50 1.00 2.50 5.00 10.00 25.00 50.00 75.00 90.00 95.00 97.50 99.00 99.50 99.75  Case 1 ($,000,000) 488.5 506.4 525.7 554.0 578.3 606.4 653.4 705.5 757.7 804.9 832.7 857.0 885.4 904.6 922.5  Case 9 ($,000,000) 618.9 628.3 638.4 653.3 666.1 680.9 705.6 733.1 760.5 785.2 800.0 812.8 827.7 837.8 847.2  Table 4.44 Cumulative Probability of the Project Revenue (case-1 and case-9)  Chapter  4: Risk  460  133  Management  560  660  760  860  960  project revenue ($.000,000)  Figure 4.15 Cumulative Probability of the Project Revenue (case-l and case-9) mean case skewness a 1 -11,666,560 86,717,576 0.053 9 13,424,128 56,534,840 -0.236 Table 4.45 Comparison of the Project NPV (case-l and case-9) Cumulative Case 1 Case 9 Probability (%) ($,000,000) ($,000,000) 0.25 -255.1 -145.3 0.50 -235.0 -132.2 -213.4 1.00 -118.1 2.50 -97.4 -181.6 5.00 -154.3 -79.6 10.00 -122.8 -59.0 25.00 -70.2 -24.7 -11.7 13.4 50.00 75.00 46.8 51.6 90.00 85.9 99.5 106.4 95.00 131.0 124.2 97.50 158.3 99.00 190.1 144.9 211.7 99.50 159.0 99.75 231.7 172.1 Table 4.46 Cumulative Probability of the Project NPV (case-l and case-9)  kurtosis 2.043 2.819  Chapter  4: Risk  134  Management  Figure 4.16 Cumulative Probability of the Project NPV (case-1 and case-9)  In this case, significant improvements for both reducing the uncertainty and increasing the project's expected net present value are observed.  In practice, many of tightenings described  may not be achievable, but the process is clear - examine each variable in turn, determine how its uncertainty can be reduced, and then determine the residual uncertainty.  The goal is to  achieve the type of result shown in Figure 4.16 - tighten or steepen the distribution, and shift it in the positive direction. Even if the tightening examined could be achieved, the example project would still , in all likelihood, be infeasible because there is a 40% chance of not obtaining the minimum attractive rate of return.  Thus, additional strategies would be required to  further reduce risk.  Chapter  4: Risk Management  135  4.3 Conclusions As suggested in the previous section, even when the range of the distribution of highly sensitive primary variables is decreased by half, the effect on overall project risks is not significant except when considered in combination (case-9).  On a variable-  variable basis, improvements are found only in case-4 ( traffic volume growth rate).  However, in practice, it is very difficult  to  distribution  tighten  parameters,  up  the  because  they  are  for  traffic  related  to  volume  uncertain  growth economic  conditions, road development plans, and many other factors. This indicates that it is very difficult for a highway operator alone to reduce risks . Therefore, it would seem that it is very important that risk sharing be negotiated with the government and some guarantee of support be received.  For example, if the  government guarantees a certain traffic volume, the situation improves as indicated below in case-10.  Although parameters for traffic volume should be deterministic for case-10, the model requires probabilistic values for primary variables. parameters  Therefore, are  used.  very  tight  Tables  4.47  parameters for case-1 and case-10.  distributions and  4.48  for  the  describe  the  Chapter  4: Risk  136  Management  2.5% 0.350 0.9996  case-1 case-10  5.0% 0.500 0.9997  50.0% 1.000 1.000  95.0% 1.350 1.0003  97.5% 1.400 1.0004  Table 4.47 Five Percentile Estimate Parameters for Traffic Volume  case-1 case-10  Mean 0.9723 1.0000  Standard Deviation 0.2667 0.0002  >/^  /^  -1.0 0.0  5.9 9.0  Table 4.48 Statistics Information of Five Percentile Estimate Parameters for Traffic Volume  Tables 4.49, 4.50, and Figure 4.17 show the comparison between case-1 and case-9 in terms of the project revenue, and Tables 4.51, 4.52, and Figure 4.18 show the comparison between the two cases in terms of the project NPV. case 1 10  mean 705,507,584 729,600,320  a 77,309,352 72,625,800  skewness 0.190 0.276  Table 4.49 Comparison of the Project Revenue (case-1 and case-10)  kurtosis 1.411 1.518  Chapter  4: Risk  Management  137  cumulative Case 1 Case 9 probability(%) ($,000,000) ($,000,000) 0.25 525.7 488.5 0.50 506.4 542.5 560.7 1.00 525.7 2.50 587.3 554.0 5.00 610.1 578.3 10.00 606.4 636.5 25.00 653.4 680.6 50.00 729.6 705.5 75.00 757.7 778.6 90.00 822.7 804.9 95.00 832.7 849.1 97.50 857.0 871.9 99.00 885.4 898.5 99.50 916.7 904.6 99.75 933.5 922.5 Table 4.50 Cumulative P r o b a b i l i t y of the P r o j e c t Revenue ( c a s e - l and case-lO)  case-1 case-1  460  560  660  760  860  960  project re venue ($,000,000)  Figure 4.17 Cumulative Probability of the Project Revenue (case-1 and case-10)  Chapter  4: Risk  138  Management  mean case skewness a 1 -11,666,560 86,717,576 0.053 8 12,426,176 82,569,424 0.094 Table 4.51 Comparison of the Project NPV (case-1 and case-10)  kurtosis 2.043 2.169  Case 1 Cumulative Case 9 Probability (%) ($,000,000) ($,000,000) 0.25 -255.1 -219.3 -235.0 0.50 -200.3 -213.4 -179.7 1.00 -181.6 -149.4 2.50 -154.3 -123.4 5.00 10.00 -122.8 -93.4 -70.2 25.00 -43.3 -11.7 12.4 50.00 75.00 46.8 68.1 99.5 118.2 90.00 131.0 148.2 95.00 97.50 158.3 174.3 99.00 190.1 204.5 211.7 99.50 225.1 99.75 231.7 244.2 Table 4.52 Cumulative Probability of the Project NPV (case-l and case-10)  Id  n o  case-1 a  case-10  £ U  -280  -180  -80  20  120  220  net present value ($,000,000)  Figure 4.18 Cumulative Probability of the Project NPV (case-1 and case-10)  Chapter 4: Risk Management  139  In case-10, there is no obvious improvement on the uncertainty of overall  project  improves.  risks.  However,  its profitability  clearly  Therefore, obtaining certain guarantees concerning  such factors as traffic volume must be recognized as possible and almost essential risk management strategies.  Chapter 5 Conclusions and Recommendations 5.1 Conclusions The primary objectives of this thesis were to model economic and financial performance of user-pay highway facilities and to explore the sensitivity of project performance to changes in primary variables, uncertainty surrounding such projects, and ways of reducing the uncertainty.  The analytical model developed requires three kinds of input data: work package duration; work package costs; and revenue streams. Special attention was given to the revenue phase. The general features of the analytical model are as follows.  1. This model consists of three levels: work package/revenue stream level; project performance level; and project decision level. 140  Chapter 5: Conclusions  2.  and Recommendations  141  The work package/revenue stream level involves three  derived variables: work package duration; work package cost; and revenue stream. 3.  The project performance level also involves three derived variables: project duration; project cost; and project revenue.  4.  The project decision level involves two derived variables: project net present value (NPV); and project internal rate of return (IRR).  5. Each derived variable is described by its expected value, standard deviation, skewness, and kurtosis. 6.  This model can be applied to closed toll collection systems (manual or automatic collection), closed toll collection systems (manual or automatic collection), and their hybrids.  7.  The model is dependent on traffic volume forecast, and can also deal with any traffic volume forecasting method as long as it provides the interchange pair traffic volume for each vehicle type in base years.  The results of a sensitivity and risk analysis of a Japanese project and which focused mainly on the revenue phase are as follows.  1. In most cases, the highly sensitive primary variables are as follows: (1)revenue stream early start time; (2)toll rate growth parameters;  Chapter  5:  Conclusions  and Recommendations  142  (3)traffic volume growth parameters; (4)tolls; (5)traffic volume; (6)inflation rate; and (7)parameter for consignment cost of toll collection. 2. However, even if the uncertainty of these sensitive variables is decreased, their impacts on overall project risks are not great except in the case of traffic volume growth rate. 3. One of the most effective risk management strategies is to negotiate risk sharing with the government and to receive some guarantee of support.  5.2 Recommendations for Future Work Recommendations for future work are presented in three categories: computer programs; correlation between primary variables for revenue streams; and deterministic input for primary variables.  5.2.1 Computer Programs One of the primary objectives of this thesis was to model economic and financial performance of user-pay highway facilities.  This model is based on the program "AMMA",  which is a modified version of "TIERA" (Ranasinghe, 1990) "AMMA", unlike "TIERA", can be used on personal computers  Chapter 5: Conclusions  and Recommendations  143  It was planned to be used in conjunction with the program "TERQ", a more user-friendly program capable of creating input data files with relative ease.  However, since "TERQ"  has not been completed yet, the analytical model requires users to do a lot of work creating input data files.  It is  strongly recommended that "TERQ" be completed as soon as possible.  The analytical model, namely "AMMA", uses 2.5,  5.0, 50.0, 95.0, and 97.5 percentile estimates.  However,  because of the difficulty in assessing the 2.5 and 97.5 percentiles subjectively, 5.0, 25.0, 50.0, 75.0, and 95.0 percentile estimates seem to be more suitable for the model.  5.2.2 Correlation between Primary Variables for Revenue Streams The analytical model can theoretically deal with correlation between primary variables.  However, since  there are many primary variables, e.g. the smallest revenue stream has 181 primary variables, and the biggest revenue stream has 297 primary variables for the sample project, this thesis sets all correlation coefficients to zero. However, especially in the revenue phase, many primary variables are correlated with each other, e.g. interchange pair traffic volumes, and volumes in different years. Therefore, it is recommended that the correlation between primary variables be considered, and their impacts be measured.  Chapter  5:  Conclusions  and Recommendations  144  5.2.3 Deterministic Input for Primary Variables As mentioned in chapter four,  the model requires  probabilistic values for most primary variables.  However,  in order to examine risk management strategies, it is sometimes necessary to set some deterministic variables . Therefore, it is recommended that the model be modified to accept both deterministic and probabilistic values.  Bibliography [1] Andersson, Roland, "A Bridge to Faro - a Cost-benefit Analysis", Journal of Advanced Transportation. Volume 19, Number 3, 1985: 251-269 [2] Ang, A.H-s., Abdelnour, J., and Chaker, A.A.," Analysis of Activity Networks under Uncertainty", Journal of Engineering Mechanics Division. ASCE, Volume 101, N u m b e r Eiyi4 , 1 9 7 5 :  373-387  [3] Atkins, A.S., Eade, A.R., and Fisher, N.W.F., "A Model for the Financial Analysis of Toll Roads", ProceedingsSixth Conference. Australian Road Research Board. 1972: Paper Number 807 [4] Beesley, Michael and Hensher, David A., "Private Toll roads in Urban Areas. Some Thoughts on the Economic and Financial Issues.", Transportation. Volume 16, Number 4, 1990: 329-341 [5] Bushell, George, "An Optimizing Model of Traffic Assignment for the Freeway System of Southern Ontario", Centre for Urban and Community Studies, University of Toronto, Research Paper No. 40, 1970 [6] Campbell, Bruce and Humphrey, Thomas F., "Methods of Cost-effectiveness Analysis for Highway Projects", National Cooperative Highway Research Program Synthesis of Highway Practice. No 142, 1988 [7] Christofferson, Kevin Richard, "A Benefit/Cost Analysis of Reconstructing the Alaska Highway to R.A.U. 100 Status", Master thesis. University of British Columbia. Canada, 1980 [8] Dalton, P.M. and Harmelink, M.D., "Multipath Traffic Assignment: Development and Tests", the Systems Research and development Branch. Research and development Division. Ministry of Transportation and Communications, Ontario. 1974 [9] Davinroy, thomas, "Traffic Assignment", Institute of Transportation and Traffic Encrineering. Barkley. University of California. 1962 145  Bibliography  14 6  [10] Davis, Harmer E., Moyer, Ralph A., Kennedy, Norman, and Lapin, Howard S., "Toll-road Developments and their Significance in the Provision of Expressways", Institute of Transportation and Traffic Engineering. University of California. U.S.A. 1953 [11] Duffus, Leonnie N., Alfa, Attahiru Sule, and Soliman, Afifi H., "The Reliability of Using the Gravity Model for Forecasting Trip Distribution", Transportation. Volume 14, 1987: 175-192 [12] Geltner, David and Moavenzadeh, Fred, "An Economic Argument for Privatization of Highway Ownership", Transportation Research Record, Volume 1107, 1987: 1420 [13] Gittings, Gary L., "Some Financial, Economic, and Social Policy Issues Associated with Toll Finance.", Transportation Research Record. Volume 1107, 1987: 2030 [14] Huber, Matthew J., Boutwell, Harvey B., and Witheford, David K., "Comparative Analysis of Traffic Assignment Techniques with Actual Highway Use", National Cooperative Highway Research Program. Highway Research Board. No. 58, 19 6 8 [14] Japan Highway Public corporation, Information", Tokyo, Japan 1992  "the General  [15] Japan Highway Public corporation, "the Planning and Surveying Standards for Ordinary Toll Roads", Tokyo, Japan, 19 8 3 [16] Japan Highway Public corporation, "Outline of Expressway Traffic Volume Estimation", Unpublished, Tokyo, Japan, 1993 [17] Johansen, Frida, "Economic Arguments on Toll Roads", Transportation Research Record 1107, 1987: 80-84 [18] Kadiyali, L.R., "Traffic Engineering and Transportation Planning", Ministry of Shipping and Transport, New Delhi. 1983  Bibliography  14 7  [19] Morellet, Oliver, "A Demand Model for Intercity Private Car Traffic", Report of the Fifty-eight Round Table on Transport Economics, European Conference of Ministers of Transport. 1981: 9-20 [20] Neveu, Alfred J., " Quick-Response Procedures to Forecast Rural Traffic: Background Document", Transportation Analysis Report 3, Planning Division. New York State Department of Transportation, 1982 [21] Newell, G.F,, "Traffic Networks", The MIT Press. 1980  Flow on Cambridge.  Transportation Massachusetts.  [22] Ranasinghe, M., "Analytical Method for Quantification of Economic Risks During Feasibility Analysis for Large Engineering Projects.", Ph.D. Thesis. University of British Columbia. Canada, 1990 [23] Robertson, Richard B., "Overview of Toll Financing in Countries that are Members of the Organization for Economic Cooperation and Development", Transportation Research Record. Volume 1107, 1987: 65-67 [24] Rusch, W.A., "Toll Highway Financing" National Cooperative Highway Research Program Synthesis of Highway Practice. No 117, 1984 [25] Russell, A.D., Civil 522 - Course Notes", University of British Columbia. Vancouver. Canada. 1992 [26] Sharp, Clifford, Button, Kenneth, and Deadman, Derek, "The Economics of Tolled Road Crossing", Journal of Transport Economics and Policy. 1986: 255-274 [27] Schneider, Suzanne, "Toll Financing of U.S. Highways", Congress of the United States. Congressional Budget Office. 1985 [28] Thomas, Roy, "Traffic Assignment Techniques", Centre for Transport Studies. Department of Civil Engineering. University of Salford. 1991 [29] Waters, W.G. and Meyers, Shane J., "Benefit Cost Analysis of a Toll Highway - British Columbia Coquihalla", CTRF conference proceedings. 1987: 494-513  Bibliography  14 8  [30] Weisbrod, Glen E. and Beckwith, James, "Measuring Economic Development Benefits for Highway Decisionmaking: the Wisconsin Case", Transportation Quarterly. Volume 46, Number 1, 1992: 57-79 [31] Wuestefeld, Norman H., "Toll Roads", Transportation Quarterly. Volume 42, Number 1, 1988: 5-22  Appendix A Discounted Work Package Cost The following figure shows a cash flow diagram of work Package #i.  Uniform repayment of financing is assumed  $ TT  -J  _j  i_  Tp Tsci  TT  - Tp  T  T  WP#i  c  amortization of financing  Coi{T) L  Tci  '  u r  TRT  Pi  time  _| n  WPCi is the discounted ith work package cost Coi (T) is the function for constant dollar cash flow for the ith work package TBCI  is start time of Work Package#i  Tci is work package duration Tp  is construction phase duration  TT  is total project duration (construction and operation phase)  TRT is operation phase duration f is the equity fraction, 149  Appendix  A: Discounted  Work Package  Oci, r and y a r e i n f l a t i o n ,  Cost  15 0  i n t e r e s t and d i s c o u n t  rates  r e s p e c t i v e l y which a r e i n v a r i e d with t i m e . First,  f i g u r e out t h e amount of annual repayment f o r  work p a c k a g e .  Pi.  FW a t end of WP#i i s :  FW at Tp is : riTp-Tsd-Tci)  = (1-/)-e*"^'" .g-Crp-r.^) .^-^^^^(T)-e^'^-''dT  FW at Tp is also described as: CTT-TP  \  Pi-e-'-'dt  Jo  Therefore, Pi = (!-/).e*'-^-y<^/'-^-). f^"Coi(T)•e^'^-^-'dTl  Then, discounted ith work package cost is.  £~^'e'-'dt  ith  Appendix  A: Discounted  Work Package  Cost  151  Appendix B Input Data for Revenue Stream The following tables shows input data for revenue streams.  B.l Closed System (Fixed Toll Rate) nAL nP nWC nOL nBR  iby ird  fee(l,J,K,L) ptr(I)  ptv(I) traf(l,J,K,L)  Input Data the number of interchanges(IC) the number of vehicle types weather classification periodic overlay periodic bridge repainting  deterministic deterministic deterministic deterministic deterministic  (General Data) start time of the revenue stream revenue stream duration  automatically calculated  (Data related to Toll Rate) toll rate of vehicle type L between IC #J and #K at the first year toll growth rate parameter at year I (Data related to Traffic Volume) tiaffic volume growth rate parameter at year I traffic volimie of vehicle type L between IC #J and #K at the first year  152  Appendix  lb2 lb4 lb6 lt2 lt4 lt6 le2 le4 le6 Itn Itj Ito cc2 cc4 cm2 cm4 cm6 ell cl4 cr2 cr4 cr6 cp2 cp4 q36 ctn ctj cto csh cso co2 co4 co6 pcot  Idir Ivdir  B: Input  Data for  Revenue  Stream  (Maintenance Cost) 2 lane bridge length 4 lane bridge length 6 lane bridge length 2 lane tunnel length 4 lane tunnel length 6 lane tunnel length 2 lane earthwork section length 4 lane earthwork section length 6 lane earthwork section length length of tunnel with no ventilation length of tunnel with jet fan length of tunnel with other ventilation road cleaning cost (2 lanes) (4 lanes or more) road maintenance cost (2 lanes) (4 lanes) (6 lanes) lighting cost (1 or 2 lanes) (4 or 6 lanes) bridge repair cost (2 lanes) (4 lanes) (6 lanes) bridge paint cost (2 lanes) (4 lanes) (6 lanes) tunnel maintenance cost (no ventilation) tunnel maintenance cost (jet fan) tunnel maintenance cost (others) snow and ice control cost (heavy snow area)) (ordinary snow area) overlay cost (2 lanes) (4 lanes) (6 lanes) other maintenance cost parameter (Operation Cost) labor cost of operation office (director) (vice director)  153  Appendix  Ichi leng Iwor tl ital itbl itcl itdl itel t2 ital itb2 itc2 itdZ ite2 t3 ita3 itb3 itc3 itd3 ite3 t4 ita4 itb4 itc4 itd4 ite4 t5 itaS itb5 itc5 itd5 ite5 ita6 itb6  B: Input  Data for  Revenue  Stream  (chief) (clerk or engineer) (worker) traffic volume(boundary-l) the number of directors needed for less traffic volume than tl the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed traffic volume(boundary-2) the number of directors needed for less traffic volume than t2 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed traffic volume(boundary-3) the number of directors needed for less traffic volume than t3 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed traffic volume(boundary-4) the number of directors needed for less traffic volume than t4 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed traffic volume(boimdary-5) the number of directors needed for less traffic volume than t5 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the niunber of workers needed the number of directors needed for more traffic volume than t5 the number of vice directors needed  154  Appendix  itc6 itd6 ite6 Itc tcl itctl tc2 itct2 tc3 itct3 tc4 itct4 tc5 itctS tc6 itct6 tc7 itct? tc8 itctS tc9 itct9 tclO itctlO tell itct 11 tcl2 itct 12 tcl3  B: Input  Data for  Revenue  Stream  the number of chiefs needed the number of clerks and engineers needed the number of workers needed labor cost of toll collection (clerk) traffic volume(boimdary-l) the number of clerks needed for less traffic volimie thantl traffic volume(boundary-2) the number of toll collection clerks needed for less traffic volume than t2 traffic volume(boimdary-3) the number of toll collection clerks needed for less traffic volume than t3 traffic volume(boundary-4) the nimiber of toll collection clerks needed for less traffic volume than t4 traffic volume(boundary-5) the number of toll collection clerks needed for less traffic volimie than t5 traffic volume(boundary-6) the number of toll collection clerks needed for less traffic volume than t6 traffic volume(boundary-7) the number of toll collection clerks needed for less traffic volume than t7 traffic volume(boundary-8) the number of toll collection clerks needed for less traffic volume than t8 traffic volume(boundary-9) the number of toll collection clerks needed for less traffic volume than t9 traffic volume(boundary-lO) the number of toll collection clerks needed for less traffic volume than tlO traffic volume(boundary-l 1) the number of toll collection clerks needed for less traffic volimie than tl 1 traffic volume(boundary-12) the number of toll collection clerks needed for less traffic volume than tl2 traffic volume(boundary-13)  155  Appendix  itctl3 tcl4 itctl4 tcl5 itctl5 tcl6 itctl6 tcl7 itctl7 itctlS ptct ptcm  ibrcol ibrco2 pobo pho flr  B: Input  Data  for  Revenue  Stream  the number of toll collection clerks needed for less traffic volume than tl3 traffic volume(boundary-14) the number of toll collection clerks needed for less traffic volume than tl4 traffic volume(boundary-15) the number of toll collection clerks needed for less traffic volume than tl5 traffic volume(boundary-16) the number of toll collection clerks needed for less traffic volimie than tl6 traffic volume(boundary-17) the number of toll collection clerks needed for less traffic volume than tl7 the number of toll collection clerks needed for more traffic volume than tl7 (consigment costs of toll collection) are (toll collection labor costs) * ptct(parameter) toll collection machine maintenance costs) are (consigment costs of toll collection) * ptcm(parameter) cost parameter of building and repainting expenses etc. cost parameter of building and repainting expenses etc. operation bureau overhead parameter headquarters overhead inflation rate (maintenance and operation costs)  Table B.l Closed System (Fixed Toll Rate)  156  Appendix  B: Input  Data for  Revenue  Stream  157  B.2 Closed System (Distance Proportional Toll Rate) nAL nP nWC nOL nBR  iby ird  disci ratel disc2 rate2 perKm entFee al(I) P(K) ptr(I)  ptv(I) traf(l,J,K,L)  lb2 IM lb6 lt2 lt4 lt6 le2 le4  Input Data the number of interchanges(IC) the number of vehicle types weather classification periodic overlay periodic bridge repainting (General Data) start time of the revenue stieam revenue stream duration  deterministic deterministic deterministic deterministic deterministic  automatically calculated  (Data related to Toll Rate) toll discount boimdary-1 (distance) toll discount rate-1 toll discount boundary-2 (distance) toll discount rate-2 toll rate (distance proportional part) of ordinary motor vehicle toll rate (fixed part) of ordinary motor vehicle distance between IC #1-1 and #1 toll ratios compared between ordinary motor vehicle and vehicle type K toll growth rate parameter at year I (Data related to Traffic Volume) tiaffic volume growth rate parameter at year I tiaffic volume of vehicle type L between IC #J and #K at the first year (Maintenance Cost) 2 lane bridge length 4 lane bridge length 6 lane bridge length 2 lane tunnel length 4 lane tunnel length 6 lane tunnel length 2 lane earthwork section length 4 lane earthwork section length  1  Appendix  le6 Itn Itj Ito cc2 cc4 cm2 cm4 cm6 cU cl4 cr2 cr4 cr6 qp2 cp4 cp6 ctn ctj cto csh cso co2 co4 co6 pcot  Idir Ivdir Ichi leng Iwor tl ital itbl itcl itdl itel  B: Input  Data for  Revenue  Stream  6 lane earthwork section length length of tunnel with no ventilation length of tunnel with jet fan length of tunnel with other ventilation road cleaning cost (2 lanes) (4 lanes or more) road maintenance cost (2 lanes) (4 lanes) (6 lanes) lighting cost (1 or 2 lanes) (4 or 6 lanes) bridge repair cost (2 lanes) (4 lanes) (6 lanes) bridge paint cost (2 lanes) (4 lanes) (6 lanes) tunnel maintenance cost (no ventilation) tunnel maintenance cost (jet fan) tunnel maintenance cost (others) snow and ice control cost (heavy snow area)) (ordinary snow area) overlay cost (2 lanes) (4 lanes) (6 lanes) other maintenance cost parameter (Operation Cost) labor cost of operation office (director) (vice director) (chief) (clerk or engineer) (worker) traffic volume(boundary-l) the number of directors needed for less tiaffic volume than tl the number of vice directors needed the mmiber of chiefs needed the number of clerks and engineers needed the number of workers needed  158  Appendix  t2 ita2 itb2 itc2 itd2 ite2 t3 ita3 itb3 itc3 itd3 ite3 t4 ita4 itb4 itc4 itd4 ite4 t5 ita5 itbS itc5 itd5 ite5 ita6 itb6 itc6 itd6 ite6 Itc tcl itctl tc2 itct2  B: Input  Data for  Revenue  Stream  traffic volume(boimdary-2) the number of directors needed for less traffic volume than t2 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the mmiber of workers needed traffic volimie(boundary-3) the number of directors needed for less traffic volume than t3 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed traffic volume(boundary-4) the number of directors needed for less traffic volume than t4 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed traffic volume(boundary-5) the number of directors needed for less traffic volume than t5 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed the number of directors needed for more traffic volume than t5 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed labor cost of toll collection (clerk) tiaffic volume(boundary-l) the number of clerks needed for less traffic volume thantl tiaffic volume(boundary-2) the number of toll collection clerks needed for less tiaffic volume than t2  159  Appendix  tc3 itct3 tc4 itct4 tc5 itctS tc6 itct6 tc7 itct? tc8 itctS tc9 itct9 tclO itctlO tell itct 11 tcl2 itct 12 tcl3 itctlS tcl4 itct 14 tcl5 itct 15 tcl6  B: Input  Data  for  Revenue  Stream  traffic volume(boundary-3) the number of toll collection clerks needed for less traffic volimie than t3 traffic volume(boundary-4) the number of toll collection clerks needed for less traffic volume than t4 traffic volume(boundary-5) the number of toll collection clerks needed for less traffic volume than t5 traffic volume(boundary-6) the nimiber of toll collection clerks needed for less traffic volume than t6 traffic volume(boundary-7) the number of toll collection clerks needed for less traffic volume than t7 traffic volume(boimdary-8) the number of toll collection clerks needed for less traffic volume than t8 traffic volume(boundary-9) the number of toll collection clerks needed for less traffic volume than t9 traffic volume(boundary-lO) the number of toll collection clerks needed for less tiaffic volume than tlO tiaffic volume(boundary-l 1) the number of toll collection clerks needed for less tiaffic volume than tl 1 tiaffic volume(boimdary-12) the number of toll collection clerks needed for less tiaffic volume than tl2 tiaffic volume(boundary-13) the number of toll collection clerks needed for less tiaffic volume than tl3 traffic volimie(boundary-14) the number of toll collection clerks needed for less tiaffic volimie than tl4 tiaffic volume(boundary-15) the number of toll collection clerks needed for less traffic volume than tl5 tiaffic volume(boundary-16)  160  Appendix  itctl6 tcl7 itctl7 itctlS ptct ptcm  ibrcol ibrco2 pobo pho fir  B: Input  Data for  Revenue  Stream  the number of toll collection clerks needed for less traffic volimie than tl6 traffic volume(boundary-17) the number of toll collection clerks needed for less traffic volimie than tl7 the number of toll collection clerks needed for more traffic volume than tl7 (consigment costs of toll collection) are (toll collection labor costs) * ptct(parameter) toll collection machine maintenance costs) are (consigment costs of toll collection) * ptcm(parameter) cost parameter of building and repainting expenses etc. cost parameter of building and repainting expenses etc. operation bureau overhead parameter headquarters overhead inflation rate (maintenance and operation costs)  Table D.2 Closed System (Distance Proportional Toll Rate)  161  Appendix  B: Input  Data for  Revenue  162  Stream  B.3 Open System (Fixed Toll Rate) nAL nP nTG TGL(J) nWC nOL nBR  iby ird  Fee P(K) ptr(I)  ptv(I) traf(l,J,K,L)  lb2 IM lb6 lt2 lt4 lt6 le2 le4 le6 Itn Itj Ito  Input Data the number of interchanges(IC) the number of vehicle types the number of toll gates locations of toll gates weather classification periodic overlay periodic bridge repaintingr (General Data) start time of the revenue stream revenue stream duration (Data related to Toll Rate) toll rate of ordinary motor vehicle toll ratios compared between ordinary motor vehicle and vehicle type K toll growth rate parameter at year I (Data related to Traffic Volume) traffic volume growth rate parameter at year I traffic volume of vehicle type L between IC #J and #K at the first year (Maintenance Cost) 2 lane bridge length 4 lane bridge length 6 lane bridge length 2 lane tunnel length 4 lane tunnel length 6 lane tunnel length 2 lane earthwork section length 4 lane earthwork section length 6 lane earthwork section length length of tunnel with no ventilation length of tunnel with jet fan length of tunnel with other ventilation  deterministic deterministic deterministic deterministic deterministic deterministic deterministic  automatically calculated  Appendix  cc2 cc4 cm2 cm4 cm6 ell cl4 cr2 cr4 cr6 qj2  q34  cp6 ctn ctj cto csh cso co2 co4 co6 pcot  Idir Ivdir Ichi leng Iwor tl ital itbl itcl itdl itel t2 ita2 itb2  B: Input  Data for  Revenue  Stream  road cleaning cost (2 lanes) (4 lanes or more) road maintenance cost (2 lanes) (4 lanes) (6 lanes) lighting cost (1 or 2 lanes) (4 or 6 lanes) bridge repair cost (2 lanes) (4 lanes) (6 lanes) bridge paint cost (2 lanes) (4 lanes) (6 lanes) tunnel maintenance cost (no ventilation) turmel maintenance cost (jet fan) tunnel maintenance cost (others) snow and ice control cost (heavy snow area)) (ordinary snow area) overlay cost (2 lanes) (4 lanes) (6 lanes) other maintenance cost parameter (Operation Cost) labor cost of operation office (director) (vice director) (chief) (clerk or engineer) (worker) traffic volume(boxmdary-l) the nimiber of directors needed for less traffic volume than tl the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed traffic volume(boundary-2) the nimiber of directors needed for less traffic volume than t2 the number of vice directors needed  163  Appendix  itc2 itd2 ite2 t3 ita3 itb3 itc3 itd3 ite3 t4 ita4 itb4 itc4 itd4 ite4 t5 ita5 itb5 itc5 itd5 ite5 ita6 itb6 itc6 itd6 ite6 Itc tcl itctl tc2 itct2 tc3 itct3 tc4  B: Input  Data for  Revenue  Stream  the number of chiefs needed the number of clerks and engineers needed the number of workers needed traffic volume(boundary-3) the number of directors needed for less traffic volume than t3 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed traffic volume(boundary-4) the number of directors needed for less traffic volume than t4 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed traffic volume(boimdary-5) the number of directors needed for less traffic volume than t5 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed the number of directors needed for more traffic volume than t5 the number of vice directors needed the number of chiefs needed the number of clerks and engineers needed the number of workers needed labor cost of toll collection (clerk) traffic volume(boundary-l) the number of clerks needed for less traffic volume thantl traffic volume(boundary-2) the number of toll collection clerks needed for less traffic volume than t2 traffic volume(boundary-3) the number of toll collection clerks needed for less traffic volume than t3 traffic volume(boundary-4)  164  Appendix  itct4 tc5 itct5 tc6 itct6 tc7 itct? tc8 itctS tc9 itct9 tclO itctlO tell itctll tcl2 itctl2 tcl3 itctl3 tcl4 itctl4 tcl5 itctl5 tcl6 itct 16 tcl7 itctl7  B: Input  Data for  Revenue  Stream  the number of toll collection clerks needed for less traffic volimie than t4 traffic volume(boundary-5) the number of toll collection clerks needed for less traffic volimie than t5 traffic volume(boundary-6) the number of toll collection clerks needed for less traffic volume than t6 traffic volume(boundary-7) the number of toll collection clerks needed for less tiaffic volimie than t7 traffic volume(boimdary-8) the nimiber of toll collection clerks needed for less tiaffic volume than t8 traffic volume(boundary-9) the number of toll collection clerks needed for less tiaffic volume than t9 traffic volume(boundary-10) the number of toll collection clerks needed for less tiaffic volume than tlO traffic volume(boundary-l 1) the number of toll collection clerks needed for less tiaffic volume than tl 1 tiaffic volume(boundary-12) the number of toll collection clerks needed for less traffic volume than tl2 traffic volume(boundary-13) the number of toll collection clerks needed for less traffic volume than tl3 traffic volume(boundary-14) the number of toll collection clerks needed for less traffic volume than tl4 tiaffic volume(boundary-15) the number of toll collection clerks needed for less traffic volume than tl5 traffic volume(boundary-16) the number of toll collection clerks needed for less traffic volume than tl6 traffic volume(boundary-17) the number of toll collection clerks needed for less traffic volume than tl7  165  Appendix tcl8 itctlS itctl9 ptct ptcm  ibrcol ibrco2 pobo pho fir  B: Input  Data for  Revenue  Stream  traffic volume(boundary-18) the number of toll collection clerks needed for less traffic volume than tl8 the number of toll collection clerks needed for more traffic volume than tl8 (consigment costs of toll collection) are (toll collection labor costs) * ptct(parameter) toll collection machine maintenance costs) are (consigment costs of toll collection) * ptcm(parameter) cost parameter of building and repainting expenses etc. cost parameter of building and repainting expenses etc. operation bureau overhead parameter headquarters overhead inflation rate (maintenance and operation costs)  Table D.3 Open System (Fixed Toll Rate)  166  Appendix C Interchange Pair Traffic Volume and Traffic Volume and Toll Rate Growth Parameters C.l Interchange Pair Traffic Volume Tables C.l to C.9 shows interchange pair traffic volume for the sample project. They are described by daily traffic volume, and their units are vehicles/day.  167  Appendix  C: Traffic  Volume  and  Growth  vehicle type-1 (light motor vehicle) I.C. #3  168  Rates  I.C. # 4 660  I.C. #5 449 756  I.C. #6 1,636 853 2,275  I.C. # 4 1,400  I.C. #5 1,846 2,892  I.C. #6 4,585 2,660 6,785  I.C. # 4 176  I.C. #5 278 187  I.C. #6 723 448 1,099  I.C. # 4 141  I.C. #5 183 117  I.C. #6 505 346 862  I.C. # 4 12  I.C. #5 39 15  I.C. #6 44 37 85  I.C. #4 2,389 0 0  I.C. #5 2,795 3,967 0 0  I.C. #6 7,493 4,344 11,106 0 0  I.e. #2 I.C . #1  vehicle type-2 (ordinary motor vehic le) I.C. #3 I.C. #2 I.C . #1  vehicle type-3 (medium-sized motor vehicle) I.C. #3 I.C. #2 I.C . #1  vehicle type-4 (large-sized motor vehicle) I.C. #3 I.C. #2 I.C . #1  vehicle type-5 (special large-sized motor vehic! e) I.C. #3 I.C. #2 I.C . #1  (total) I.C. # 3 I.C. #2  0 I.C . #1 0 0 :.l: I n t e r c h a n g B P a i r Tr r a f f i c  Year f o r RVS #1  Volume a t Base  Appendix  C: Traffic  Volume  and  Growth  I.C. #4 333 411  I.C. #5 469 333 610  I.C. #6 1,676 880 955 1,536  I.C. #4 704 947  I.C. #5 1,923 1,495 2,272  I.C. #6 4,751 2,740 3,233 4,306  I.C. #4 26 156  I.C. #5 306 154 104  I.C. #6 727 461 396 881  I.C. #4 19 120  I.C. #5 198 96 69  I.C. #6 506 358 304 672  2 10  I.C. #5 43 17 5  I.C. #6 46 39 41 64  I.C. #4 1,084 1,644 0  I.C. #5 2,939 2,095 3,060 0  I.C. #6 7,706 4,478 4,929 7,459 0  vehicle type-1 (light motor vehicle) I.C. #3 7  I.e. #2  169  Rates  I.C . #1  vehicle type-2 (ordinary motor vehic le) I.C. #3 22  I.C. #2 I.C . #1  vehicle type-3 (medium-sized motor vehicle) I.C. #3 I.C. #2  6  I.C . #1  vehicle type-4 (large-sized motor vehicle) I.C. #3 6  I.C. #2 I.C . #1  vehicle type-5 (special large-sized motor vehici e) I.C. #4 I.C. #3 I.C. #2  0  I.C . #1  (total)  I.C. #2 I.C . #1  0  I.C. #3 41 0  Table C.2: Interchange Pair Traffic Volume at Base Year for RVS #2.  Appendix  C: Traffic  Volume  and  Growth  vehicle type-1 (light motor vehicle) I.C. #3 351  I.e. #2  170  Rates  I.C. #4 328 552  I.C. #5 401 269 836  I.C. #6 1,969 983 823 2,086  I.C. #4 703 1,414  I.C. #5 1,647 1,112 3,269  I.C. #6 5,493 3,084 2,883 6,348  I.C. #4 27 192  I.C. #5 270 110 169  I.C. #6 770 490 344 1,138  I.C. #5 173 62 119  I.C. #6 538 382 262 925  2 12  I.C. #5 41 11 13  I.C. #6 51 44 41 86  I.C. #4 1,079 2,322 0  I.C. #5 2,532 1,564 4,406 0  I.C. #6 8,821 4,983 4,353 10,583 0  I.C . #1  vehicle type-2 (ordinary motor vehic le) I.C. #3 991  I.C. #2 I.C . #1  vehicle type-3 (medium-sized motor vehicle) I.C. #3 72  I.C. #2 I.C . #1  vehicle type-4 (large-sized motor vehicle) I.C. #3 38  I.C. #2  I.C. #4 19 152  I.C . #1  vehicle type-5 (special large-sized motor vehici e) I.C. #4 I.C. #3 I.C. #2  6  I.C . #1  (total)  I.C. #2 I.C . #1  0  I.C. #3 1,458 0  Table C.3: Interchange Pair Traffic Volume at Base Year for RVS #3.  Appendix  C: Traffic  Volume  and Growth  Rates  vehicle type-1 (light motor vehicle) I.C. #3 402  I.e. #2  171  I.C. #4 341 562  I.C. #5 402 327 883  I.C. #6 2,144 1,058 810 2,234  I.C. #4 727 1,439  I.C. #5 1,651 1,447 3,566  I.C. #6 6,008 3,353 2,716 6,689  I.C. #4 28 195  I.C. #5 277 131 244  I.C. #6 1,344 534 331 1,396  I.C. #4 19 154  I.C. #5 183 76 175  I.C. #6 923 399 264 1,160  2 13  I.C. #5 41 14 20  I.C. #6 150 59 36 115  I.C. # 4 1,117 2,363 0  I.C. #5 2,554 1,995 4,888 0  I.C. # 6 10,569 5,403 4,157 11,594 0  I.C . #1  vehicle type-2 (ordinary motor vehicle) I.C. #3 1,128  I.C. #2 I.C . #1  vehicle type-3 (medium-sized motor vehicle) I.C. #3 87  I.C. #2 I.C . #1  vehicle type-4 (large-sized motor vehicle) I.C. #3 44  I.C. #2 I.C . #1  vehicle type-5 (special large-sized motor vehici e) I.C. #4 I.C. #3 I.C. #2  6  I.C . #1  (total)  I.C. #2 I.C . #1  0  I.C. #3 1,667 0  Table C.4: Interchange Pair Traffic Volume at Base Year for RVS #4.  Appendix  C: Traffic  Volume  and  Growth  vehicle type-1 (light motor vehicle)  i.e. #3 I.C . #1  I.e. #2 75  428 285  I.C. #4 352 486 303  I.C. #5 422 327 424 628  I.C. #6 2,326 743 817 1,597 1,113  I.C. #4 752 1,127 787  I.C. #5 1,745 1,438 1,798 2,462  I.C. #6 6,671 2,251 2,736 5,859 2,589  I.C. # 4 29 125 163  I.C. #5 292 136 132 123  I.C. #6 1,543 518 277 991 434  I.C. #4 20 76 135  I.C. #5 188 78 86 99  I.C. #6 1,076 411 208 815 366  2 10 11  I.C. #5 43 14 14 6  I.C. #6 169 53 40 85 28  I.C. #4 1,155 1,824 1,399  I.C. #5 2,690 1,993 2,454 3,318  I.C. #6 11,785 3,976 4,078 9,347 4,530  vehicle t y p e - 2 (ordinary motor vehic le)  I.C . #1  I.C. #2 290  I.C. #3 1,181 1,055  vehicle type-3 (medium-sized motor vehicle)  I.C . #1  I.C. #2 38  I.C. #3 112 143  vehicle type-4 (large-sized motor vehicle)  I.C . #1  I.C. #2 29  I.C. #3 60 90  vehicle type-5 (special large-sized motor vehici e) I.C. #4 I.C. #2 I.C . #1  3  I.C. #3 10 11  (total)  I.C . #1  Table C.5  I.C. #2 435  I.C. #3 1,791 1,584  172  Rates  Interchange Pair Traffic Volume at Base Year for RVS #5.  Appendix  C: Traffic  Volume and Growth  vehicle type-1 (light motor vehicle)  I.C . #1  I.e. #2 80  I.C. #3 460 302  I.C. #5 464 446 490 688  I.C. #6 2,529 782 755 1,652 1,164  I.C. #4 802 1,199 832  I.C. #5 1,956 2,128 2,124 2,745  I.C. #6 7,235 2,357 2,497 5,996 2,699  I.C. #4 31 135 173  I.C. #5 315 159 148 134  I.C. #6 1,837 557 283 1,032 474  I.C. #4 22 84 142  I.C. #5 203 94 97 111  I.C. #6 1,290 443 213 855 393  I.C. #5 49 15 16 7  I.C. #6 205 61 42 91 28  I.C. #5 2,987 2,842 2,875 3,685  I.C. #6 13,096 4,200 3,790 9,626 4,758  I.C. #4 376 518 318  vehicle type-2 (ordinary motor vehic le)  I.C . #1  I.C. #2 312  I.C. #3 1,267 1,134  vehicle type-3 (medium-sized motor vehicle)  I.C . #1  I.C. #2 42  I.C. #3 120 151  vehicle type-4 (large-sized motor vehicle)  I.C . #1  I.C. #2 31  I.C. #3 65 96  vehicle type-5 (special large-sized motor vehici e) I.C. #4 I.C. #2 I.C . #1  4  I.C. #3 10 13  2 11 12  (total)  i.e. #3 I.C . #1  Table C.6  I.C. #2 469  1,922 1,696  173  Rates  I.C. #4 1,233 1,947 1,477  Interchange Pair Traffic Volume at Base Year for RVS #6.  Appendix  C: Traffic  Volume  and  Growth  vehicle type-1 (light motor vehicle)  I.C . #1  I.e. #2 110  I.C. #3 586 437  I.C. #4 437 534 371  I.C. #5 558 482 493 770  I.C. #6 3,528 950 875 1,624 1,419  I.C. #4 922 1,241 960  I.C. #5 2,205 2,215 1,915 3,081  I.C. #6 10,366 3,690 2,946 6,216 3,583  I.C. #4 34 146 189  I.C. #5 309 217 83 83  I.C. #6 2,286 774 354 953 722  I.C. #5 201 136 45 68  I.C. #6 1,677 599 289 785 634  I.C. #5 47 24 12 3  I.C. #6 266 111 39 91 50  I.C. #5 3,320 3,074 2,548 4,005  I.C. #6 18,123 6,124 4,503 9,669 6,408  vehicle type-2 (ordinary motor vehic le)  I.C . #1  I.C. #2 457  I.C. #3 1,627 1,706  vehicle type-3 (medium-sized motor vehicle)  I.C . #1  I.C. #2 50  I.C. #3 141 91  vehicle type-4 (large-sized motor vehicle)  I.C . #1  I.C. #2 38  I.C. #3 93 130  I.C. # 4 24 97 156  vehicle type-5 (special large-sized motor vehic! e) I.C. # 4 I.C. #2 I.C . #1  6  I.C. #3 14 19  5 12 13  (total)  Table  174  Rates  I.C. #4 I.C. # 3 1,422 2,461 I.C. #2 2,030 I.C . #1 661 2,383 1,689 C.7: I n t erchang( 3 P a i r Tr r a f f i c Y e a r f o r RVS # 7  Volume at Base  Appendix  C: Traffic  Volume  and  Growth  I.C. #4 497 602 402  I.C. #5 636 542 538 1,114  I.C. #6 4,002 980 1,009 1,580 2,177  I.C. #4 1,051 1,386 1,093  I.C. #5 2,496 2,497 2,052 4,944  I.C. #6 11,532 3,815 3,448 5,858 7,146  I.C. # 4 40 156 196  I.C. #5 350 239 98 387  I.C. #6 2,063 759 420 744 3,667  I.C. #4 28 93 169  I.C. #5 229 147 51 309  I.C. #6 1,491 603 324 608 3,194  5 14 17  I.C. #5 55 31 14 39  I.C. #6 239 107 55 71 371  I.C. #4 1,621 2,251 1,877  I.C. #5 3,766 3,456 2,753 6,793  I.C. #6 19,327 6,264 5,256 8,861 16,555  vehicle type-1 (light motor vehicle)  I.C . #1  I.e. #2 195  I.C. #3 617 829  vehicle type-2 (ordinary motor vehic le)  I.C . #1  I.C. #2 908  I.C. #3 1,656 3,315  vehicle type-3 (medium-sized motor vehicle)  I.C . #1  I.C. #2 1 19  I.C. #3 155 346  vehicle t y p e - 4 (large-sized motor vehicle)  I.C . #1  I.C. #2 88  I.C. #3 90 267  vehicle type-5 (special large-sized motor vehici e) I.C. #4  I.C . #1  I.C. #2 10  I.C. #3 16 35  (total)  I.C . #1  I.C. #2 1,320  I.C. #3 2,534 4,792  175  Rates  Table C.8: Interchange Pair Traffic Volume at Base Year for RVS #8.  Appendix  C: Traffic  Volume  and Growth  vehicle type-1 (light motor vehicle) 560 679 441  1,193  I.C. #6 4,443 1,075 1,109 1,732 2,287  I.C. #4 1,183 1,559 1,200  I.C. #5 2,768 2,657 2,339 5,290  I.C. #6 12,614 4,194 3,811 6,322 7,364  I.C. #5  I.C. #6 2,319  I.C. #5 I.C. #4 I.C. #3  I.e. #2 I.C . #1  705 967  219  vehicle type-2 (ordinary motor vehic le)  I.C . #1  I.C. #2 1,035  I.C. #3 1,888 3,846  vehicle type-3 (medium-sized motor vehicle) I.C. #4 I.C. #3 I.C. #2 I.C . #1  177 460  146  44 176 215  vehicle type-4 (large-sized motor vehicle) I.C. #3 I.C. #2 106  104 357  32  1,208 188  vehicle type-5 (special large-sized motor vehici e) I.C. #3 I.C . #1  15  17 46  I.C . #1  I.C. #3 2,891 5,676  256 125 58 264  826 464 803  3,562 I.C. #6 1,684 659 365 664  3,143 I.C. #6 276  1 14  6 15 20  61 31 17 27  62 79 385  I.C. #4 1,825 3,637 2,064  I.C. #5 4,181 3,599 3,120 7,088  I.C. #6 21,336 6,868 5,811 9,600 16,741  (total)  I.C. #2 1,521  387 214 105 314  I.C. #5 I.C. #4  I.C. #2  709 572 601  I.C. #5 I.C. #4  I.C . #1  176  Rates  Table C.9: Interchange Pair Traffic Volume at Base Year for RVS #9.  Appendix  C: Traffic  Volume  and Growth  111  Rates  C.2 Traffic Volume Growth Parameters Table C.IO shows traffic volume growth parameters used for deterministic feasibility analysis. RVS # 1 2 3 4 5 6 7  8  9  Year in RVS 1 1 1 1 1 2 1 2 1 2 3 4 1 2 3 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14  Parameter 559 567 574 582 590 597 605 618 630 643 655 668 681 693 706 718 731 741 751 761 770 780 790 800 810 820 830 840 849 859  Table C.IO Traffic Volume Growth Parameters  Appendix  C: Traffic  Volume  and Growth  Rates  178  C.3 Toll Rate Growth Parameters Table C.ll shows toll rate growth parameters used for deterministic feasibility analysis. RVS # 1 2 3 4 5 6 7  8  9  Y e a r in RVS 1 1 1 1 1 2 1 2 1 2 3 4 1 2 3 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14  Parameter 1.0000 1.0000 1.0000 1.0404 1.0404 1.0404 1.1041 1.1041 1.1041 1 . 1717 1.1717 1.1717 1.2434 1 .2434 1.2434 1.3195 1.3195 1.3195 1.4002 1.4002 1.4002 1.4859 1.4859 1.4859 1.5769 1.5769 1.5769 1.6734 1.6734 1.6734  Table C.ll Toll Rate Growth Parameters  Appendix D Source Code of the Model  Appendix D shows source code of the model  179  Appendix  Main Program  D: Source  Code of  WPDURA  the  Model  180  VARBLE TRANS -  INV DECOMP DGMULT  WPDFF MMTWPL COVAR EAST  WPCOST  NETWRK  EARLY  TANSP  CDFUNC ESTMMT  INPOL  VARBLE TRANS  -  WPCMMT  INV DECOMP DGMULT WPCFF MMTWPL  WPCFF COVAR REVSTR  VARBLE TRANS  -  INV DECOMP DGMULT  RVSMMT  RVSFF — MMTWPL  RVSFF  RVSF11-13  RVSF11 -13  COVAR PRJCST  TANSP  INV DECOMP DGMULT  PRJREV  TANSP  INV DECOMP DGMULT  WPCMMT  WPCFF MMTWPL  TANSP  INV  PRJNPV PRJIRR  DECOMP DGMULT RVSMMT  RVSFF • MMTWPL  CDFUNC  INTPOL  Figure D.l Program Structure  RVSF11 -13  INV DECOMP DGMULT  Appendix  D: Source  Code of  main program  AMMA  sub-routine  WPDURA EAST  WPCOST REVSTR PRJCST PRJREV PRJNPV PRJIRR  CDFUNC  INTPOL  VARBLE TRANS TANSP  WPDFF  WPCMMT  the  Model  181  evaluate the first four moments of the work package duration. evaluate the first four moments of the early start time of work packages. obtain the calendar month of the early start time. evaluate the first four moments of the work package cost. evaluate the first four moments of the net revenue stream. approximate the first four moments of the project cost at the MARR. approximate the first four moments of the project revenue at the MARR. approximate the first four moments of the project NPV at the MARR. approximate the cumulative distribution function and the first four moments of the project IRR. obtain values of cumulative distribution function of a dependent variable approximated by a pearson typed distribution. interpolate the betal and beta2 values of the pearson table by a method of linear interpolation. approximate a variable to a pearson type distribution by using five percentile estimates. transform a set of correlated variables to a set of uncorrelated variables. transform correlated work package costs/revenue streams to uncorrelated work package costs/revenue. check the type of functional form for work package duration. estimate the function at the mean values of the transformed variables. evaluate the first four moments of the work package cost for different discount rates.  Appendix  D: Source  Code of  RVSMMT WPCFF  RVSFF  MMTWPL  COVAR  NETWRK EARLY  ESTMMT INV DECOMP DGMULT RVSFll 13 SPARSE FOOl TRACE  the  Model  182  evaluate the first four moments of the revenue streams for different discount rates. check the type of functional form for work package cost. estimate the function at the mean values of the transformed variables. check the type of functional form for revenue streams. estimate the function at the mean values of the transformed variables. approximate the first four moments of a dependent variables at work package/revenue stream level (by Taylor series). approximate the correlation between two dependent variables by using information between the primary variables and their partial derivatives. evaluate the first four moments of work package early start time (by PNET). evaluate the first four moments of a path early start time by uncorrelating the work package durations. approximate the first four moments for early start time (if PNET is used). invert a matrix decompose A to A=L*Ltranspose (by Choleski method). calculate matrix * matrix e.g. transformation matrix (L"^xD"^) the functional forms for revenue streams for toll highway projects save huge arrays that contain mainly zero. called by "RVSF12" trace the procedure  Table D.l Program List  Appendix D: Source  Code of the Model  183  C Amma.FOR C modified by Toshiaki Hatakama in July 1994 in order to adjust C the program to toll highway projects that require a lot of primary C variables (e.g. 200) for revenue streams. C However, this program limits the number of primary variables to 300 C due to memory capacity. C C C C C C  For example, if the number of interchanges is 6, the number of vehicle types is 5, toll collection system is closed system (fixed toll rates) , and a revenue stream duration is 14 years, the number of primary variables of the revenue stream is 297. This is almost the limit. If you have big enough RAM, you can increase this number.  C C C C C C  AMMA is capable of dealing with correlations between variables. However, due to memory capacity, correlation coefficients for revenue streams are automatically calculated as zero. In other w o r d s , work package duration and cost input files should include correlation coefficients, but revenue stream input file does not include them.  C In addition, save memory spaces, subroutine SPARSE is used. Most C correlation coefficients are often zero. SPARSE can save these C spaces. See source code. C Common blocks in the original program C replaced by Dummy Arguments.  (written in 1990) are  C This program requires 2.5, 5.0, 50.0, 95.0, and 97.5 percentile C estimates (note : not 5.0, 25.0, 50.0, 75.0, 9 5 , 0 ) . C C C C C C C  Step functions are used for operation cost estimates, there is a problem when partial derivatives are calculated. Even small changes in some primary variables may cause big differences because their ranks sometimes change. See operation cost estimates in RVSFll, 1 2 , and 13.inc for reference. Therefore, AMMA uses a trick to deal with this, namely, parameters KT and KP. See REVSTR, RVSMMT, and RVSFll, 1 2 , and 13.inc.  PROGRAM AMMA  IMPLICIT REAL*4 (A-H,0-Z) CHARACTER*64 FNAME  C if you have 16M or more Ram, choose "enough" = 1 C if not, choose any number but 1. $DEFINE enough = 0  Appendix  D: Source  Code of  the Model  184  REAL*4 PEARSN (:,:) ALLOCATABLE PEARSN REAL*4 WPTIME  (:,:), CORRD  {:,:), ESTART  (:,:)  INTEGER IWPC (:), NWPCF (:), NDVR (:) INTEGER NRVSF (:), NDRV (:) REAL*4 XUCOST  (:,:,:), TRIWPC  REAL*4 BOTTLE  (:,:), XUREV  (:,:,:), COST  (:,:), CORRC  (:,:,:), REV (:,:), CORRR  (:,:)  (:,:)  $IF enough .EQ. 1 REAL*4 TRIRVS (:,:,:) $ELSE REAL*4 TRIRVS (:) $ENDIF REAL*4 PCOST ALLOCATABLE ALLOCATABLE ALLOCATABLE ALLOCATABLE INCLUDE  (4), PREV (4) WPTIME, CORRD, ESTART IWPC, NWPCF, NDVR, NRVSF, NDRV, BOTTLE XUCOST, TRIWPC, COST, CORRC XUREV, TRIRVS, REV, CORRR  'DEBUG.CMN'  CALL TRACE  (1, "MAIN",  C get certain parameters  'Amma 2.0 begins  execution.')  from a startup file, such as  OPEN READ  (UNIT=1, FILE='AMMA.INI•, STATUS='UNKNOWN') (1, *) NPEARS ! the size of the pearson table (always ! 2655) READ (1, •) MAXDVC ! max # of variables for COST (-25) READ (1, *) MAXDVR ! max # Of variables for REVENUE (-3 00) READ (1, *) IDEBUG ! 0=silent, l=enter/exit, 2=more... CLOSE {UNIT=1) C Read in the Pearson Distribution Definition and store in an array. C the pearson table should REALLY be (17,NPEARS). C that way, you don't have to refer to NPEARS all the time. ALLOCATE (PEARSN (NPEARS, 17)) OPEN (UNIT=1, FILE='PEARSON', STATUS='UNKNOWN') DO 10 1=1,2655 10 READ (1,9901) (PEARSN(I,J), J=l,17) CLOSE (UNIT=1)  C Get all the input file names from the Pipe between Terq and AMMA C fName is read into as many times as is required to get at the C actual data (the program 'comments' the parameters... OPEN READ  (UNIT=90, FILE='TERQAMMA.PIP', (90,*) fName  STATUS='UNKNOWN')  Appendix  D: Source  READ READ  Code of the Model  185  (90,*) fName (90,*) fName  READ (90,*) fName READ (90,*) fName ! LR filename, usually 'tTerq.LR' OPEN (UNIT=10, FILE=fName, STATUS='UNKNOWN' ) READ (90,*) fName READ (90,*) fName ! D filename, usually 'tTerg.D' OPEN (UNIT=11, FILE=fname, STATUS='UNKNOWN' ) READ (90,*) fName READ (90,*) fName ! C filename, usually ' t T e r g . C OPEN (UNIT=12, PILE=fName, STATUS='UNKNOWN' ) READ (90,*) fName READ (90,*) fName ! R filename, usually 'tTerq.R' OPEN (UNIT=13, FILE=fName, STATUS='UNKNOWN' ) READ (90,*) fName READ (90,*) fName ! Output filename, usually OPEN {UNIT=7, FILE=fName, STATUS='UNKNOWN' ) CALL TRACE (1, 'MAIN', fName) CLOSE  'tTerq.OUT'  (UNIT=90)  C EXCEL.CSV is a 'Comma Separated Value' file for EXCEL to play C with... C This file is used to draw cumulative probability distributions. OPEN  +  (UNIT=20, F I L E = ' A M M A . C S V ,  STATUS='UNKNOWN')  READ (11, 9902) NWP ! number of Work Packages, inc. start/fin.  ALLOCATE ALLOCATE  (WPTIME (4, NWP)) (CORRD (NWP, NWP))  C set the global error variable to 0. C if there is a problem, this gets set to something other than 0, C and the program jumps to the STOP statement. lERR = 0  C C  CALL TRACE (1, 'MAIN', 'calling Work Package DURAtion.') CALL WPDURA (PEARSN, WPTIME, CORRD) READ from unit 11 (correlation of primary variables) CALLS VARBLE, TRANS, WPDFF, MMTWPL & COVAR (the reader!) IF  (0 < lERR) THEN CALL TRACE (1, 'MAIN', GO TO 10 00 ENDIF ALLOCATE  (ESTART  'WPDURA Set lERR,  (4, NWP))  exiting.')  Appendix  D: Source  Code of  the Model  18 6  CALL TRACE (1, 'MAIN', 'calling EArly STart.') CALL EAST (PEARSN, WPTIME, CORRD, ESTART) READ from unit 10, just one line with system parameters CALLS NETWRK, which CALLS EARLY, CDFUNC & ESTMMT  C C  IF  (0 < lERR) THEN CALL TRACE (1, 'MAIN', GO TO 1000 END IF  exiting.')  + +  READ (12, 9 903) DR, ! minimum attractive rate of return FRA ! equity fraction  +  READ (13, 9904) NRS ! the number of revenue  ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE  C C  'EAST set lERR,  streams  (IWPC (NWP)) (NWPCF (NWP)) (NDVR (NWP)) (XUCOST (4, NWP, MAXDVC)) (TRIWPC (NWP, NWP, NWP)) (COST (4, NWP)) (CORRC (NWP, NWP))  CALL TRACE (1, 'MAIN', 'calling Work Package COST.') CALL WPCOST (DR, FRA, + PEARSN, + WPTIME, + ESTART, + IWPC, NWPCF, NDVR, + COST, + XUCOST, TRIWPC, + CORRC) READ from unit 12, alot of work package stuff CALLS VARBLE, TRANS, WPCMMT, WPCFF & COVAR (the reader!) IF (0 < lERR) THEN CALL TRACE (1, 'MAIN', 'WPCOST set lERR, exiting.') GO TO 1000 ENDIF ALLOCATE ALLOCATE ALLOCATE  (NRVSF (NRS)) (NDRV (NRS)) (XUREV (4, NRS, MAXDVR))  C this is a sparse array, so go figure... $IF enough .EQ. 1 ALLOCATE (TRIRVS (NRS, MAXDVR, MAXDVR)) $ELSE NSIZ = (MAXDVR * 3 * NRS) + 6 NSIZ = 10002 ! and this is an optimal patch for the time being... ALLOCATE (TRIRVS (NSIZ)) CALL SPA_INIT3 (TRIRVS, NSIZ, NRS, MAXDVR, MAXDVR) $ENDIF  Appendix  D: Source  ALLOCATE ALLOCATE ALLOCATE  C C  Code of  the Model  18 7  (REV (4, NRS)) (CORRR (NRS,NRS)) (BOTTLE (NRS, 30))  CALL TRACE (1, 'MAIN', 'calling REVenue STReam.') CALL REVSTR (PEARSN, + DR, + WPTIME, + ESTART, + NRVSP, NDRV, + XUREV, TRIRVS, + REV, CORRR, + BOTTLE) READ from unit 13, tons of data into NRVSF, etc. CALLS VARBLE, TRANS, RVSMMT, RVSFF & COVAR IF (0 < lERR) THEN CALL TRACE (1, 'MAIN', 'REVSTR set lERR, exiting.') GO TO 1000 END IF DEALLOCATE DEALLOCATE  (WPTIME, CORRD) (ESTART)  C THE PROJECT PERFORMANCE  LEVEL  'calling PRoJect  CoST.')  C  CALL TRACE (1, 'MAIN', CALL PRJCST (DR, + COST, + CORRC, + PCOST) CALLS TANSP  'calling PRoJect  REVenue.')  c  CALL TRACE (1, 'MAIN', CALL PRJREV (DR, + REV, + CORRR, PREV) + CALLS TANSP  C if (constant, current or total dollars = 0 ) , then we're done. IF  (DR == O.ODO) THEN CALL TRACE (1, 'MAIN', 'minumum attractive rate=0, + exiting . ') GO TO 1000 END IF  C THE PROJECT DECISION LEVEL  CALL TRACE  (1, 'MAIN',  'calling PRoJect Net Present  Value.')  Appendix + +  D: Source  Code of  the Model  18 8  CALL PRJNPV (DR, PCOST, PREV)  C If you are trying to run a huge toll highway project, stop here. C You need to modify the program to IRR, because it may take 20 C minutes per discount rate.  CALL TRACE  (1, 'MAIN', 'calling PRoJect Internal Rate of Return!•) CALL PRJIRR (PEARSN,FRA, + IWPC, NWPCF, NDVR, + CORRC, TRIWPC, + XUCOST, COST, + NRVSF, NDRV, + CORRR, TRIRVS, + XUREV, REV, + BOTTLE) CALLS WPCMMT, TANSP, RVSMMT, CDFUNC +  C  1000  9 90  9901 9902 9903 9904  DEALLOCATE DEALLOCATE DEALLOCATE DEALLOCATE  (IWPC, NWPCF, NDVR, NRVSP, (CORRC, XUCOST, COST) (CORRR, XUREV, REV) (BOTTLE)  CALL TRACE STOP  (1, 'MAIN',  'that•'S all,  CALL TRACE GOTO 1000  (1, 'MAIN',  'damn.')  FORMAT (8F8.4,7F7 . 4,2F4.1) FORMAT (13) FORMAT (2F8.3) FORMAT (13) END INCLUDE INCLUDE  'TRACE.MJW' 'ANSI.MJW'  $IF enough .NE. 1 INCLUDE 'SPARSE.MJW' $ENDIF  NDRV)  folks!')  Appendix  D: Source  Code of  the  Model  C WpDura.FOR C modified by Toshlaki Hatakama in July, 1994. C THE ROUTINE TO EVALUATE THE FIRST FOUR MOMENTS OF THE WORK C PACKAGE DURATION BY APPLYING THE FRAMEWORK  SUBROUTINE WPDURA +  IMPLICIT INCLUDE  (PEARSN, WPTIME,CORRD)  REAL*4(A-H,0-Z) 'DEBUG.CMN"  REAL*4 PEARSN REAL*4 WPTIME  (2655, 17) (4, * ) , CORRD  (NWP, *)  INTEGER IWPD{:),NWPDF{:),NDVR{:) ALLOCATABLE IWPD,NWPDF,NDVR REAL*4 PRCEST(:,:) REAL*4 CALC(:,:) ALLOCATABLE PRCEST,CALC REAL*4 X{:),Z(:),SZ(:),GZS{:),GZL{:) REAL*4 XWPD (:,:,:), ZWPD(:,:,:) ALLOCATABLE X, Z , SZ , GZS,GZL,XWPD,ZWPD REAL*4 W P D C O ( : , : , : ) , PWPDl(:), PWPD2{:), PWPDX(:,:) REAL*4 TRIWPD{:,:), STFO(:) ALLOCATABLE WPDCO,PWPDl,PWPD2,PWPDX,TRIWPD, STFO CALL TRACE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE  (2, 'WPDURA',  'starting.')  (IWPD(NWP)) (NWPDF(NWP)) (NDVR(NWP)) (PRCEST(5,NWP)) (CALC(4,NWP)) (X(MAXDVC)) (Z(MAXDVC)) (SZ(MAXDVC)) (GZS(MAXDVC)) (GZL(MAXDVC)) (XWPD(4,NWP,MAXDVC)) (ZWPD(4,NWP,MAXDVC)) (WPDCO(NWP,MAXDVC,MAXDVC)) (PWPDl(MAXDVC)) (PWPD2(MAXDVC)) (PWPDX(NWP,MAXDVC)) (TRIWPD (MAXDVC, MAXDVC)) (STFO(NWP))  C initialize the first four moments of the start work package  189  Appendix 2  D: Source  Code of  DO 2 K=l,4 WPTIME(K,1)  the Model  190  = O.DO  C basic data about the work packages DO 15 0 INWP=2,NWP  C C C C C  type of IWPD(I) IWPDd) IWPD(I) IWPD(I)  10  work = 1, = 2, = 3, = 4,  package duration : holistic or decomposed detailed estimate holistic ??? direct input  READ(11,10)IWPD(XNWP) FORMAT (12) SELECT CASE  (IWPD(INWP))  C detailed estimate CASE (1) C NWPDF(I) = type of functional form C NDVR(I) = number of discrete primary  20  READ (11,20) NWPDF(INWP), FORMAT(12,13)  variables  NDVR(INWP)  C approximate the primary variables in the functional forms C for work package durations to pearson type distributions C to obtain the first four moments for them. C C C C  NNVR = number of primary variables... why are we getting an array dimension from something we just read in that is specific to only one data set? something funny is going on here. NNVR = NDVR(INWP) IF (NNVR .GT. MAXDVC) THEN CALL TRACE (1, 'WPDURA' , 'MAXDVC exceeded.') lERR = 1 GOTO 1000 ENDIF DO 5 0 JPV=1,NNVR  C subjective estimates for each variable in the C functional form for the work package duration.  READ (11, 8001) A,B,C,D,E CALL VARBLE (PEARSN, A,B,C,D,E, C1,C2,C3,C4) IF (lERR .EQ. 1) GOTO 9001 XWPD (1, INWP, JPV) = CI XWPD (2, INWP, JPV) = C2 XWPD (3, INWP, JPV) = C3 XWPD (4, INWP, JPV) = C4  Appendix D: Source 50  Code of the Model  191  CONTINUE  C correlation coefficients between the primary variables in C the work package, correlation matrix is positive definite.  70  80 90  DO 9 0 JPV = 1,NNVR JPVl = JPV+1 IF (JPVl.LE.NNVR) THEN READ(11,70) ( W P D C O d N W P , JPV,K) , K = JPVl, NNVR) FORMAT{2 0F6.2) DO 8 0 K=JPVl,NNVR WPDCO(INWP,K,JPV) ENDIF CONTINUE  = WPDCO(INWP,JPV,K)  C calculate the first four moments for a WP duration when C the duration is estimated holistically. C why are there TWO ways to do this??? CASE (2,3) JPV = 1  READ (11, 8001) A,B,C,D,E CALL VARBLE (PEARSN, A,B,C,D,E, C1,C2,C3,C4) IF (lERR .EQ. 1) GOTO 9002 WPTIME (1, INWP) = CI WPTIME (2, INWP) = C2 WPTIME (3, INWP) = C3 WPTIME (4, INWP) = C4 C moments of the work package durations are entered CASE (4)  125  15 0  directly  READ(11,12 5) (WPTIME(K,INWP),K=1,4) FORMAT(4F25.6) END SELECT CONTINUE  C correlation between work package durations? C looks to me like defining some zeros in the matrix. C making the matrix triangular?  160 17 0  NWPMl = NWP-1 DO 170 INWP=2,NWPMl INWPl = INWP+1 IF (INWPl .LE. NWPMl) THEN DO 160 J = INWPl, NWPMl CORRD (INWP,J) = O.ODO CORRD (J,INWP) = O.ODO ENDIF CONTINUE  Appendix  D: Source  Code of  the Model  192  C WHEN DURATIONS ARE ESTIMATED WHOLISTICALLY OR FROM MOMENTS. DO 2 00 INWP=2,NWPM1 IF (IWPD(INWP).6E.2) THEN INWPl = INWP+1 IF (INWPl .LE, NWPMl) THEN DO 190 J=INWP1,NWPMl IF (IWPD(J).GE.2) THEN READ (11, 18 0) C O R R D d N W P , J) FORMAT(FS.2) CORRD(J, INWP) = C O R R D d N W P , J) ENDIF CONTINUE ENDIF ENDIF CONTINUE  180  190  2 00  C THE FIRST FOUR MOMENTS OF THE WORK PACKAGE DURATION WHEN THE C DURATION IS ESTIMATED FROM A DECOMPOSITION. DO 300 INWP=2,NWP C WHEN WORK PACKAGE DURATIONS ARE ESTIMATED WHOLISTICALLY C OR FOR THE WORK PACKAGES TO PHASE PROJECTS WITH A TIME C LAG OR FOR THE FINISH WORK PACKAGE. IF  (IWPD(INWP).EQ.l)  THEN  C TRANSFORM CORRELATED VARIABLES TO UNCORRELATED C ONLY THE LINEAR CORRELATION IS CONSIDERED.  +  VARIABLES.  NNVR = NDVR (INWP) CALL TRANS (INWP,NNVR,NWP,MAXDVC, XWPD,ZWPD,WPDCO,TRIWPD) IF (0 < lERR) GO TO 1000  C ESTIMATE G(Z) FROM THE g(X) GIVEN BY THE USER AT THE MEAN C VALUES OF Z (THE TRANSFORMED VARIABLES) AND THE PARTIAL C DERATIVES WITH RESPECT TO THE TRANSFORMED VARIABLES.  210  DO 210 JPV=1,NNVR Z(JPV) = ZWPD(1,INWP,JPV)  220  DO 22 0 JPV=1,NNVR X(JPV) = O.ODO DO 22 0 KSV=1,NNVR X(JPV) = X(JPV) + TRIWPD(JPV,KSV) * Z(KSV)  C THE VALUE OF G(Z) AT THE MEAN VALUES OF Z  CALL WPDFF(NWPDF  (INWP), X, GZ)  C THE PARTIAL DERAVATIVES OF THE TRANSFORMED C JPV Is the primary variable index  VARIABLES  Appendix  D: Source  Code of  the Model  C KSV is the secondary variable index C KTV is the tertiary (third) variable C i think....  193 index...  DO 2 90 JPV=1,NNVR Z(JPV) = Z W P D d , INWP, JPV) * 0.9 9D0 SZ(JPV) = Z W P D d , INWP, JPV) * O.OIDO DO 240 KSV=1,NNVR X{KSV) = O.ODO DO 24 0 LTV=1,NNVR X(KSV) = X(KSV) + TRIWPD(KSV,LTV) * Z(LTV)  240  C THE VALUE FOR G(Z) WHEN Z(J) IS LESS THAN THE MEAN VALUE C (NEGATIVE INCREMENT)  CALL WPDFF(NWPDF  (INWP), X, GZS (JPV))  Z(JPV) = Z W P D d , INWP, JPV) * I.OIDO DO 2 60 KSV=1,NNVR X(KSV) = O.ODO DO 2 60 LTV=1,NNVR X(KSV) = X(KSV) + TRIWPD(KSV,LTV) * Z(LTV) 2 60  CONTINUE  C THE VALUE C (POSITIVE  FOR G(Z) WHEN INCREMENT)  Z(J)  CALL WPDFF(NWPDF C 1st & 2 n d p a r t i a l  derivatives  PWPDl(JPV) PWPD2(JPV) + Z(JPV) CONTINUE  2 90 C the first  CALL  3 00  THAN  (INWP),  THE MEAN  VALUE  X, GZL(JPV))  wrt Z(J)  = ( G Z L ( J P V ) - G Z S ( J P V ) ) / (2.0D0 * S Z ( J P V ) ) = (GZL(JPV) + GZS(JPV) - 2.0D0 * GZ) / (SZ(JPV)**2)  = ZWPD(1,INWP,JPV)  four m o m e n t s  MMTWPL  + + +  IS M O R E  for the work package  duration  (INWP,NNVR, NWP,ZWPD, GZ,PWPD1,PWPD2, WPTIME,STFO(INWP))  E N D IF CONTINUE  C APPROXIMATE THE CORRELATION BETWEEN THE WORK C MOMENT APPROXIMATIONS AT THE PROJECT LEVEL.  PACKAGES FOR  C ESTIMATE g(X) GIVEN B Y T H E USER A T MEAN OF X A N D T H E FIRST C PARTIAL DERAVATIVE WITH RESPECT TO THE CORRELATED VARIABLES. NWPMl  = NWP-1  Appendix  D: Source  Code of  the Model  194  DO 350 INWP=2,NWPM1 IF (IWPD(INWP),EQ.l) THEN NNVR = NDVR(INWP) C as kludgy as this may seem, WPDFF can potentially make C a reference to ALL elements of X.... DO 33 0 JPV=1,NNVR 330 X(JPV) = XWPD(1,INWP,JPV) C THE FIRST PARTIAL DERAVATIVE OF THE CORRELATED DO 340 JPV=1,NNVR X(JPV) = XWPD(1,INWP,JPV) SZ(JPV) = XWPD(1,INWP,JPV)  VARIABLES  • 0.99D0 * O.OIDO  C THE VALUE FOR g(X) WHEN X(J) IS LESS THAN THE MEAN VALUE C (NEGATIVE INCREMENT)  CALL WPDFF X(JPV)  (NWPDF  (INWP), X, GZS (JPV))  = XWPD(1,INWP,JPV)  * 1.0IDO  C THE VALUE FOR g(X) WHEN X(J) IS MORE THAN THE MEAN VALUE C (POSITIVE INCREMENT)  CALL WPDFF(NWPDF  (INWP), X, GZL (JPV))  C THE FIRST PARTIAL DERAVATIVE WITH RESPECT TO Z(J)  + 340 350  PWPDX(INWP,JPV) = (GZL(JPV) - GZS(JPV)) / (2.0D0 * SZ(JPV)) X(JPV) = XWPD(1,INWP,JPV) CONTINUE ENDIF CONTINUE  C ESTIMATE THE CORRELATION BETWEEN TWO WORK PACKAGE  DURATIONS  JU = 11 NN = NWP-1 DO 380 INWP=2,NN IF (IWPD(INWP) .EQ. 1) THEN NI = NDVR(INWP) INWPl = INWP+1 IF (INWPl .LE. NN) THEN DO 370 JWP=INWP1,NN IF (IWPD{JWP) .EQ. 1) THEN NJ = NDVR(JWP) C MJW moved this read out of COVAR, C 'cause why make the call if you do NADA?  ("Nothing")  READ (JU, *) NDCV IF (NDCV == 0) THEN CORRD (INWP, JWP) = O.ODO  Appendix  D: Source  Code of  the Model  19 5  CORRD (JWP, INWP) = O.ODO ELSE CALL COVAR(JU, NDCV, INWP,JWP,NI,NJ, + + + + +  370  3 80  PWPDX, XWPD, WPDCO, STFO(INWP),STFO(JWP), CORRD) ENDIF ENDIF CONTINUE ENDIF ENDIF CONTINUE  1000 DEALLOCATE DEALLOCATE DEALLOCATE DEALLOCATE DEALLOCATE DEALLOCATE DEALLOCATE CALL TRACE  (IWPD, NWPDF, NDVR) (PRCEST, CALC) (X, Z, SZ, GZS, GZL) (XWPD, ZWPD) (WPDCO) (PWPDl, PWPD2, PWPDX) (TRIWPD,STFO) (2, 'WPDURA',  'exiting.')  RETURN 8001  FORMAT(5F20.4)  9001 WRITE (7, 9 9 01) INWP, JPV 9901 FORMAT (/,'WP#(',13,') var(',I2,') GOTO 100 0  != Pearson  Type.',/)  9002 WRITE (7, 9902) INWP 9902 FORMAT (/,'WP#(',13,').Duration != Pearson Dist.',/) GOTO 1000  END  Appendix  D: Source  Code of  the Model  19 6  C East.FOR C modified by Toshiaki Hatakama in July, 1994. C ROUTINE TO EVALUATE THE FIRST FOUR MOMENTS OF THE EARLY START C TIME OF WORK PACKAGES USING A PRECEDENCE NETWORK AND OBTAIN C THE CALENDAR MONTH OF THE EARLY START TIME. C= SUBROUTINE EAST  (PEARSN, WPTIME, CORRD, ESTART)  C= IMPLICIT REAL*4(A-H,0-Z) INCLUDE •DEBUG.CMN' REAL*4 PEARSN REAL*4 WPTIME REAL*4 ESTART  (NPEARS, *) (4, * ) , CORRD (4, *)  (NWP, *)  CHARACTER*3 LM (:) INTEGER LY (:) REAL*4 SDET{:), SKET(:), A K E T ( : ) , AMEET(:) ALLOCATABLE LM, LY, SDET, SKET, AKET, AMEET C this is ment to ease the burden of calculating some of the days. C the last index is 1=7 day ww, 2=6 day ww, 3=5 day ww. INTEGER DAYS (13, 3) CHARACTER*3 MONTHS (12) DATA DAYS/ + 0,22,42,64, 86,108,130,151,173,195,217,239,261, + 0,27,51,77,103,130,156,182,209,235,261,287,313, + 0,31,59,90,120,151,181,212,243,273,304,334,365/  + + C C C C C C C C C  ! 5 day week ! 6 day week ! 7 day week  DATA MONTHS/ •JAN',•FEB',•MAR',•APR','MAY','JUN', 'JUL•,•AUG•,•SEP',•OCT',•NOV',•DEC'/  START AND FINISH DATES IN CALENDAR TIME AND THE TIME UNIT IDS = day start IMS = month start lYS = year start IDF = day finish IMF = month finish lYF = year finish NUNT = time unit (l=day, 2=month, 3=year) NWW = (5,6,7) = number of days in work week. CALL TRACE ALLOCATE ALLOCATE  (2, 'EAST',  'starting.')  (LM (NWP), LY (NWP)) (SDET (NWP), SKET (NWP), AKET  (NWP), AMEET  (NWP))  READ (10, 9910) IDS, IMS, lYS, IDF, IMF, lYF, NUNT, NWW IF (NWW < 5 .OR. 7 < NWW) THEN lERR = 1 WRITE (7, 9901)  Appendix  D: Source  Code of  the Model  GO TO 1000 ENDIF IP  (lYS == 0) THEN SDATE = O.ODO GO TO 400 ENDIF IWW = NWW - 4 lYB ICHS ND NDS  = = = =  1988 lYS - lYB ICHS * DAYS (13, IWW) ND + IDS + DAYS (IMS, IWW)  IF (0 < ICHS) GO TO 180 IF (IMS < 3) GO TO 200 180 NDS = NDS + 1 JS = IFIX (ICHS / 4.) IF (2 < IMS) GO TO 190 NDS = NDS + JS - 1 GO TO 2 00 190 NDS = NDS + JS 200 SELECT CASE (NUNT) CASE (1) SDATE = FLOAT CASE (2) SDATE = FLOAT CASE (3) SDATE = FLOAT END SELECT  (NDS) (NDS) / 30.4167D0 (NDS) / 365.ODO  IF (lYF == 0) GO TO 400 ICHF = lYF - lYB NF = ICHF * DAYS (13, IWW) NDF = NF + IDF + DAYS (IMF, IWW) IF IF  (0 < ICHF) GO TO 380 (IMF < 3) GO TO 400  3 80 NDF = NDF + 1 JF = IFIX (ICHF / 4.) IF (2 < IMF) THEN NDF = NDF + JF ELSE NDF = NDF + JF - 1 ENDIF  400 CALL NETWRK (PEARSN, WPTIME, CORRD, ESTART, TRCOR) IF (0 < lERR) GO TO 1000 C the work package durations in the specified time unit  197  Appendix  D: Source  WRITE WRITE  Code of  the  198  Model  (7, 9911) (7, 9912)  DO 1590 I = 1,, NWP IF (WPTIME (2, I) == O.ODO) THEN SDTME = O.ODO SKTME = O.ODO AKTME = O.ODO ELSE SDTME = WPTIME (2, I) ** 0.5D0 SKTME = WPTIME (3, I) / (WPTIME (2, I) ** 1.5D0) ASKT = 1.2D0 * (SKTME ** 2)+2 .0 AKTME s WPTIME (4, I) / (WPTIME (2, I) ** 2) IF (AKTME < ASKT) THEN AKTME = ASKT ENDIF ENDIF SELECT CASE CASE  (NUNT) (1) AMTME = SDTME = CASE (2) AMTME = SDTME = CASE (3) AMTME = SDTME = END SELECT  WPTIME SDTME  (1, I)  WPTIME SDTME  (1, I)  WPTIME SDTME  (1, I)  / 30 .4167D0 / 30 .4167D0  * 12 ,0D0 • 12 . ODO  1570 WRITE E (7, 9913) I, AMTME, SDTME, SKTME, AKTME 1590 CONTINUE WRITE WRITE  (7, 9914) TRCOR (7, 9915)  DO 2250 I == 1, IF (ESTART SDET (I) SKET (I) AKET (I) ELSE SDET (I) SKET (I) AKET (I) ENDIF  NWP (2, I) == O.ODO) THEN = O.ODO = O.ODO = O.ODO = ESTART (2, I) ** 0.5D0 = ESTART (3, I) / (ESTART (2, I) ** 1.5D0 = ESTART (4, I) / (ESTART (2, I) ** 2)  C convert the early start time of a work package to calendar C time from absolute time. SELECT CASE C 7 day ww. daily CASE  (NWW -t- NUNT (7) AMST AMEET SDET  (I) (I)  1)  ESTART ESTART SDET  (1, I) (1, I) (I)  SDATE 30.4167D0 30.4167D0  Appendix  D: Source  Code of  monthly CASE (8) AMST AMEET SDET C 7 day WW, yearly CASE (9) AMST AMEET SDET C 5 day ww (daily) CASE (5) AMST SDET C 6 day ww (daily) CASE (6) AMST SDET END SELECT  the Model  199  C 7 day WW,  = (ESTART (I) = ESTART (I) = SDET  (1, I) + SDATE) * 30.4167D0 (1, I) (I)  = (ESTART (I) = ESTART (I) = SDET  (1, I) + SDATE) * 365.ODO (1, I) * 12.ODO (I) * 12.ODO  = ESTART (I) = SDET  (1, I) (I) / 21.75D0  = ESTART (I) = SDET  (1, I) (I) / 26.0833D0  LYY = IFIX (AMST / DAYS LY(I) = lYB + LYY LDC LDD IF IF  (13,  IWW))  = IFIX (AMST) = MOD (LDC, DAYS (13, IWW)) (0 < LYY) GO TO 1710 (LDD < DAYS (2, IWW)) GO TO 1730  1710  JJ = IFIX (LYY / 4.) IF (DAYS (2, IWW) < LDD) GO TO 1720 LDD = LDD - JJ + 1 GO TO 1730  1720  LDD = LDD - JJ  1730  ITEMP = 1 DO 1731, WHILE  ( (DAYS (ITEMP + 1,IWW) ITEMP < 12 ) ITEMP = ITEMP + 1  + 1731 2250  LM (I) = MONTHS  <= LDD)  (ITEMP)  C the early start times o£ the work packages  2300  DO 2300 I = 1, NWP WRITE (7, 9916) I, LM (I), LY (I), + AMEET (I), SDET (I), SKET (I), AKET(I)  C the project duration WRITE WRITE  : E.S.T of the Nth work package  (7, 9917) TRCOR (7, 9918)  SELECT CASE (NUNT) CASE (1) AMP = ESTART CASE (2)  (1, NWP) / 30.4167D0  .AND.  Appendix  D: Source  Code of  the Model  AMP = ESTART CASE (3) AMP = ESTART END SELECT  2 00  (1, NWP) (1, NWP) * 12.ODO  SDP = SDET (NWP) SKP = SKET (NWP) AKP = AKET (NWP) WRITE  +  (7, 9903) LM (NWP), LY (NWP), AMP, SDP, SKP, AKP  CALL CDFUNC (PEARSN, AMP, SDP, SKP, AKP, V1,V2,V3,V4,V5,V6,V7, V 8 , V9,VIO,Vll,V12,V13,V14,V15)  WRITE (20, 9930) + V1,V2,V3,V4,V5,V6,V7, V8, V9,VIO,Vll,V12,V13,V14,V15 1000 CALL TRACE DEALLOCATE DEALLOCATE RETURN  (2, 'EAST', 'exiting.') (LM, LY) (SDET, SKET, AKET, AMEET)  9901 FORMAT ('EAST: Work Week should be 5, 6 or 7 days.') C 9902 FORMAT (•***** WHEN WORK WEEK =(5,6), TIME UNIT sb DAYS.') 9903 FORMAT (A3,' / ',I4,4F15.2) 9910 FORMAT 9911 FORMAT MONTHS.') 9912 FORMAT + 9913 FORMAT  (213,15,213,15,212) (/,'Work Package Durations',/,'The TIME UNIT is ("W.P.ft  Exp.Value===== ', 'S.Dev.======== Skewness (14,6X,2F15.3,2F8.2)  Kurtosis')  9914 FORMAT + 9915 FORMAT + 9916 FORMAT  (/,'Work Package Early Start Times for a Transitional ', 'Correlation o f , F5.2,/,'The TIME UNIT is MONTHS.') ('W.P.tt Exp.Month===== Exp.Value===== ', 'S.Dev========= Skewness Kurtosis') (I4,7X,A3," / ',14,4X,2F15.2,2F8.2)  9917 FORMAT + 9918 FORMAT +  (/,'The Project Duration for a Transitional ', 'Correlation o f , F5.2,/,'The TIME UNIT is MONTHS.') ('Month Exp.Value===== ', •S.Dev========= Skewness Kurtosis")  9930 FORMAT  (' Project Duration export for EXCEL',  +  / , •  +  /,'  +  / , •  +  / , •  +  / ,  +  +  /,' /. • /.• /,' /.•  +  / , •  + + +  •  ' ,F20.2, ',F20.2, ' ,F20.2, ',F20.2, •,F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20.2,  , 0.25' , 0.50 , 1.00 , 2.50' , 5,00' ,10.00' ,25.00' ,50.00' ,75.00' ,90.00' ,95.00'  / / / / / / r  / / / /  Appendix  D:  + + + +  Source /, /, /, /,  END  Code  of  the  Model  ' , F 2 0 . 2 , • ,97 . 5 0 ' , •,F20.2,',99.00•, ',F20.2,',99.50', ',F20.2,',99.75')  2 01  Appendix  D: Source  Code of  the Model  2 02  C WpCost.POR C modified by Toshiaki Hatakama in July, 1994. C THE ROUTINE TO EVALUATE THE FIRST FOUR MOMENTS OF THE WORK C PACKAGE COST BY APPLYING THE FRAMEWORK  SUBROUTINE WPCOST + + + + + +  (DR,FRA,PEARSN, WPTIME, ESTART, IWPC, NWPCF, NDVR, COST, XUCOST, TRIWPC, CORRC)  IMPLICIT REAL*4(A-H,0-Z) INCLUDE •DEBUG.CMN' REAL*4 PEARSN (NPEARS, *) REAL*4 WPTIME (4, *) REAL*4 ESTART (4, *) INTEGER IWPC (*), NWPCF {*), NDVR (*) REAL*4 XUCOST (4, NWP, * ) , TRIWPC (NWP, NWP, *) REAL*4 COST (4, * ) , CORRC (NWP, •) INTEGER NNVR, NTYP (50) REAL*4 X ( 2 5 ) , SZ(25), 6ZS(25),  GZL(25)  REAL*4 XCOST (:,:,:), WPCCO (:,:,:), PWPCX ALLOCATABLE XCOST, WPCCO, PWPCX  (:,:)  REAL*4 STFO (:), TRI (:,:) ALLOCATABLE STFO, TRI CALL TRACE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE  (2, 'WPCOST',  'starting.')  (STFO (NWP)) (TRI (MAXDVC, MAXDVC)) (XCOST (4, NWP, MAXDVC)) (WPCCO (NWP, MAXDVC, MAXDVC)) (PWPCX (NWP, MAXDVC))  C the first four moments of the start work package COST COST COST COST  (1, 1) (2, 1) (3, 1) (4, 1)  = = = =  O.DO O.DO O.DO O.DO  C basic data about the work packages IWPC (1) = 0 NWPCF (1) = 0 NDVR (1) = 0 NTYP (1) = 0  Appendix  D: Source  DO 300  Code of  the  203  Model  1=2,NWP  READ (12, 8020) IWPC(I) ! type of work package ! l=decomposed ! 2=wholistic ! 3=direct input  cost  GOTO (10, 150, 200) IWPC(I) GOTO 9003 ! something's worng  C type of functional form and the number of primary 10  READ (12, 8030) NWPCF NNVR = NDVR (I)  (I), NDVR  (I), NTYP  variables (I)  C DURATION AND EARLY FINISH TIME ARE PRIMARY VARIABLES IN C ALL THE FUNCTIONAL FORMS FOR WORK PACKAGE COST. (THE LINK C BETWEEN TIME AND COST BECAUSE COST IS TIME DEPENDENT). C Var#l is the duration of the work package XCOST XCOST XCOST XCOST  (1, (2, (3, (4,  I, I, I, I,  1) = WPTIME 1) = WPTIME 1) = WPTIME 1) s WPTIME  (1, (2, (3, (4,  I) I) I) I)  (1, (2, (3, (4,  I) I) I) I)  C Var#2 is the early finish time XCOST XCOST XCOST XCOST  (1, (2, (3, (4,  I, I, I, I,  ESTART ESTART ESTART ESTART  2) 2) 2) 2)  + + + +  WPTIME WPTIME WPTIME WPTIME  (1, (2, (3, (4,  I) I) I) I)  C Var#3 is the project duration, aka the time at which the loan is due. XCOST XCOST XCOST XCOST  (1, (2, (3, (4,  I, I, I, I,  3) 3) 3) 3)  ESTART ESTART ESTART ESTART  (1, (2, (3, (4,  NWP) NWP) NWP) NWP)  C Var#4 is the revenue phase duration, which equals the C work package duration. IF  (11 <= NWPCF  (I)) THEN  XCOST XCOST XCOST XCOST  4) 4) 4) 4)  (1, (2, (3, (4,  I, I, I, I,  = = = =  DO 35 J=l,4 JJ = J+1 DO 34 K=JJ,NNVR  WPTIME WPTIME WPTIME WPTIME  (1, (2, (3, (4,  NWP) NWP) NWP) NWP)  finish  Appendix  D: Source  Code of  the  WPCCO(I,J,K) 34 35  Model  2 04  = O.ODO  WPCCO(I,K,J) = O.ODO CONTINUE CONTINUE  C APPROXIMATE THE PRIMARY VARIABLES IN THE FUNCTIONAL FORMS C FOR WORK PACKAGE COST TO PEARSON TYPE DISTRIBUTIONS TO C OBTAIN THE FIRST FOUR MOMENTS FOR THEM.  37  40  DO 4 0 J=5,NNVR IF (1 <: NTYP (I)) THEN ! direct read the moments READ (12, 37) (XCOST (K, I, J ) , K = 1, 4) FORMAT (4F3 0.5) ELSE READ (12, 8010) A,B,C,D,E CALL VARBLE (PEARSN, A,B,C,D,E, CI, C2, C3, C4) IF (lERR == 1) GO TO 9001 XCOST (1, I, J) = CI XCOST (2, I, J) = C2 XCOST (3, I, J) = C3 XCOST (4, I, J) = C4 ENDIF CONTINUE  C CORRELATION COEFFICIENTS BETWEEN THE PRIMARY VARIABLES IN C THE WORK PACKAGE. CORRELATION MATRIX IS POSITIVE DEFINITE.  41  42 45  50  DO 45 J = 5,NNVR JJ = J+1 IF (NNVR < JJ) (30 TO 45 READ (12, 41) (WPCCO (I, J, K ) , K = JJ, NNVR) FORMAT(2 0F6.2) DO 42 K=JJ,NNVR WPCCO(I,K,J) = W P C C O d , J CONTINUE CONTINUE ELSE DO 50 J=l,3 JJ = J+1 DO 5 0 K=JJ,NNVR W P C C O d , J,K) = O.ODO WPCCO(I,K,J) = O.ODO  C APPROXIMATE THE PRIMARY VARIABLES IN THE FUNCTIONAL FORMS C FOR WORK PACKAGE COST TO PEARSON TYPE DISTRIBUTIONS TO C OBTAIN THE FIRST FOUR MOMENTS FOR THEM. C SUBJECTIVE ESTIMATES FOR OTHER VARIABLES IN THE C FUNCTIONAL FORM FOR THE WORK PACKAGE COST.  70  DO 100 J=4,NNVR IF (1 < NTYP (I)) THEN READ (12, 70) (XCOST FORMAT (4F30.5) ELSE  (K, I, J ) , K = 1, 4)  Appendix  100  D: Source  Code of  the Model  2 05  READ (12, 8010) A,B,C,D,E CALL VARBLE (PEARSN, A,B,C,D,E, C1,C2,C3,C4) IF (lERR == 1) GO TO 9001 XCOST (1, I, J) = CI XCOST (2, I, J) = C2 XCOST (3, I, J) = C3 XCOST (4, I, J) = C4 ENDIF CONTINUE  C CORRELATION COEFFICIENTS BETWEEN THE PRIMARY VARIABLES IN C THE WORK PACKAGE. CORRELATION MATRIX IS POSITIVE DEFINITE.  110 120 140  DO 14 0 J = 4,NNVR JJ = J+1 IF (JJ <= NNVR) THEN READ (12, 110) (WPCCO (I,J,K),K=JJ,NNVR) FORMAT (20F6.2) DO 120 K=JJ,NNVR WPCCO (I,K,J) = WPCCO (I,J,K) ENDIF CONTINUE ENDIF GO TO 3 00  C THE FIRST FOUR MOMENTS FOR A WORK PACKAGE COST WHEN THE C COST IS ESTIMATED WHOLISTICALLY. 150  J =1 READ (12, 8010) A,B,C,D,E CALL VARBLE (PEARSN, A,B,C,D,E, C1,C2,C3,C4) IF (0 < lERR) GO TO 9002 COST COST COST COST  (1, I) = CI (2, I) = C2 (3, I) = C3 (4, I) = C4  Q**********************************************  XUCOST XUCOST XUCOST XUCOST  (1, I, 1) = CI (2, I, 1) = C2 (3, I, 1) = C3 (4, I, 1) = C4  Q**********************************************  GO TO 3 00  C MOMENTS OF THE WORK PACKAGE DURATIONS ARE ENTERED DIRECTLY 200 210 300  READ (12, 210) (COST FORMAT (4F25.6) CONTINUE  (K, I),K=1,4)  ! Go back and get the next work package  Info.  Appendix  D: Source  Code of  the Model  206  C CORRELATION BETWEEN WORK PACKAGE COSTS.  310 320  NN = NWP-1 DO 320 1=2,NN JJ = I+l IF (JJ <= NN) THEN DO 310 J=JJ,NN CORRC(I,J) = O.ODO CORRC(J,I) = O.ODO ENDIF CONTINUE  C WHEN WORK PACKAGE COSTS ARE INPUT AS MOMENTS.  330  340 35 0 C C C C C C  DO 350 1=2,NN IF (2 < IWPC(I)) THEN JJ = I+l IF (NN < JJ) GO TO DO 340 J=JJ,NN IF (2 < IWPC(J)) READ(12,330) PORMAT(F6.2) CORRC(J,I) = ENDIF CONTINUE ENDIF CONTINUE  350 THEN CORRC(I,J) CORRC(I,J)  THE FIRST FOUR MOMENTS OF THE WORK PACKAGE COST WHEN THE COST IS ESTIMATED FROM A DECOMPOSITION. WHEN WORK PACKAGE COST ARE ESTIMATED WHOLISTICALLY OR FOR THE FINISHED WORK PACKAGE, TRANSFORM CORRELATED VARIABLES TO UNCORRELATED VARIABLES. ONLY THE LINEAR CORRELATION IS CONSIDERED. DO 400 I = 2, NWP IF (IWPC(I) == 1) THEN NNVR = NDVR(I) CALL TRANS (I, NNVR, NWP, MAXDVC, + XCOST, + XUCOST, + WPCCO, TRI) IF (lERR == 1) GO TO 1000  C THE TRANSFORMATION  MATRIX FOR A WORK  PACKAGE  DO 3 60 J=1,NNVR DO 360 K=1,NNVR T R I W P C d , J,K) = TRI(J,K) TRIWPC{I,K,J) = TRI(K,J) 3 60  CONTINUE  C t h i s Is t h e o n l y p l a c e w h e r e C O S T C by anything when IWPC{I) = 1 . . .  Is a f f e c t e d  Appendix  + + + + 400  D: Source  Code of  the Model  2 07  CALL WPCMMT (I, DR, FRA, NWPCF, NDVR, XUCOST, TRIWPC, COST, STFO (I)) ENDIF CONTINUE  C APPROXIMATE THE CORRELATION BETWEEN THE WORK PACKAGES FOR C MOMENT APPROXIMATIONS AT THE PROJECT LEVEL. C ESTIMATE g(X) GIVEN BY THE USER AT MEAN OF X AND THE FIRST C PARTIAL DERAVATIVE WITH RESPECT TO THE CORRELATED VARIABLES.  43 0  NN = NWP-1 DO 450 1=2,NN IF (1 < IWPC(I)) GO TO 450 NNVR = NDVR(I) DO 43 0 J=1,NNVR X(J) = XCOST (1, I, J) CONTINUE  C THE FIRST PARTIAL DERAVATIVE DO 44 0 J=1,NNVR X(J) = XCOST SZ(J) = XCOST  OF THE CORRELATED  VARIABLES  (1, I, J) * 0.99D0 (1, I, J) * O.OIDO  C THE VALUE FOR g(X) WHEN X(J) IS LESS THAN THE MEAN VALUE C (NEGATIVE INCREMENT)  Q  *********************  CALL X(J)  WPCFF(NWPCF(I),DR,FRA,X,GZS(J)) = XCOST (1, I, J) * I.OIDO  C THE VALUE FOR g(X) WHEN X(J) IS MORE THAN THE MEAN VALUE C (POSITIVE INCREMENT)  Q  ***********************  CALL  WPCFF(NWPCF(I),DR,FRA,X,GZL(J))  C THE FIRST PARTIAL DERAVATIVE WITH RESPECT TO Z(J)  44 0 450  PWPCX(I,J) = (GZL(J) - GZS(J)) / (2.0D0 * SZ (J) X(J) = XCOST (1, I, J) CONTINUE CONTINUE  C ESTIMATE THE CORRELATION BETWEEN TWO WORK PACKAGE COSTS. C COVAR does something to the SECOND set of values of XCOST. C check this carefully.  Appendix  D: Source  Code of the Model  208  JU = 12 NN = NWP-1 DO 500 I = 2, NN IF ( I W P C d ) == 1) THEN NI = NDVR (I) JJ = I+l IF (JJ <= NN) THEN DO 470 J=JJ,NN IF (IWPC(J) == 1) THEN NJ = NDVR (J) READ (JU, *) NDCV IF (NDCV == 0) THEN CORRC (I, J) = O.ODO CORRC (J, I) = O.ODO ELSE CALL COVAR (JU,NDCV, I,J,NI,NJ, + PWPCX, + XCOST, + WPCCO, + STFO (I),STFO{J), + CORRC) ENDIF ENDIF 47 0 CONTINUE ENDIF ENDIF 5 00 CONTINUE 1000 DEALLOCATE CALL TRACE RETURN  (XCOST, WPCCO, STFO, TRI) (2, 'WPCOST', "exiting.")  8010 FORMAT(5F20.4) 802 0 FORMAT(12) C 8030 FORMAT (12, 13, 12) 8030 FORMAT (14, 14, 14) 9001 WRITE (7,9901) I, J 9901 FORMAT ('WPCOST: WP(",13,").Var(',12,") GOTO 1000  is not PEARSON.")  9002 WRITE (7, 9902) I 9902 FORMAT ("WPCOST: WP(",I3,") is not PEARSON.") GOTO 1000 9003 WRITE (7, *) "What Gives! Type greater than 3?" GOTO 1000 END  Appendix  D: Source  Code of  the  Model  2 09  C RevStr.FOR C modified by Toshiaki Hatakama in July, 1994. C THE ROUTINE TO EVALUATE THE FIRST FOUR MOMENTS OF THE NET C REVENUE STREAM BY APPLYING THE FRAMEWORK TO THE WP/RS LEVEL. C calls VARBLE, RVSMMT  SUBROUTINE REVSTR + + + + + + + +  (PEARSN, DR, WPTIME, ESTART, NRVSF, NDRV, XUREV, TRIRVS, REV, CORRR, BOTTLE)  C if you have 16M Ram, chhose "enough" = 1. C if not, choose any number but 1. $DEFINE enough = 0 IMPLICIT REAL*4 (A-H,0-Z) INCLUDE •DEBUG.CMN' REAL*4 PEARSN REAL*4 WPTIME REAL*4 ESTART INTEGER NRVSF REAL*4 BOTTLE $IF enough .EQ. 1 REAL*4 XUREV $ELSE REAL*4 XUREV $ENDIP REAL*4 REV  (NPEARS, *) (4, *) (4, *) (*), NDRV (*) (NRS, *)  (4, NRS, * ) ,  TRIRVS  (NRS, MAXDVR,  (4, NRS, * ) ,  TRIRVS  (*)  (4, * ) ,  *)  CORRR(NRS, *)  REAL*4 X (300), SZ, GZS, GZL REAL*4 XREV (:,:,:), RVSCO(:,:,:), ALLOCATABLE XREV, RVSCO, PRVSX  PRVSX(:,:)  REAL*4 STFO(:), TRI(:,:) ALLOCATABLE STFO, TRI C basic data about the revenue CALL TRACE ALLOCATE ALLOCATE  (1, 'REVSTR',  (STFO (XREV  streams 'starting.')  (NRS)) (4, NRS, MAXDVR))  C Only 1 Multi-Megabyte Array per application, please.... C we can't get rid of this because TRANS & COVAR do alot of work with  Appendix  D: Source  Code of  the Model  210  C it. ALLOCATE ALLOCATE  (RVSCO (PRVSX  (NRS, MAXDVR, MAXDVR)) (NRS, MAXDVR))  DO 100 INRS = 1, NRS  + + + +  C C C C C  PRINT *, 'Reading in REVenue STReam #•, INRS READ (13, 9 901) type of functional form NRVSF (INRS), number of primary variables NDRV (INRS), the work package number LL, the fraction of the duration after PERT which the revenue begins...  if this is a toll highway project, read more basic data. we have to pass extra info to our custom RVSFF functions, so we're going to do it in X, our WONDER-VECTOR. the first element of X tells how many elements are sacred to RVSFnn.  + +  SELECT CASE (NRVSF (INRS)) CASE (11) ! 'closed' toll highway (one toll booth per gate] READ (13, 9905) BOTTLE (INRS, 1 ) , ! nAL = # of interchanges BOTTLE (INRS, 2) ! nP = # of vehicle types READ  +  READ +  READ +  CASE  (13, 9906) BOTTLE (INRS, 3)  (13, 9 906) BOTTLE (INRS, 4)  (13, 9 906) BOTTLE (INRS, 5)  ! nWC = weather ! class (1,2,...)  ! nOL = overlay ! years(0,1,2,..)  ! nBR = bridge repaint ! year(0,1,2,...)  + + +  (12) ! 'open' toll highway (some may not have gates) READ (13, 9907) BOTTLE (INRS, 1 ) , ! nAL = # of interchanges BOTTLE (INRS, 2 ) , ! nP = # of vehicle types BOTTLE (INRS, 6) ! nTG = # of toll gates  +  DO 50 J = 1, BOTTLE (INRS, 6) READ (13, 9908) BOTTLE (INRS, (J + 6)) ! toll gate  50  READ +  READ +  (13, 9906) BOTTLE (INRS, 3)  (13, 9906) BOTTLE (INRS, 4)  ! nWC = weather ! (1,2, . . .)  ! nOL = overlay  location  class  Appendix  D-. Source  Code of  the  211  Model ! years(0,1,2,..)  READ  CASE + +  (13, 9906) BOTTLE (INRS, 5)  ! nBR = bridge repaint ! year(0,1,2,...)  (13) ! 'closed' toll highway (fixed toll) READ (13, 9 9 05) BOTTLE (INRS, 1 ) , ! nAL = # of interchanges BOTTLE (INRS, 2) nP = # of vehicle types READ  (13, 9906) BOTTLE (INRS, 3)  READ  ! nWC = weather ! (1,2, . . .)  (13, 9906) BOTTLE (INRS, 4)  READ  class  ! nOL = overlay ! years(0,1,2,..)  (13, 9 906) BOTTLE (INRS, 5)  > nBR = bridge repaint ! year(0,1,2,...)  END SELECT NNVR C C C C  NDRV  (INRS)  the start time of the revenue stream is a primary variable in all the functional forms for a revenue stream, the link between time and revenue because revenue is time dependent. variable#l is the start time of the revenue stream. XREV XREV XREV XREV  (1, (2, (3, (4,  INRS, INRS, INRS, INRS,  1) 1) 1) 1)  ESTART ESTART ESTART ESTART  (1, (2, (3, (4,  LL) LL) LL) LL)  + + + +  PERT PERT PERT PERT  * * * *  WPTIME WPTIME WPTIME WPTIME  C approximate the primary variables in the functional forms C for revenue streams to pearson type distributions to C obtain the first four moments for them. DO 65 J = 1, NNVR DO 60 K = 1, NNVR RVSCO (INRS, J, K) = O.ODO CONTINUE RVSCO (INRS, J, J) = l.ODO CONTINUE  60 65  DO 90 J = 2, NNVR C subjective estimates for other variables in the C functional form for the revenue streams.  + +  READ (13, 9902) A,B,C,D,E CALL VARBLE (PEARSN, A,B,C,D,E, XREV (1, INRS, J ) , XREV (2, INRS, J ) ,  5%ile estimate  (1, (2, (3, (4,  LL) LL) LL) LL)  Appendix  D: Source  Code of  the Model  212  +  XREV  (3, INRS, J ) ,  +  XREV  (4, INRS, J))  90  IF (0 < lERR) GOTO 9000  100 CONTINUE C the first four moments of the revenue stream. C DR is fixed. C in PRJIRR, we will vary DR to get a desired ... ALLOCATE (TRI (MAXDVR, MAXDVR)) OPEN OPEN  IRR.  (UNIT = 121, FILE = 'REVl.SEN', STATUS = 'UNKNOWN') (UNIT = 12 2, FILE = •REV2.SEN', STATUS = 'UNKNOWN')  DO 3 00 INRS = 1, NRS C transform correlated variables to uncorrelated variables.  +  NNVR = NDRV(INRS) CALL TRANS (INRS, NNVR, NRS, MAXDVR, XREV, XUREV, RVSCO, TRI) IF (lERR == 1) GO TO 1000  C the transformation matrix for a revenue  stream  DO 2 00 J = 1, NNVR DO 2 00 K = 1, NNVR $IF enough  .EQ. 1 TRIRVS  (INRS, J, K) = TRI (J, K)  $ELSE CALL S P A S E T S  (TRIRVS, TRI (J, K ) , INRS, J, K)  $ENDIF 2 00  CONTINUE WRITE WRITE  (121, *) 'sensitivity coefficientl for RVS #',INRS (122, •) 'sensitivity coefficient2 for RVS #',INRS  CALL RVSMMT + + + 3 00  (INRS, DR, BOTTLE, NRVSF, NDRV, XUREV, TRIRVS, REV, STFO (INRS))  CONTINUE DEALLOCATE (TRI)  C approximate the correlation between the revenue streams for C moment approximations at the project level. C estimate g(x) given by the user at mean of X and the first C partial derivative with respect to the correlated variables. DO 450 INRS = 1,NRS NNVR = NDRV(INRS)  Appendix  D: Source  Code of  the Model  213  DO 43 0 J=1,NNVR X{J) = XREV (1, INRS, J) CONTINUE  43 0 C ROCK  (-1%) AND ROLL  (+1%) THE VARIABLES TO GET THE PARTIALS  DO 44 0 J=1,NNVR SZ = XREV  ! the increment...  X  (J) = XREV (1, INRS, J) * 0.99D0 ! rock CALL RVSFF (NRVSF (INRS), J, 1, DR, BOTTLE, INRS, X, 6ZS)  X  (J) = XREV (1, INRS, J) * I.OIDO ! roll CALL RVSFF (NRVSF (INRS), J, 3, DR, BOTTLE, INRS, X, 6ZL)  +  + X  (J) = XREV  PRVSX CONTINUE CONTINUE  440 450  (1, INRS, J) * O.OIDO  (1, INRS, J)  ! reset  (INRS, J) = (GZL - GZS) / (2.0D0 * SZ)  C ESTIMATE THE CORRELATION BETWEEN TWO REVENUE STREAMS. C COVAR does something to the SECOND set of values of XREV. C check this carefully. JU = 13 PRINT *, 'about to call COVAR, many times...' DO 500 INRS = 1, NRS  + + + + +  NI = NDRV (INRS) JJ = INRS + 1 IF (JJ <= NRS) THEN DO 470 J=JJ,NRS NJ = NDRV (J) READ (JU, *) NDCV IF (NDCV == 0) THEN CORRR (INRS, J) = O.ODO CORRR (J, INRS) = O.ODO ELSE CALL COVAR (JU,NDCV, INRS,J,NI,NJ, PRVSX, XREV, RVSCO, STFO (INRS), STFO (J), CORRR) ENDIF  47 0  CONTINUE ENDIF  500 CONTINUE 1000 DEALLOCATE(XREV,  RVSCO, STFO)  Appendix  D: Source  CALL TRACE RETURN  Code of  the Model  (2, •REVSTR',  214  'exiting.')  9000 WRITE (6, *) INRS, J, '--> Bogositude to the max." WRITE (6, *) A,B,C,D,E WRITE (7, 9909) INRS, J GOTO 1000 9901 9902 9905 9906 9 9 07  FORMAT {14,14,14,FIO.5) FORMAT (5F20.4) FORMAT (214) FORMAT (12) FORMAT (314)  9908 FORMAT  (FIO.2)  9909 FORMAT  (/, 'RS(',13 , ' ) .VAR(',14, ' ) is NOT pearson  END  dist.',/)  Appendix  D: Source  Code of  the Model  C PrjCst.FOR C modified by Toshiaki Hatakama in July, 1994. C ROUTINE TO APPROXIMATE THE FIRST FOUR MOMENTS OF THE PROJECT C COST AT THE MINIMUM ATTRACTIVE RATE OF RETURN (OR IN TOTAL C DOLLARS WHEN THE MARR IS EQUAL TO Z E R O ) .  + + +  SUBROUTINE PRJCST (DR, COST, CORRC, PCOST)  IMPLICIT REAL*4(A-H,0-Z) INCLUDE 'DEBUG.CMN' REAL*4 COST (4, * ) , CORRC (NWP, * ) , PCOST (*) REAL*4 X (:,:), Z (:,:), TRI (:,:), COR (:,:), PD (:) ALLOCATABLE X, Z, TRI, COR, PD CALL TRACE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE  (2, 'PRJCST',  'starting.')  (X (4, NWP)) (Z (4, NWP)) (TRI (NWP-2, NWP- 2)) (COR (NWP-2, NWP-2)) (PD (NWP))  IF (DR /= O.ODO) THEN WRITE (7, 9901) DR ELSE WRITE (7, 9902) ENDIF WRITE (7, 9903) DO 100 I = 1, NWP IF  100  (COST (2, I) == O.ODO) THEN SDWPC = O.ODO SKWPC = O.ODO AKWPC = O.ODO ELSE SDWPC = COST (2, I) ** 0.5D0 SKWPC = COST (3, I) / (COST (2, I) ** 1.5D0) ASKP = 1.2D0* (SKWPC ** 2) + 2.0D0 AKWPC = COST (4, I) / (COST (2, I) ** 2) IF (AKWPC .LT. ASKP) AKWPC = ASKP ENDIF WRITE (7, 9904) I, COST (1, I ) , SDWPC, SKWPC, AKWPC  C first four moments of the project cost at MARR PCOST PCOST PCOST  (1) = O.ODO (2) = O.ODO (3) = O.ODO  215  Appendix  D: Source  PCOST  Code of  the Model  216  (4) = O.ODO  C all this segment is here for is to move the variables into a C slightly different place for the benefit of TANSP.... C TANSP needs to take an offset of some sort, later. DO 120 K = I X (1, X (2, X (3, X (4, IF (I DO  110  1 = 2 , (NWP - 1) -1 K) = COST (1, I) K) = COST (2, I) K) = COST (3, I) K) = COST (4, I) < (NWP - 1)) THEN 110 J = (I + 1 ) , (NWP - 1) L = J -1 TEMP = CORRC (I, J) COR (K, L) = TEMP COR (L, K) = TEMP  ENDIF CONTINUE  12 0  C transform the correlated W.P costs to uncorrelated W.P costs C hand TANSP another parameter, namely where to start work? CALL TANSP + + + IF  ({NWP - 2 ) , X, Z, COR,TRI) (0 < lERR) GO TO 500  C first partial deravatives of the transformed W.P costs, second C partial deravative is zero because the function is linear.  150  DO 150 1 = 2 , (NWP - 1) PD (I) = O.ODO DO 15 0 J = 2, (NWP - 1) PD (I) = PD (I) + TRI (J - 1, I - 1)  DO 2 00 I = 2, (NWP - 1) PCOST (1) = PCOST (1) + PD (I) * Z (1, PCOST (2) = PCOST (2) + PD (I) ** 2 * Z (2, PCOST (3) = PCOST (3) + PD (I) ** 3 * Z (3, FC = O.ODO IF (I < (NWP - 1)) THEN DO 180 J = (I + 1 ) , (NWP - 1) 180 FC = FC + 6.0D0 * + (PD (I) * PD (J)) ** 2 * Z (2, + 1) ENDIF 200 PCOST (4) = PCOST (4) + FC + PD (I) ** 4  I - 1) I - 1) I - 1)  I - 1) * Z (2, J -  * Z (4, I - 1)  C Standard deviation, skewness and kurtosis of project SDPC = PCOST SKPC = PCOST AKPC = PCOST  (2) ** 0.5D0 (3) / (PCOST (2) ** 1.5D0) (4) / (PCOST (2) *• 2)  cost  Appendix  D: Source  Code of the  Model  IF (DR == O.ODO) THEN WRITE (7, 9906) ELSE WRITE (7, 9905)DR ENDIF WRITE (7, 9907) WRITE (7, 9908) PCOST ( 1 ) , SDPC, SKPC, AKPC  +  CALL CDFUNC (PEARSN, PCOST ( 1 ) , SDPC, SKPC, AKPC, V1,V2,V3,V4,V5,V6,V7, V 8 , V9,VIO,Vll,V12,V13,V14,V15)  WRITE (20, 9910) + V1,V2,V3,V4,V5,V6,V7, V 8 , V9,VIO,Vll,V12,V13,V14,V15  500 CALL TRACE DEALLOCATE RETURN  (2, 'PRJCST', 'exiting.') (X, Z, T R I , COR, PD)  9 901 FORMAT (/,'WP Costs (Discount rate of ', F 6 . 3 , ')') 9902 FORMAT (/,'WP Costs (Total Dollars)') 9 9 03 FORMAT ('W.P.# Exp.Value===== S.Dev========= • + 'Skewness====== Kurtosis======') 9904 FORMAT (I4,6X,4F15.3)  9905 FORMAT of',F6.3,')') 9906 FORMAT 9907 FORMAT + 9908 FORMAT  (/,'The Project Cost  (discount rate of Return  (/,'The Project Cost (Total Dollars)') (' Exp.Value===== S.Dev========= ', 'Skewness====== Kurtosis======') (10X,4F15.3)  9 910 FORMAT (' Project Cost export for EXCEL' , 0 25 + /, •,F20.2, + /, ',F20,2, , 0 50 + /, ',F20.2, , 1 00 + /, ',F20.2, , 2 50 + /, ',F20.2, , 5 00 + /, ',F20.2, ,10 00 + /, ' ,F20 2, ,25 00' + /, ' ,F20 2, ,50. 00' + /, ' ,F20 2, ,75.00', + /, ' ,F20 2, ,90.00', + /, ' ,F20 2, ,95.00' , + /, ' ,F20.2, ,97.50' , + /, ',F20,2, ,99.00' , + /, ',F20.2, ,99.50' , + /. ',F20.2, ,99.75- ) END  217  Appendix  D-. Source  Code of  the Model  218  C PrjRev.FOR C modified by Toshiakl Hatakama in July, 1994. C ROUTINE TO APPROXIMATE THE FIRST FOUR MOMENTS OF THE PROJECT C REVENUE AT THE MINIMUM ATTRACTIVE RATE OF RETURN (OR IN TOTAL C DOLLARS WHEN THE MARR IS EQUAL TO Z E R O ) .  + + +  SUBROUTINE PRJREV (DR, REV, CORRR, PREV)  IMPLICIT REAL*4 (A-H,0-Z) REAL*4 REV (4, * ) , PREV (4), CORRR REAL*4 Z (:,:), TRI (:,:), PD (:) ALLOCATABLE Z, TRI, PD INCLUDE  •DEBUG.CMN'  CALL TRACE ALLOCATE ALLOCATE ALLOCATE  (NRS, *)  (2, ' P R J R E V ,  'starting.')  (Z (4, NRS)) (TRI (NRS, NRS)) (PD (NRS))  IF  (DR == O.ODO) THEN WRITE(7,9901) ELSE WRITE(7,9902)DR ENDIF WRITE(7,9903) DO 80 I = 1, NRS IF  (REV (2, I) == O.ODO) THEN SDRVS = O.ODO SKRVS = O.ODO AKRVS = O.ODO ELSE SDRVS = REV (2, I) ** 0.5D0 SKRVS = REV (3, I) / (REV (2, I) ** 1.5D0) ASKR = 1.2D0 * (SKRVS ** 2) + 2.ODO AKRVS = REV (4, I) / (REV (2, I) ** 2) IF (AKRVS < ASKR) THEN AKRVS = ASKR ENDIF ENDIF 80  WRITE  (7, 9904) I, REV (1, I ) , SDRVS, SKRVS, AKRVS  C first four moments of the project revenue at MARR  Appendix  D: Source  PREV PREV PREV PREV  (1) (2) (3) (4)  = = = =  Code of  the  Model  219  O.ODO O.ODO O.ODO O.ODO  C transform the correlated RVS to uncorrelated  RVS  CALL TANSP + + + + IF  (NRS, REV, Z, CORRR, TRI) (lERR > 0) GO TO 500  C first partial derivatives of the transformed RVS. C second partial derivatives are zero because the function is linear. DO 150 1 = 1 , NRS PD(I) = O.ODO DO 150 J = 1, NRS PD (I) = PD (I) + TRI  150  (J, I)  00 200 1 = 1 , NRS PREV (1) = PREV (1) + PD (I) * Z (1, I) PREV (2) = PREV (2) + PD (I) ** 2 * Z (2, I) PREV (3) = PREV (3) + PD (I) ** 3 * Z (3, I) FR = O.ODO IF (I < NRS) THEN DO 180 J = I + 1, NRS IF (NRS < J) THEN PRINT *, 'why are we here...?' PRINT *, PRINT *, ENDIF FR = FR + 6.0D0 * (PD (I) * PD(J)) ** 2 * * Z (2, I) • Z (2, J) 180 CONTINUE ENDIF 200 PREV (4) = PREV (4) + FR + PD (I) ** 4 * Z (4, I) C standard deviation, skewness and kurtosis of project SDPR = PREV SKPR = PREV AKPR = PREV  revenue  (2) ** 0.5D0 (3) / (PREV (2) ** 1.5D0) (4) / (PREV (2) ** 2)  IF  (DR == O.ODO) THEN WRITE (7, 9905) ELSE WRITE (7, 9906)DR ENDIF WRITE (7, 9907) WRITE (7, 9908) PREV(l), SDPR, SKPR, AKPR  +  CALL CDFUNC (PEARSN, PREV (1), SDPR, SKPR, AKPR, V1,V2,V3,V4,V5,V6,V7, V8, V9,VIO,Vll,V12,V13,V14,V15)  Appendix  D-. Source  Code of  the  Model  WRITE (20, 9910) + V1,V2,V3,V4,V5,V6,V7, V 8 , V9,VIO,Vll,V12,V13,V14,V15 500  DEALLOCATE CALL TRACE RETURN  (Z, TRI, PD) (2, ' P R J R E V ,  'exiting.')  9901 FORMAT 9902 FORMAT  (/,'Net Revenue Streams in Total $s') {/,'Net Revenue Streams (Discount Rate',F6.3,')')  9903 FORMAT + 9904 FORMAT  ('RevStr#  9905 FORMAT 9906 FORMAT 9907 FORMAT + 9908 FORMAT  (/,'The Project Revenue in Total Dollars') (/,'The Project Revenue (Discount Rate',F6.3,')') (' Exp.Value===== s.Dev========= ', 'Skewness====== Kurtosis======') (10X,4F15.3)  9910 FORMAT  (• Project Revenue export for EXCEL'  + + + + + + + + + + + + + + +  END  Exp.Value===== S.Dev==== 'Skewness====== Kurtosis: (14,6X,4F15.3)  /, • /, /, /, /, /, /, /, /, /, /, /, /, /, /,  ',F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20.2, ',F20 . 2 , ',F20.2, ',F20.2, ',F20.2,  , 0.25', , 0.50', , 1.00' , , 2.50', , 5.00', ,10.00' , ,25.00', ,50.00', ,75.00' , ,90.00' , ,95.00' , ,97.50' , ,99.00' , ,99.50' , ,99.75 ')  220  Appendix  D: Source  Code of  the Model  221  C PrjNPV.FOR C modified by Toshiaki Hatakama In July, 1994 C ROUTINE TO APPROXIMATE THE FIRST FOUR MOMENTS OF THE PROJECT C NET PRESENT VALUE A T THE MINIMUM ATTRACTIVE RATE OF RETURN C (OR IN TOTAL DOLLARS WHEN THE MARR IS EQUAL TO Z E R O ) .  + +  SUBROUTINE PRJNPV (DR, PCOST, PREV)  IMPLICIT  REAL*4(A-H,0-Z)  REAL*4 P C 0 S T ( 4 ) , P R E V ( 4 ) , NPV (4) C the first four moments of project net present value CALL TRACE NPV NPV NPV NPV C standard  (2, ' P R J N P V ,  'Starting.')  (1) = PREV (1) - PCOST (1) (2) = PREV (2) + PCOST (2) (3) = PREV (3) - PCOST (3) (4) = PREV (4) + PCOST (4) + 6.0D0 * PREV (2) * PCOST (2) deviation, skewness and kurtosis of project NPV  SDNPV = NPV (2) **0.5D0 SKNPV = NPV (3) / (NPV (2) ** 1.5D0) AKNPV = NPV (4) / (NPV (2) ** 2) WRITE WRITE WRITE  +  (7, 9901) DR (7, 9902) (7, 9903) NPV ( 1 ) , SDNPV, SKNPV, AKNPV  CALL CDFUNC (PEARSN, NPV (1), SDNPV, SKNPV, AKNPV, VI,V2,V3,V4,V5,V6,V7, V 8 , V9,VIO,Vll,V12,V13,V14,V15)  WRITE (20, 9910) + V1,V2,V3,V4,V5,V6,V7, V 8 , V9,VIO,Vll,V12,V13,V14,V15 CALL TRACE RETURN  (2, ' P R J N P V ,  'exiting.')  9901 FORMAT 9902 FORMAT + 9903 FORMAT  (/,'The Project NPV at a Discount Rate of',F6.3) (' Exp.Value===== S.Dev========= ', 'Skewness====== Kurtosis======') (10X,4F15.3)  9910 FORMAT  (' Project Net Present Value export for EXCEL',  + + + + +  /,' / , • / , • / , •  /,'  •,F20 .2, ',F20.2, ',F20.2, •,F20 .2, ',F20.2,  ', ', ', ', ',  0.25' , 0.50', 1.00' , 2.50", 5.00',  Appendix  D:  Source /.' /.' /,' /.' /.'  + + + + + + + + + +  /. ' /,• /,' /,' / , •  END  Code  of the Mo  ,F20.2, ,F20.2, ,F20.2, ,F20.2, ,F20.2, ,F20.2, ,F20 . 2 , ,F20.2, ,F20.2, ,F20.2,  ,10.00 ,25.00 ,50.00 ,75.00 ,90.00 ,95.00 , 97.50 ,99.00 ,99.50 , 99.75  222  Appendix C C C C  D: Source  Code of  the Model  PrjIrr.FOR modified by Toshiaki Hatakama in July, 1994. in order to calculate IRR, it is necessary to improve subroutine, because, it takes too long.  223  this  C ROUTINE TO APPROXIMATE THE CUMULATIVE DISTRIBUTION FUNCTION C AND THE FIRST FOUR MOMENTS OF PROJECT INTERNAL RATE OF RETURN.  SUBROUTINE PRJIRR + + + + + + +  (PEARSN, FRA, IWPC, NWPCF, NDVR, CORRC, TRIWPC, XUCOST, COST, NRVSF, NDRV, CORRR, TRIRVS, XUREV, REV, BOTTLE)  C if you have 16M RAM, chhose "enough" = 1. C if not, choose any number but 1.  $DEFINE enough = 0 IMPLICIT REAL*4(A-H,0-Z) INCLUDE 'DEBUG.CMN' PARAMETER  (JSZ=50,ISZ=10)  REAL*4 PEARSN (NPEARS, *) INTEGER IWPC (*), NWPCF (*), NDVR (*), NRVSF (*), NDRV (*) REAL*4 CORRC (NWP, * ) , TRIWPC (NWP, NWP, *) REAL*4 XUCOST (4, NWP, * ) , COST (4, * ) , CORRR (NRS, *) $IF enough .EQ. 1 REAL*4 TRIRVS (NRS, MAXDVR, *) $ELSE REAL*4 TRIRVS {*) $ENDIF REAL*4 REAL*4 REAL*4 REAL*4  XUREV (4, NRS, * ) , REV (4, *) BOTTLE (NRS, •) STFO X (:,:), Z (:,:), COR (:,:), TRI (:,:)  ALLOCATABLE X, Z, COR, TRI C correlation arrays, etc REAL*4 REAL*4 REAL*4  PDC(JSZ) PDR(300) PIRR(300)  n  n  n tier  n  fD  (D  d  •0  w  •d *o *o  lO  II  SO  II  II  o o o  II  o  o o o o O O O O o o o o  SO  Sd  *0 SO  'O SO  *0 SO  «: x s < a H bo to lO II  II  II  to to lo II  II  o o o o o  II  o  o o o o o o a D O O O O o o o o o o  to II  to to II  II  a  to II  II  o o o o o  II  o  o o o o o o a t3 a H O U o o o o o o  H  h^  i^  O (0  II  II  II  II  o o o o o o o o o o d o o a o o o o o o  II  •o •O "O so so so K:  II  II II  so so  < a n t-'  50 K  m  o a  a o D so so o a a fo Q v so $0 so g M H  V  so so so so  II  II  M  II  o o o o o  o o • o o o o o o d d d d a o d o o o o o o o o  so so so so  < a  II  M  o o d o  II  II  II  II  II  II  o o o o o o *  II  II  II  II  o o o o o  II  ID  H S  01  O  II  (D  II  o  o  o o o o o o o d d d d d d o o o o o o d o o o o o o d d d d d d o o o o o o o  S 0 n ft  "O (D  o d o  >  n >  O  n n H H N  H SO  n  0  pi  o c  o  >i  fD  —, —^ 1^ it^  to  01  n m o  CO  10  so H  so so  H  o o a CD  o H, rt tr (t  PI  1^ rt p> (D  o  rt H-  ID  IQ  o a (D  rt Ml  o  t<  PI  Q.  to to  Appendix  D: Source  Code of  the Model  2 25  DRF2 = 0 . ODO DRG2 = 0 .ODO 1 DRM2 := 3.ODO DRT2 = 0 .ODO DRU2 = O.ODO DRV2 = O.ODO DRW2 = O.ODO DRX2 = O.ODO DRy2 = O.ODO C the cycle to obtain the cumulative distribution function for C project internal rate of return at various Discount Rates C between 1% and 300%  10  DR = FLOAT (I) / 100.ODO IF (300 < I) GO TO 1200 ! give u p .  C call WPCMMT a number of times to generate the first four moments C of the work package costs NN = NWP - 1 DO 30 J = 2, NN IF (1 < IWPC (J)) THEN COST (1, J) = O.ODO COST (2, J) = O.ODO COST (3, J) = O.ODO COST (4, J) = O.ODO ELSE CALL WPCMMT (J, DR, FRA, + NWPCF, NDVR, + XUCOST, TRIWPC, + COST, STFO) ENDIF 30 CONTINUE C first four moments of the project APRC SPRC TPRC FPRC  = = = =  O.ODO O.ODO O.ODO O.ODO  NNVR = NWP-2 NN = NWP-1 ALLOCATE  (COR (NNVR,  DO 50 M = 2, K = M -1 X (1, K) = X (2, K) = X (3, K) = X (4, K) = JJ = M + 1  NNVR))  NN COST COST COST COST  (1, (2, (3, (4,  M) M) M) M)  cost  Appendix  D: Source  Code of  the Model  22 6  IF  (JJ <= NN) THEN DO 40 J = JJ, NN L = J -1 TEMP = CORRC (M, J) COR (K, L) = TEMP COR (L, K) = TEMP CONTINUE ENDIF CONTINUE  C 40 50  C transform the correlated W.P costs to uncorrelated W.P costs ALLOCATE  (TRI (NNVR,  NNVR))  CALL TANSP (NNVR, X, Z, COR, TRI) IF (0 < lERR) GO TO 1200 DEALLOCATE (COR) C first partial deravatlves of the transformed W.P costs. DO 80 M = 2, NN PDC (M) = O.ODO DO 80 J = 2, NN PDC (M) = PDC (M) + TRI (J - 1, M - 1)  80  DEALLOCATE (TRI) DO 110 M = 2, NN APRC = APRC + PDC (M) * Z (1, M - 1) SPRC = SPRC + PDC (M) ** 2 * Z (2, M - 1) TPRC = TPRC + PDC (M) ** 3 * Z (3, M - 1) FC = O.ODO  100 +  110  C C C C  JJ = M + 1 IF (NN >= JJ) THEN DO 100 J=JJ, NN FC = FC + 6.0D0 * (PDC (M) * PDC (J)) ** 2 * Z (2, M - 1) * Z (2, J - 1) ENDIF FPRC = FPRC + FC + PDC{M) ** 4 * Z (4, M - 1) CONTINUE  first four moments of the net revenue this is where the major time is being do we have to shake all the leaves? can we shake the whole tree at once? DO 140 J = 1, NRS STFO = O.ODO 14 0 CALL RVSMMT (J, DR, BOTTLE, + NRVSF, NDRV, + XUREV, TRIRVS, + REV, STFO)  streams spent..  Appendix  D: Source  Code of  the Model  C first four moments of the project revenue APRR SPRR TPRR FPRR  = = = =  O.ODO O.ODO O.ODO O.ODO  C transform the correlated RVS to uncorrelated RVS. ALLOCATE  (TRI (NRS, NRS))  CALL TANSP + + + +  (NRS, REV, Z, CORRR, TRI) IF (0 < lERR) GO TO 1200  DO 150 M = 1, NRS PDR (M) = O.ODO DO 150 J = 1, NRS PDR (M) = PDR (M) + TRI {J, M)  150  DEALLOCATE (TRI) DO 200 M = 1, NRS APRR SPRR TPRR FR  180 +  200  = = = =  APRR + PDR (M) * Z (1, M) SPRR + PDR (M) ** 2 * Z (2, M) TPRR + PDR (M) ** 3 * Z (3, M) O.ODO  JJ = M + 1 IF (JJ <= NRS) THEN DO 180 J=JJ,NRS PR = FR + 6.0DO * (PDR (M) * PDR (J)) ** 2 * Z (2, M) * Z (2, J) ENDIF  FPRR = FPRR + FR + PDR (M) •* 4 * Z (4, M)  C first four moments of project net present value ANPV SNPV TNPV FNPV  = = = =  APRR SPRR TPRR FPRR  + +  APRC SPRC TPRC FPRC + 6 . ODO * SPRR * SPRC  C Standard deviation, skewness and kurtosis of project NPV SDNPV = SNPV ** 0.5D0 SKNPV = TNPV / (SNPV ** 1.5D0)  227  Appendix  D: Source  AKNPV  Code of  the Model  228  = FNPV / (SNPV ** 2)  C values of the cumulative distribution function approximated C for the net present value of the project  CALL CDFUNC + + + +  (PEARSN, ANPV,SDNPV,SKNPV,AKNPV, VA, VB, VC, VD , VE , VF, VG, VM, VT,VU,VV,VW,VX,VY,VZ)  C probability of NPV = 0 at this discount rate  IF  (I = = 1) THEN VAl = VA ENDIF IF (0. ODO < = VAl)GO TO 205 IF (0 < KM) GO TO 205 KM = 1 205  IF { IF IF IF IF IF IF  (VA < (VB < (VC < (VD < (VE < (VF <  IF IF  (VG < O.ODO (VM < O.ODO  IF (VT < IF (VU < IF (VV < IF (VW < IF (VX < IF (VY < IF 210  O.ODO O.ODO O.ODO O.ODO O.ODO O.ODO  O.ODO O.ODO O.ODO O.ODO O.ODO O.ODO  (VZ < O.ODO)  .AND. .AND. .AND. .AND. .AND. .AND.  O.ODO <  VA) GO TO 490  O.ODO O.ODO O.ODO O.ODO O.ODO O.ODO  VB) VC) VD) VE) VF) VG)  <= <= <= <= <= <=  GO GO GO GO GO GO  TO TO TO TO TO TO  210 230 250 270 290 310  .AND. O.ODO <= VM) GO TO 330 .AND. O.ODO <= VT) GO TO 350 .AND. .AND. .AND. .AND. .AND. .AND.  O.ODO O.ODO O.ODO O.ODO O.ODO O.ODO  <= <= <= <= <= <=  VU) VV) VW) VX) VY) VZ)  GO GO GO GO GO GO  TO TO TO TO TO TO  370 390 410 430 450 470  GO TO 500  KM = I PIRR (I) = 0.0025D0 + ((0.ODO-VA)* 0.0025D0/(VB-VA) ) PRBl = PIRR(I) DRBl = FLOAT(I) / 100.ODO GO TO 490  230  PIRR(I) = 0.0050D0 + ((0.ODO-VB)*0.0050DO/(VC-VB)) IF (PRB2.GT.O.ODO) GO TO 240 PRB2 = PIRR(I) DRB2 = FLOAT(I) / 100.ODO  Appendix  D: Source  Code of  the Model  240  PRCl = PIRR(I) DRCl = FLOAT(I) / 100.ODO IF (PRB2.LE.PIRR(I)) GO TO 490 PRB2 = PIRR(I) DRB2 = FLOAT(I) / 100.ODO GO TO 4 90  250  PIRR(I) = O.OIOODO + ((0.ODO-VC)*0.015ODO/(VD-VC)) IF (PRC2.GT.O.ODO) GO TO 260 PRC2 = PIRR(I) DRC2 = FLOAT(I) / 100.ODO PRDl = PIRR(I) DRDl = F L O A T d ) / 100.ODO IF {PRC2 . L E . P I R R d ) ) GO TO 490 PRC2 = PIRR(I) DRC2 = FLOAT(I) / 100.ODO GO TO 490  260  270  280  290  300  310  320  330  340  PIRR(I) = 0.0250D0 + ({0.ODO-VD)*0.0250D0/(VE-VD)) IF (PRD2.GT.O.ODO) GO TO 280 PRD2 = PIRR(I) DRD2 = F L O A T d ) / 100.ODO PREl = P I R R d ) DREl = F L O A T d ) / 100.ODO IF (PRD2 . L E . P I R R d ) ) GO TO 490 PRD2 = PIRR(I) DRD2 = F L O A T d ) / 100.ODO GO TO 4 90 PIRR(I) = 0.0500D0 + {(0.ODO-VE)*0.0500D0/(VF-VE)) IF {PRE2.GT.O.ODO) GO TO 300 PRE2 = PIRR(I) DRE2 = F L O A T d ) / 100.ODO PRFl = P I R R d ) DRFl = F L O A T d ) / 100.ODO IF {PRE2 . L E . P I R R d ) ) GO TO 490 PRE2 = PIRR(I) DRE2 = F L O A T d ) / 100.ODO GO TO 4 90 P I R R d ) = O.IOOODO + ({ 0 . ODO-VF) *0 .150 ODO/(VG-VF) ) IF (PRF2.GT.O.ODO) GO TO 320 PRF2 = P I R R d ) DRF2 = F L O A T d ) / 100.ODO PRGl = P I R R d ) DRGl = F L O A T d ) / 100.ODO IF (PRF2 . L E . P I R R d ) ) GO TO 490 PRF2 = PIRR(I) DRF2 = F L O A T d ) / 100,ODO GO TO 4 90 PIRR(I) = 0.2500D0 + ((0,ODO-VG)*0.2500D0/(VM-VG)) IF {PRG2.GT.O.ODO) GO TO 340 PRG2 = PIRR(I) DRG2 = F L O A T d ) / 100.ODO PRMl = PIRR(I) DRMl = F L O A T d ) / 100.ODO  22 9  Appendix  D: Source  Code of  the Model  IF (PRG2.LE.PIRR(I)) GO TO 490 PR62 = PIRR(I) DRG2 = FLOAT(I) / 100.ODO GO TO 490 350  360  370  380  390  400  410  420  430  440  P I R R d ) = 0.5000D0 + ( ( 0 . ODO - VM) *0 . 2 5 OODO/(VT-VM) ) IF {PRM2.GT.O.ODO) GO TO 360 PRM2 = PIRR(I) DRM2 = FLOAT(I) / 100.ODO PRTl = PIRR(I) DRTl = FLOAT(I) / 100.ODO IF (PRM2.LE.PIRR(I)) GO TO 490 PRM2 = PIRR(I) DRM2 = FLOAT(I) / 100,ODO GO TO 490 P I R R d ) = 0.7500D0 + ({0 . ODO-VT) * 0 .1500D0/(VU-VT) ) IF (PRT2.GT.O.ODO) GO TO 380 PRT2 = PIRR(I) DRT2 = FLOAT(I) / 100.ODO PRUl = PIRR(I) DRUl = FLOAT(I) / 100.ODO IF (PRT2.LE.PIRR(I)) GO TO 490 PRT2 = P I R R d ) DRT2 = FLOAT(I) / 100.ODO GO TO 4 90 PIRR(I) = 0.9000D0 + ((0.ODO-VU)*0.05OODO/{VV-VU)) IF (PRU2.GT.O.ODO) GO TO 400 PRU2 = P I R R d ) DRU2 = F L O A T d ) / 100.ODO PRVl = P I R R d ) DRVl = F L O A T d ) / 100. ODO IF (PRU2.LE.PIRR(I)) GO TO 490 PRU2 = PIRR(I) DRU2 = F L O A T d ) / 100.ODO GO TO 4 90 P I R R d ) = 0.9500D0 + ((0 . ODO-VV) *0 . 025 ODO/(VW-VV) ) IF (PRV2.GT.O.ODO) GO TO 420 PRV2 = PIRR(I) DRV2 = FLOAT(I) / 100.ODO PRWl = PIRR(I) DRWl = F L O A T d ) / 100. ODO IF (PRV2.LE.PIRR(I)) GO TO 490 PRV2 = PIRR(I) DRV2 = FLOAT(I) / 100.ODO GO TO 4 90 P I R R d ) = 0.9750D0 + ((0 . ODO-VW) *0 . 0150D0/(VX-VW) ) IF (PRW2.GT.O.ODO) GO TO 440 PRW2 = P I R R d ) DRW2 = FLOAT(I) / 100.ODO PRXl = PIRR(I) DRXl = FLOAT(I) / 100.ODO IF (PRW2.LE.PIRR(I)) GO TO 490 PRW2 = P I R R d )  23 0  Appendix  D: Source  Code of  the Model  231  DRW2 = FLOAT(I) / 100.ODO GO TO 4 90 450  460  470  480  490  PIRR(I) = 0.9900D0 + ((0.ODO-VX)* 0.0050D0/(VY-VX) ) IP (PRX2.GT.O.ODO) GO TO 460 PRX2 = PIRR(I) DRX2 = FLOAT(I) / 100.ODO PRYl = PIRR(I) DRYl = FLOAT(I) / 100.ODO IF (PRX2.LE.PIRR(I)) 60 TO 490 PRX2 = P I R R d ) DRX2 = FLOAT(I) / 100.ODO GO TO 4 90 P I R R d ) = 0.9950D0 + ( (0 . ODO-VY) *0 . 0025D0/(VZ-VY) ) IF {PRY2.GT.O.ODO) GO TO 480 PRy2 = PIRR(I) DRY2 = FLOAT(I) / 100.ODO IF (PRY2.LE.PIRR(I)) GO TO 490 PRy2 = P I R R d ) DRY2 = F L O A T d ) / 100.ODO  I = I+l GO TO 10  C we're done, and we have the desired value of IRR, 5 00  CONTINUE PRINT*,'after line 500'  C C C C C  the fractile estimates (0.01, 0.025, 0.05, 0.10, 0.25, 0.5, 0.75, 0.90, 0.95, 0.975 & 0.99) to approximate the expected value and standard deviation of the internal rate of return using the approximations given by E.S.PEARSON AND J.W.TUKEY and to plot the cumulative distribution function.  C the 0.005 fractile estimate for internal rate of return  505 510  IF (PRBl.EQ.O.0D0.AND.PRB2.EQ.O.ODO) GO TO 510 IF (DRBl.GT.O.ODO) GO TO 505 DIRB = DRB2 GO TO 515 DIRB = DRBl + {{0.005D0-PRBl) * {DRB2-DRB1) / {PRB2-PRB1)) GO TO 515 DIRB = O.ODO  C the 0.01 fractile estimate for internal rate of return 515  520  IF (PRCl.EQ.O.0D0.AND.PRC2.EQ.O.ODO) GO TO 525 IF (DRCl.GT.O.ODO) GO TO 520 DIRC = DRC2 GO TO 530 DIRC = DRCl + { (0 . OlDO-PRCl) * (DRC2-DRC1) / (PRC2-PRC1))  Appendix 525  D: Source  Code of the Model  232  GO TO 53 0 DIRC = O.ODO  C the 0.025 fractile estimate for internal rate of return 530  540 550  IF (PRDl.EQ.O.ODO.AND.PRD2.EQ.O.ODO) GO TO 550 IF (DRDl.GT.O.ODO) GO TO 540 DIRD = DRD2 GO TO 5 60 DIRD = DRDl + ( {0 . 025D0-PRDl) * (DRD2-DRD1) / GO TO 5 60 DIRD = O.ODO  C the 0.05 560  570 580  600 610  630 640  660 670  fractile estimate for internal rate of return  IF (PRMl.EQ.O.ODO.AND.PRM2.EQ.O.ODO) GO TO 670 IF (DRMl.GT.O.ODO) GO TO 660 DIRM = DRM2 GO TO 68 0 DIRM = DRMl + ((0.50D0-PRMl) * (DRM2-DRM1) / (PRM2-PRM1)) GO TO 680 DIRM = O.ODO  C the 0.75 680  fractile estimate for internal rate of return  IF (PRGl.EQ.O.ODO.AND.PRG2.EQ.O.ODO) GO TO 640 IF (DRGl.GT.O.ODO) GO TO 630 DIRG = DRG2 GO TO 650 DIRG = DRGl + {(0.25D0-PRGl) * (DRG2-DRG1) / (PRG2-PRG1)) GO TO 650 DIRG = O.ODO  C the 0.50 650  fractile estimate for internal rate of return  IF (PRFl.EQ.O.ODO.AND.PRF2.EQ.O.ODO) GO TO 610 IF (DRFl.GT.O.ODO) GO TO 600 DIRF = DRF2 GO TO 62 0 DIRF = DRFl + ({0.lODO-PRFl) * (DRF2-DRF1) / (PRF2-PRF1)) GO TO 62 0 DIRF = O.ODO  C the 0.25 620  fractile estimate for internal rate of return  IF (FREl.EQ.O.ODO.AND.PRE2.EQ.O.ODO) 60 TO 580 IF (DREl.GT.O.ODO) GO TO 570 DIRE = DRE2 GO TO 5 90 DIRE = DREl + { (0 .05D0-PREl) * (DRE2-DRE1) / (PRE2-PRE1)) GO TO 5 90 DIRE = O.ODO  C the 0.10 590  (PRD2-PRD1))  IF IF  fractile estimate for internal rate of return (PRTl.EQ.O.ODO.AND.PRT2.EQ.O.ODO) (DRTl.GT.O.ODO) GO TO 690  GO TO 700  Appendix  690 700  D: Source  720 730  the Model  233  DIRT = DRT2 GO TO 710 DIRT = DRTl + ((0.7 EDO -PRTl) * {DRT2-DRT1) / (PRT2-PRT1)) GO TO 710 DIRT = O.ODO  C the 0.90 710  Code of  fractile estimate for internal rate of return  IF (PRUl.EQ.O.0D0.AND.PRU2,EQ.O.ODO) GO TO 730 IF (DRUl.GT.0.ODO) GO TO 720 DIRU = DRU2 GO TO 740 DIRU = DRUl + {{0,90D0-PRUl) * {DRU2-DRU1) / (PRU2-PRU1)) GO TO 740 DIRU = O.ODO  C the 0.95 fractile estimate for internal rate of return 740  750 760  IF (PRVl.EQ.O.0D0.AND.PRV2.EQ.O.ODO) GO TO 760 IF (DRVl.GT.O.ODO) GO TO 750 DIRV = DRV2 GO TO 770 DIRV = DRVl + {(0.95D0-PRVl) * {DRV2-DRV1) / (PRV2-PRV1)) GO TO 77 0 DIRV = O.ODO  C the 0.975 fractile estimate for internal rate of return 770  780 790  IF (PRWl.EQ.O.ODO.AND.PRW2.EQ.O.ODO) GO TO 790 IF (DRWl.GT.O.ODO) GO TO 780 DIRW = DRW2 GO TO 800 DIRW = DRWl + ((0.975D0-PRWl) * (DRW2-DRW1) / (PRW2-PRW1)) GO TO 80 0 DIRW = O.ODO  C the 0.99 fractile estimate for internal rate of return 800  805 810 815  820 825  IF (PRXl.EQ.O.ODO.AND.PRX2.EQ.O.ODO) GO TO 810 IF (DRXl.GT.O,0D0) GO TO 805 DIRX = DRX2 GO TO 815 DIRX = DRXl + ((0,99D0-PRXl) * (DRX2-DRX1) / (PRX2-PRX1)) GO TO 815 DIRX = O.ODO IF (PRYl.EQ.O.ODO.AND.PRY2.EQ.O.ODO) GO TO 825 IF (DRYl.GT.O.ODO) GO TO 820 DIRY = DRY2 GO TO 830 DIRY = DRYl + ((0.995D0-PRYl) * (DRY2-DRY1) / (PRY2-PRY1)) GO TO 83 0 DIRY = O.ODO  PRINT*,'cheking point A'  Appendix  D-. Source  Code of  C check the fractile 830  IF  the  Model  23A  estimates  ( D I R B . L T . D I R C . A N D . D I R C . L T , D I R D ) GO  TO  835  IF (DIRB.GT.DIRD) GO TO 835 DIRC = DIRE + {(0.01D0-0.005D0)*(DIRD-DIRB)/(0.025D0O.OOSDO)) 835  ( D I R C . L T . D I R D , A N D . D I R D . L T . D I R E ) GO TO 840 IF (DIRC.GT.DIRE) GO TO 840 DIRD = DIRC + ( (0.025D0-0.01D0)*(DIRE-DIRC)/(0,05D0-0,01D0) )  840  IF (DIRD.LT.DIRE.AND.DIRE,LT.DIRF) GO TO 845 IF (DIRD,GT,DIRF) GO TO 845 DIRE = DIRD + ( (0,05D0-0,025D0)*(DIRF-DIRD)/(0,1D0-0,025D0))  845  IF (DIRE,LT,DIRF,AND.DIRF.LT.DIRG) GO TO 850 IF (DIRE.GT.DIRG) GO TO 850 DIRF = DIRE + ((O.lDO-0.05D0)*(DIR6-DIRE)/(0.25D0-0.05D0))  850  IF (DIRF.LT.DIRG.AND.DIRG.LT.DIRM) GO TO 855 IF (DIRF.GT.DIRM) GO TO 855 DIRG = DIRF + ( (0.25D0-0.1D0)*(DIRM-DIRF)/(0.5D0-0.1D0) )  855  IF  IF  ( D I R G . L T . D I R M . A N D . D I R M . L T . D I R T ) GO  TO  860  IF (DIRG.GT.DIRT) GO TO 860 DIRM = DIRG + ((0.5D0-0.25D0)*(DIRT-DIRG)/(0.75D0-0.25D0)) 860  IF (DIRM.LT.DIRT.AND.DIRT.LT.DIRU) GO TO 865 IF (DIRM.GT.DIRU) GO TO 865 DIRT = DIRM + ((0.75D0-0.5D0)*(DIRU-DIRM)/(0.9D0-0.5D0))  865  IF  ( D I R T . L T . D I R U . A N D . D I R U . L T . D I R V ) 60 TO 870 IF (DIRT.GT.DIRV) GO TO 870 DIRU = DIRT + ((0.9D0-0.75D0)•(DIRV-DIRT)/(0.95D0-0.75D0))  870  IF (DIRU,LT.DIRV,AND.DIRV.LT.DIRW) GO TO 875 IF (DIRU.GT.DIRW) GO TO 875 DIRV = DIRU + ((0.95D0-0.9D0)*(DIRW-DIRU)/(0.975D0-0.9D0))  875  IF (DIRV.LT.DIRW.AND.DIRW.LT.DIRX) GO TO 880 IF (DIRV.GT.DIRX) GO TO 880 DIRW = DIRV + ((0.975D0-0.95D0)*(DIRX-DIRV)/(0.99D0-0.95D0))  880  IF (DIRW.LT.DIRX.AND.DIRX.LT.DIRY) GO TO 900 IF (DIRW.GT.DIRY) GO TO 900 DIRX = DIRW + ((0.99D0-0.975D0)*(DIRY-DIRW)/(0.995D00.975D0)) C the expected value of internal rate of return 900  DELT = DIRV + DIRE - (2.0D0 * DIRM) AIRT = DIRM + (0.185D0 * DELT) AIRR = AIRT * 100.ODO PRINT*,'just  after line 900"  Appendix  D: Source  Code of  the Model  23 5  C the standard deviation of internal rate of return IF (DIRV <= DIRE) GO TO 950 SIGl = (DIRV - DIRE) / 3.25D0 SIRl = 3.29D0 - (O.IOODO * (DELT/SIGl)**2) IF (SIRl <= 3.08D0) GO TO 910 SIGMl = (DIRV - DIRE) / SIRl GO TO 920 910  SIGMl = (DIRV - DIRE) / 3.08D0  920  SIRR = SIGMl * 100.ODO GO TO 9 60  950  SIRR = O.ODO  960 970  WRITE (7,970) FORMAT (/,'The Internal Rate of Return for the Project (%)•) WRITE (7,980) FORMAT (' Exp.Value===== S.Dev=========') WRITE (7,990) AIRR,SIRR FORMAT (10X,2F15.3)  980 990  DIRD DIRE DIRF DIRG DIRM DIRT DIRU DIRV DIRW  = = = = = = = = =  DIRD DIRE DIRF DIRG DIRM DIRT DIRU DIRV DIRW  * * • * * * * * *  100..ODO 100,.ODO 100..ODO 100..ODO 100..ODO 100.,0D0 100..ODO 100,.ODO 100..ODO  WRITE (7, 1100) 1100 FORMAT (/,'Probable IRRs•) WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE WRITE 1101 FORMAT WRITE +  +  (7, 1101) (7, 1101) (7, 1101) (7, 1101) (7, 1101) (7, 1101) (7, 1101) (7, 1101) (7, 1101) (A4,'% =  • 2.5', DIRD DIRE DIRF DIRG DIRM DIRT DIRU DIRV DIRW ', F15.2)  • 5 .0' / '10,.0'1 / •25 .0'1 / '50,.0' / ' 75,.0't / ' 90..0- f ' 95..0' / ' 97..5' 1  (20, 9910) DIRD,DIRE,DIRF,DIRG,DIRM,DIRT,DIRU,DIRV,DIRW  PRINT*,'DIRD,DIRE,DIRF,DIRG,DIRM,DIRT,DIRU,DIRV,DIRW" DIRD,DIRE,DIRF,DIRG,DIRM,DIRT,DIRU,DIRV,DIRW  9910 FORMAT + +  (' Project IRR export for EXCEL', /,• ',F20.2,', 2.50', /,' •,F20.2,•, 5.00',  Appendix + + + + + + +  D: Source /,' /.• /,' /,'  1 .' /.' /.'  Code of  the  Model  ,F20.2, ,P20.2, ,F20.2, ,F20.2, ,F20.2, ,F20.2, ,F20.2,  ,10.00', ,25.00', ,50.00', ,75.00', ,90.00' , ,95.00' , ,97.50')  1200 DEALLOCATE (x, Z) CALL TRACE (2, 'PRJIRR', 'exiting.') RETURN END  236  Appendix  D: Source  Code of  the Model  23 7  C Varble.FOR C modified by Toshiaki Hatakama in July, 1994. C ROUTINE TO APPROXIMATE A VARIABLE TO A PEARSON TYPE C DISTRIBUTION USING FIVE PERCENTILE ESTIMATES. C PEARSN is the pearson table C EST 1 thru 5 are the 5%ile estimates C CALC 1 thru 4 are the result calculus entries C this requires 2.5, 5.0, 50.0, 95.0, and 97.5 percentiles.  €========================================================== SUBROUTINE VARBLE (PEARSN, + EST05, EST25, EST50, EST75, EST95, + CALCl, CALC2, CALC3, CALC4)  IMPLICIT REAL*4{A-H,0-Z) INCLUDE •DEBUG.CMN' REAL*4 PEARSN (NPEARS, *) REAL*4 SIGM1(600), SIGM2(600) DEL = EST75 + EST25 - 2 . ODO * EST50 CALCl = EST50 + 0.185D0 * DEL SIGl = (EST75 - EST25) / 3.25D0 SIG2 = {EST95 - EST05) / 3.92D0 IF (SIGl .EQ. O.ODO .AND. SIG2 .EQ. O.ODO)  THEN  CALCl = EST50 CALC2 = O.ODO CALC3 = O.ODO CALC4 = O.ODO GOTO 9 999 ENDIF SIGMl(l) = O.ODO SIGM2(1) = O.ODO K =2 SIGMl(K) = SIGl 50  IF (590 < K) GO TO 700 XSIGMl = SIGMl(K) - SIGMl(K-l) XCHEKl = SIGMl(K-l) * O.OOOIDO IF (DABS (XSIGMl) < DABS (XCHEKl)) GO TO 70 K = K +1  SI = 3.29D0 - O.IOODO  * (DEL/SIGMl(K-1))**2  Appendix  D: Source  Code of  the Model  IF  (3.08D0 < SI) THEN SIGMl(K) = (EST75 - EST25) / SI ELSE SIGMl(K) = (EST75 - EST25) / 3.08D0 END IF  70  GOTO 5 0 CONTINUE  C C approximated C  standard deviation from 5% and 95% estimates  ASIGMl = S I G M K K ) K =2 SIGM2(K) = SIG2 80  IF (590 < K) GO TO 700 XSIGM2 = SIGM2(K) - SIGM2(K-1) XCHEK2 = SIGM2(K-1) * O.OOOIDO IF (DABS (XSI6M2) < DABS (XCHEK2)) GO TO 100 K = K +1 S2 = 3.98D0 - 0.138D0 • (DEL/SIGM2(K-1))**2 IF (3.66D0 < S2) THEN SIGM2(K) = {EST95 - EST05) / S2 ELSE SIGM2(K) = (EST95 - EST05) / 3.66D0 END IF GOTO 8 0  100  CONTINUE ASIGM2 = SIGM2(K) IF (ASIGMl < ASIGM2) GO TO 110 SIGMAD = ASIGMl GO TO 120  110  SIGMAD = ASIGM2  120  CALC2 = SIGMAD ** 2 XA XB XC XD XE  = = = = =  (EST05 (EST25 (EST50 (EST75 (EST95  -  CALCl) CALCl) CALCl) CALCl) CALCl)  / / / / /  SIGMAD SIGMAD SIGMAD SIGMAD SIGMAD  C Select best fit distribution C compare standardised values to those of the pearson table C to obtain the skewness and the kurtosis from an approximated C pearson type distribution XX = 10.0  23 8  Appendix  D:  C  Source  Code  of  the  Model  239  NP = 0 DO 1 5 0 K = 1 , 2 6 5 5 SUMSQ = + + + +  (PEARSN (K, 4) - XA ) (PEARSN (K, 5) - XB ) (PEARSN (K, 8) - XC ) (PEARSN (K,ll) - XD ) (PEARSN (K,12) - XE )  ** ** ** ** **  2 2 2 2 2  + + + +  C if the square root of the sum of squared deviations is bigger 10, C or what we've seen previousely, don't save 'em. IP C  (SUMSQ < XX) THEN XX = SUMSQ NP = K  BETl BET2 ENDIF 150 C  = PEARSN = PEARSN  (K, 16) (K, 17)  CONTINUE IF  (O.OIDO < XX) GO TO 700  C 2.5% and 97.5% estimates CALC3 = BETl * CALC2 ** 1.5 CALC4 = BET2 * CALC2 ** 2  9999  RETURN  700  lERR = 1 GOTO 9999 END  than  Appendix  D: Source  Code of  the Model  240  C Trans.FOR C modified by Toshiaki Hatakama in July, 1994. C C C C C  ROUTINE TO TRANSFORM A SET OF CORRELATED VARIABLES TO A SET OF UNCORRELATED VARIABLES USING THE CORRELATION MATRIX. THE APPROACH IS REFFERED TO AS THE VARIABLE TRANSFORMATION METHOD. THE FIRST FOUR MOMENTS OF THE TRANSFORMED VARIABLES ARE EVALUATED FROM THE FIRST FOUR MOMENTS OF THE PRIMARY VARIABLES  C calls INV, DECOMP,  DGMULT  SUBROUTINE TRANS +  (I, NM, NSIZEl, NSIZE2, CALCl, CALC2, COR, TRI)  IMPLICIT REAL*4 (A-H,0-Z) INCLUDE "DEBUG.CMN' REAL*4 REAL*4 REAL*4 REAL*4  CALCl (4, NSIZEl, *) CALC2 (4, NSIZEl, *) COR (NSIZEl, NSIZE2, *) TRI (NSIZE2, *)  INTEGER IPERM (:) ALLOCATABLE IPERM REAL*4 SCOR (:) REAL*4 ADIG {:,:), ADIGI (:,:), TR (:,:), CORR (:) REAL*4 CORRL (:,:), CORLI (:,:) ALLOCATABLE SCOR, ADIG, ADIGI, TR, CORR, CORRL, CORLI CALL TRACE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE  (3, 'TRANS',  'Starting.')  (IPERM (NM)) (SCOR (NM)) (ADIG (NM, NM)) (ADIGI (NM, NM)) (TR (NM, NM)) (CORR (NM * NM)) (CORRL (NM, NM)) (CORLI (NM, NM))  DRATIO = l.OD-7 C diagonal matrix of the standard  deviations  DO 20 J=1,NM DO 20 K=1,NM IF (J == K) THEN ADIG(J,K) = CALCl(2,I,J)**0.5D0 ELSE ADIG(J,K) = O.ODO ENDIF  Appendix 20  D: Source  Code of  the Model  CONTINUE  C correlation matrix as a 1-D array for Cholesky  90 10 0  241  decomposition  LLN = NM - 1 DO 100 J=1,NM DO 90 K=1,NM L = (LLN * K) + J - LLN IP (J < K) THEN CORR (L) = COR(I,K,J) ELSE IP (J == K) THEN CORR (L) = l.ODO ELSE CORR (L) = O.ODO ENDIP CONTINUE CONTINUE  C the inverse of the diagonal matrix of standard deviations CALL INV (NM, NM, ADIG, IPERM, NM, ADIGI, DDET, JEXP, DCOND) IP (DDET == 0) THEN WRITE (7, 9901) I GO TO 999 9 ENDIP CALL DECOMP (CORR, NM, NM, DRATIO) IP (DRATIO <= O.ODO) THEN WRITE (7, 9902) I GO TO 9999 ENDIP  C the lower traingular matrix from the Cholesky  decomposition  DO 200 J=1,NM DO 190 K=1,NM IP (J < K) GO TO 180 L = (LLN*K) + J - LLN CORRL(J,K) = CORR(L) GO TO 190 180 190 2 00  CORRL(J,K) = O.ODO CONTINUE CONTINUE  C the inverse of the lower triangular matrix from C D CALL INV (NM, NM, CORRL, IPERM, NM, CORLI, DDET,JEXP,DCOND) IP (DDET == 0) THEN WRITE (7,9903) I GO TO 99 99 ENDIP  Appendix  D: Source  Code of  the Model  2 42  C the transformation matrix CALL DGMULT  (CORLI, ADIGI, TR, NM, NM, NM)  C the inverse of the transformation matrix C NSIZE2 had better darn well be larger than NM CALL INV (NM, NM, TR, IPERM, NSIZE2, TRI, DDET, JEXP, DCOND) IF (DDET == 0) THEN WRITE (7, 9904) I GO TO 9999 ENDIF  C C C C C C  MOMENTS OF THE TRANSFORMED UNCORRELATED VARIABLES Z = CALCKl, Z : TRANSFORMED VARIABLES X : CORRELATED VARIABLES A : THE TRANSFORMATION MATRIX CALC2(1 : EXPECTED VALUE OF THE TRANSFORMED VARIABLES  340  DO 340 J=1,NM CALC2(1,I,J) = O.ODO DO 340 K=1,NM CALC2(1,I,J) = CALC2{1,I,J) + TR(J,K) * CALC1(1,I,K)  C CALC2(2, : SECOND CENTRAL MOMENT OF THE TRANSFORMED  VARIABLES  DO 401 J=1,NM SCOR (J) = O.ODO DO 401 K=1,NM-1 TEMP = TR (J, K) IF (TEMP .NE. O.ODO) THEN DO 400 L=K+1,NM 400 SCOR (J) = SCOR (J) + TEMP * TR (J, L) * + COR (I, K, L) * + (CALCl (2, I, K) * + CALCl (2, I, L) ) ** 0.5D0 ENDIF 401 CONTINUE  450  DO 450 J=1,NM CALC2(2,I,J) = 2.0D0 * SCOR(J) DO 450 K=1,NM CALC2{2,I,J) = CALC2(2,I,J) + TR(J,K)**2 * CALC1(2,I,K)  C CALC2(3,  500  : THIRD CENTRAL MOMENT OF THE TRANSFORMED  DO 500 J=1,NM CALC2(3,I,J) = O.ODO DO 500 K=1,NM CALC2(3,I,J) = CALC2(3,I,J) + TR(J,K)**3  VARIABLES  * CALC1(3,I,K)  Appendix  D:  C CALC2(4,  600  Source  Code  of  the  243  Model  : FOURTH CENTRAL MOMENT OF THE TRANSFORMED  DO 6 0 0 J = 1 , N M C A L C 2 ( 4 , I , J ) = O.ODO DO 6 0 0 K = 1 , N M CALC2{4,I,J) = CALC2(4,I,J)  1000 CALL TRACE DEALLOCATE RETURN  + TR{J,K)**4  VARIABLES  *  CALC1(4,I,K)  (3, 'TRANS', 'exiting.') (SCOR, ADIG, ADIGI, TR, CORR, CORRL, CORLI)  9999 lERR = 1 GOTO 1000 9 9 01 FORMAT(/,'WP(',15,'), MTX INV. FAILED.',/,/) 9902 FORMAT(/,'WP(',15,'), CHOLESKY DECOMP. FAILED.',/,/) 9903 FORMAT{/,'WP(',15,'), LOWER TRI MTX INV. FAILED.',/,/) 9904 FORMAT(/,•WP{',15,'), TRNSF MTX INV. FAILED.',/,/) END  Appendix  D: Source  Code of  the Model  C WpDFP.FOR C modified by Toshiaki Hatakama in July, 1994. C Routine to check the type of functional form for work package C duration and to estimate the function at the mean values of C the transformed variables. C=========================================================== SUBROUTINE WPDFF(IFF,X,EVY) C=========================================================== IMPLICIT REAL*4(A-H,0-Z) INTEGER IFF REAL*4 EVY, X(*) GO TO (10,10,30,10,10),IFF 10  EVY = X(l) / (X(2) * X(3)) GO TO 100  30  EVY = X(l) + (3000.ODO / (X(2) * X(3))) GO TO 100  100  RETURN END  244  Appendix  D: Source  Code of  the Model  2 45  C MmTwPl.FOR C modified by Toshiaki Hatakama in July, 1994. C 07niar94 MJW C C C C  ROUTINE TO APPROXIMATE THE FIRST FOUR MOMENTS OF A DEPENDENT VARIABLE AT WORK PACKAGE/REVENUE STREAM LEVEL. IT USES THE MOMENTS OF THE TRANSFORMED VARIABLES WITH THE TRUNCATED SECOND ORDER TAYLOR SERIES EXPANSION OF THE FUNCTION.  C================================================================= SUBROUTINE MMTWPL (I,NN,NDIM,CALCl,GZ,PDl,PD2,CALC2,STFO) C================================================================= IMPLICIT REAL*4(A-H,0-Z) INCLUDE •DEBUG.CMN' REAL*4 CALCl (4, NDIM, * ) , REAL*4 PDl (•), PD2 {*)  CALC2  {4,  *)  DOUBLE PRECISION TROUBL CALL TRACE  (3, 'MMTWPL',  CALC2  (1,1) = GZ  CALC2 CALC2 CALC2  (2,1) = O.ODO (3,1) = O.ODO (4,1) = O.ODO  'starting.')  ! the expected value of the dependent ! variable  STFO = O.ODO DO 10 J=1,NN CALC2 (1,1) = CALC2  (1,1) + 0.5D0 * PD2 (J) * CALCl  C the second central moment of the dependent C from the first order approximation  (2,I,J)  variable  STFO = STFO + PD1(J)**2 • CALC1(2,I,J) C from the second order  + + +  approximation  CALC2(2,I) = CALC2(2,I) + CALC1(2,I,J) CALC1(3,I,J) (CALCl(4,I,J)  PD1(J)**2 * + PDl(J) * PD2(J) * + 0.25D0 * PD2(J)**2 * - CALCl(2,I,J)**2)  C the third central moment of the dependent  + +  variable  CALC2(3,I) = CALC2(3,I) + PD1(J)**3 * CALC1(3,I,J) + 1.5D0 * PD1(J)**2 * PD2 (J) * (CALCl(4,I,J) - CALCl(2,1,J)•*2)  C the fourth central moment of the dependent  variable  Appendix 10  D: Source  Code of  the Model  TROUBL = PDl(J) ** 4 * CALCl (4, I, J) CALC2(4,I) = CALC2(4,I) + TROUBL CALL TRACE RETURN END  (3, 'MMTWPL•,  'exiting.')  24 6  Appendix  D: Source  Code of  the Model  24 7  C CoVar.FOR C modified by Toshiaki Hatakama in July 1994. C ROUTINE TO APPROXIMATE THE CORRELATION BETWEEN TWO DEPENDENT C VARIABLES USING CORRELATION INFORMATION BETWEEN THE PRIMARY C VARIABLES AND THEIR PARTIAL DERAVATIVES. C SX is a (4,NWP,*) array, we only access SX(2,I,*) & S X ( 2 , J , * ) . C==================================================================== SUBROUTINE COVAR(JU,NDCV, I,J,NI,NJ,PX,SX,COR,STFOI,STFOJ,COC) C==================================================================== IMPLICIT REAL*4(A-H,0-Z) INCLUDE 'DEBUG.CMN' PARAMETER (JSZ = 50,KSZ = 25)  + + +  REAL*4 PX (NWP, * ) , SX (4, NWP, * ) , COR (NWP, MAXDVC, COC (NWP, •)  *),  REAL*4 COV(JSZ,JSZ),CORR(JSZ,KSZ,KSZ) REAL*4 PD(JSZ,KSZ},SD(JSZ,KSZ) INTEGER MI(KSZ),MJ(KSZ) C read the number of common variables in the functional C for the dependent variables CALL TRACE  (2, 'COVAR',  forms  'starting.')  C read the combinations of common variables  30  READ (JU, 30) (MI (K) , MJ (K) , K = l, NDCV) FORMAT(26(12,12))  C renumber the second central moment and the partial C of common variables In given order  deravatlve  DO 50 K=1,NDCV MMI = MI(K) MMJ = MJ(K) PD(I,K) = PX(I,MMI) SD(I,K) = SX(2,I,MMI) PD(J,K) = PX(J,MMJ) SD(J,K) = SX(2,J,MMJ) C the correlation coefficients between the common variables LL = K+1 IF(LL.GT.NDCV) GO TO 50 DO 40 L=LL,NDCV LLI = MI(L) LLJ = MJ(L) CORR(I,K,L) = COR(I,MMI,LLI)  Appendix  40 50  D: Source  Code of  the Model  CORR(I,L,K) = COR(I,LLI,MMI) CORR(J,K,L) = COR(J,MMJ,LLJ) CORR(J,L,K) = COR(J,LLJ,MMJ) CONTINUE CONTINUE  C renumber the second central moment and the partial C of the other variables in the functional forms  70  LL = NDCV DO 80 K = 1,NI DO 70 L=1,NDCV MMI = MI(L) IF (K.EQ.MMI) GO TO 80 CONTINUE  80  LL = LL+1 MI(LL} = K PD{I,LL) = PX(I,K) SD(I,LL) = SX(2,I,K) CONTINUE  90  100  24 8  deravative  LL = NDCV DO 100 K = 1,NJ DO 90 L=1,NDCV MMJ = MJ(L) IF (K.EQ.MMJ) GO TO 100 CONTINUE LL = LL+1 MJ(LL) = K PD(J,LL) = PX(J,K) SD(J,LL) = SX(2,J,K) CONTINUE  C the correlation between the common variables and the others.  110 120  LL = NDCV+1 DO 120 K=LL,NI MMK = M K K ) DO 110 L=1,NI MMI = MI(L) IF (MMI.EQ.MMK) GO TO 110 CORR(I,K,L) = COR{I,MMK,MMI) CORR(I,L,K) = COR(I,MMI,MMK) CONTINUE CONTINUE  140  LL = NDCV+1 DO 150 K=LL,NJ MMK = MJ(K) DO 140 L=1,NJ MMJ = MJ{L) IF (MMJ.EQ.MMK) GO TO 140 CORR{J,K,L) = COR(J,MMK,MMJ) CORR(J,L,K) = COR(J,MMJ,MMK) CONTINUE  Appendix 150  D: Source  Code of  the Model  24 9  CONTINUE  C covariance between two dependent variables I and J C from the common variables In I and J COV{I,J) = O.ODO DO 200 K=1,NDCV DO 200 L=1,NDCV IF (K.EQ.L) THEN CORR(I,K,L) = l.ODO CORR(J,K,I.) = l.ODO ENDIF 200 +  COV(I,J) = COV(I,J) + PD(I,K) * PD{J,L) • {SD(I,K) * SD(J,L))**0.5D0 * CORR(I,K,L)  C from the common variables in I and others in J NNV = NDCV+1 DO 240 K=1,NDCV DO 240 L=NNV,NJ 240 COV(I,J) = COV(I,J) + PD{I,K) * PD(J,L) + * (SD{I,K) * SD(J,L))**0,5D0 * CORR{J,K,L) C from the common variables in J and others in I NNV = NDCV+1 DO 300 K=1,NDCV DO 300 L=NNV,NI 300 COV(I,J) = COV(I,J) + PD(J,K) * PD{I,L) + * (SD(J,K) * SD(I,L))**0.5D0 * CORR{I,K,L) C the correlation coefficient between two dependent COC(I,J) = COV{I,J) / ((STFOI * STFOJ)**0.5D0) COC(J,I) = COC(I,J) 500 CONTINUE CALL TRACE RETURN END  (2, •COVAR',  'exiting.')  variables  Appendix  D: Source  Code of  the Model  250  C NetWrk.FOR C Toshiaki Hatakama in July. 1994. C NOTHING preventing this from being called BEFORE EAST... C ...directly from MAIN (AMMA). C ROUTINE TO EVALUATE THE FIRST FOUR MOMENTS OF WORK C EARLY START TIME USING THE PNET ALGORITHM C calls EARLY, CDFUNC,  PACKAGE.  ESTMMT  0==================================================================== SUBROUTINE NETWRK (PEARSN, WPTIME, CORRD, ESTART, TRCOR) C==================================================================== IMPLICIT REAL*4(A-H,0-Z) PARAMETER (JSZ=5 0) INCLUDE  •DEBUG.CMN"  REAL*4 PEARSN (NPEARS, 17) REAL*4 WPTIME (4, N W P ) , CORRD (NWP, NWP) REAL*4 ESTART (4, NWP) INTEGER LIST (200, 4 0 ) , LISREP (101, 40) CHARACTER*10 DESC (JSZ, 3) INTEGER WPNO (JSZ), NDEP (JSZ), PREWP (JSZ, 30) INTEGER SP, STACK (0:200), LIS (0:40), NTEMP (0:200) INTEGER LPP (200), LPPR (200), LISTR (200, 40) INTEGER LCOM (40), LPPS (200), LISTS (200, 40) INTEGER LPREP (200) REAL*4 CORTR  (200, 2 0 0 ) , SCOR (40)  REAL*4 REAL*4 REAL*4 REAL*4  EVAL (200), SIGM (200), RVAL (200), RSIG (200) REVAL (200), RSIGM (200) SDTME (300), SKTME (300), AKTME (300) PTE (101,101)  REAL*4 REAL*4 REAL*4 REAL*4 REAL*4  VA VF VG VW VX  (300), VB (300), VC (300), VD (300), VE (300) (300) (300), VM (300), VT (300), VU (300), VV (300) (300) (300), VY (300), VZ (300)  REAL*4 TM (101), PT (101) REAL*4 ED (JSZ), EE (JSZ), EG (JSZ), + EM (JSZ), + ET (JSZ), EV (JSZ), EW (JSZ) REAL*4 ETEMP CALL TRACE ESTART ESTART  (4,  101)  (1, 'NETWRK',  (1, 1) = O.ODO (2, 1) = O.ODO  'starting.')  Appendix  D: Source  ESTART ESTART  Code of  the Model  251  (3, 1) = O.ODO (4, 1) = O.ODO  C read the input data from file at unit 10 NDEP(l) = 0 C C C C C  all the data about to be read in (except TRCOR) goes into temp vars. it never leaves this routine, at least not without being processed. WPNO & DESC are read in, then discarded like so much trash.... TRCOR is returned to the calling routine. READ (10, 9 901) TRCOR DO 11 INWP = 2, NWP READ (10, 9902) WPNO (INWP), NDEP (INWP), + (DESC (INWP, J ) , J = 1, 3) 11 READ (10, 9903) (PREWP (INWP, J ) , J = 1, NDEP  (INWP))  J = WPN0(2) + ICHAR(DESC(2,1) (1:1) ) C initialize the arrays  12  DO 12 J = 0, 200 STACK (J) = 0  13  DO 13 J = 0, 20 LIS (J) = 0  14  DO 14 J = 0, 100 NTEMP (J) = 0  (stack machine)  C the first four moments of Estart time from PNET C set up the stack machine DO 9 90 INWP = 2, NWP SP = 0 LP = 0 LN = 0 STACK (SP) = INWP LIS (LP) = INWP NTEMP (INWP) = NDEP  (INWP)  C develop the stack with current W . P . and its predecessors  90  DO 90 J = 1, NDEP (INWP) PRED = PREWP (INWP, J) SP = SP + 1 STACK (SP) = PRED NTEMP (PRED) = NDEP (PRED)  C develop the lists of all the paths to the work packages 100  IF (SP == 0) GO TO 200 PRED = STACK (SP) IF (PRED == 1) GO TO 150 IF (NTEMP (PRED) == 0) GO TO 180  Appendix  D: Source  Code of  the Model  2 52  LP = LP + 1 LIS (LP) = PRED C predecessors of the predecessors are added to the stack DO 110 J = 1, NDEP (PRED) SP = SP + 1 STACK (SP) = PREWP (PRED, J) PPRED = PREWP (PRED, J) NTEMP (PPRED) = NDEP (PPRED)  110  GO TO 100 150  LP = LP+1 LN = LN+1 LPP{LN) = LP LIS(LP) = PRED DO 160 J=1,LP LIST(LN,J) = LIS(J)  160  C remove the work package from the stack and list 180  STACK(SP) = 0 LIS(LP) = 0 SP = SP - 1 LP = LP - 1 PRED = LIS (LP) NTEMP (PRED) = NTEMP GO TO 100  (PRED) - 1  C check the number of paths to the work package 200  IF (LN == 1) GO TO 950  C expected value and standard deviation for all paths  210 + 220 230  DO 230 J=1,LN EVAL{J) = O.ODO SIGM(J) = O.ODO LP = LPP (J) -1 DO 230 K=1,LP SCOR(K) = O.ODO Jl = LIST(J,K) EVAL{J) = EVAL(J) + WPTIME (1, Jl) MM = K+1 IF (MM <= LP) THEN DO 210 M=MM,LP J2 = LIST(J,M) SCOR(K) = SCOR(K) + C0RRD(J1,J2) * (WPTIME (2, Jl) * WPTIME (2, J2))**0.5D0 END IF SIGM(J) = SIGM{J) + WPTIME (2, Jl) + 2.0D0*SCOR(K) CONTINUE  C rearrange lists according to decreasing order of S.D MR = 0  Appendix D: Source 2 50  2 60  Code of the Model  253  SMAX = O.ODO MR = MR+1 DO 260 J=1,LN IF (SMAX < SIGM (J)) THEN SMAX = SIGM (J) MO = J ENDIF CONTINUE IF  (O.ODO < SMAX) THEN RVAL (MR) = EVAL (MO) RSIG (MR) = SIGM (MO) LPPS (MR) = LPP (MO) - 1 LP = LPPS (MR) DO 280 K = 1, LP LISTS (MR, K) = LIST  280  (MO, K)  SIGM (MO) = O.ODO GO TO 250 ENDIF C rearrange lists according to decreasing order of E.V. C Son of BOGOSORT... MR = 0 300  310  AMAX = O.ODO MR = MR+1 DO 310 J=1,LN IF (AMAX < RVAL(J)) AMAX = RVAL(J) MO = J ENDIF CONTINUE IF  330  THEN  (AMAX /= O.ODO) THEN REVAL(MR) = RVAL(MO) RSIGM(MR) = RSIG(MO) LPPR(MR) = LPPS(MO) LP = LPPR(MR) DO 330 K=1,LP LISTR(MR,K) = LISTS(MO,K)  RVAL(MO) = O.ODO 60 TO 3 00 ENDIF C transition correlation coefficient between paths DO 390 J=1,LN LP = LPPR(J) KK = J+1 IF (KK <= LN) THEN DO 385 K=KK,LN  Appendix  D: Source  Code of  the Model  2 54  MNO = 0 MP = LPPR(K) DO 360 L=1,LP Jl = LISTR(J,L) DO 360 M=1,MP J2 = LISTR(K,M) IF (Jl == J2) THEN MNO = MNO+1 LOOM(MNO) = Jl ENDIF 3 60  CONTINUE CORTR(J,K)  C no common work packages  = O.ODO  in the two paths  IF  380 + 3 85 3 90  (MNO /= 0) T H E N DO 380 L=1,MN0 Jl = L C O M ( L ) C0RTR(J,K) = CORTR(J,K) + ( W P T I M E (2, J l ) / ( { R S I G M { J ) * R S I G M ( K ) ) * * 0 . 5 D 0 ) ) ENDIF CONTINUE ENDIF CONTINUE  C select 400  the representative  paths  MREP = 0 DO 450 J=1,LN IF ( R E V A L ( J ) /= O . O D O ) T H E N MREP = MREP+1 LPREP(MREP) = LPPR(J) LP = LPREP(MREP) DO  420  420 K=1,LP LISREP(MREP,K)  = LISTR(J,K)  KK IF  43 0  450  = J+1 (KK <= L N ) T H E N DO 4 3 0 K=KK,LN IF (TRCOR <= C O R T R ( J , K ) ) CONTINUE ENDIF ENDIF CONTINUE  C if t h e r e IF C  first  is o n l y (MREP  one representative  DO  skip  == 1) G O T O 9 0 0  four moments SMAX  path,  of a representative  = O.ODO  500 J=l, MREP E T E M P (1, J) = O.ODO E T E M P (2, J) = O.ODO E T E M P (3, J ) = O . O D O  REVAI.(K)  path  = O.ODO  to line 900  Appendix  D: Source ETEMP  Code of  the Model  2 55  (4, J) = O.ODO  LN = J LP = ]:.PREP(J) IF (LP <= 1) THEN C only one work package on the path DO 470 K=1,LP Jl = LISREP(LN,K) ETEMP ETEMP ETEMP ETEMP  470  (1, J) = ETEMP (1, J) + WPTIME (1, Jl) (2, J) = ETEMP (2, J) + WPTIME (2, Jl) (3, J) = ETEMP (3, J) + WPTIME (3, Jl) (4, J) = ETEMP (4, J) + WPTIME (4, Jl)  ELSE C multiple work packages on the path  + + +  CALL EARLY (J, LN, LP, 2, WPTIME, CORRD, ETEMP, LIST, LISREP) IF (0 < lERR) GO TO 1000 ENDIF  C Standard deviation, skewness and kurtosis for the path SDTME SKTME AKTME  (J) = ETEMP (J) = ETEMP (J) = ETEMP  (2, J) ** 0.5D0 (3, J) / (ETEMP (2, J) ** 1.5D0) (4, J) / (ETEMP (2, J) ** 2)  C values of the approximated pearson  CALL CDFUNC +  distribution  (PEARSN, ETEMP (1, J ) , SDTME  (J), SKTME  (J), AKTME  (J) , + + +  VA{J) ,VB(J) ,VC(J) ,VD(J) ,VE(J) ,VF(J) ,VG(J) , VM(J), VT(J) ,VU(J) ,VV(J) ,VW(J) ,VX(J) ,VY{J) ,VZ(J) )  C maximum standard deviation for representative paths IF  500 C C C C  (SMAX < SDTME(J)) SMAX = SDTME(J) ENDIF CONTINUE  THEN  starting duration and incremental step for CDF of EST this is the only reference to an unindexed value of AETME. this means that AETME, SETME, TETME & FETME can probably be scrapped. TSTART = ETEMP (1, 1) - (3.0D0 * SMAX) TSTEP = SMAX / lO.ODO  Appendix  D: Source  Code of  the  Model  256  DO WHILE (VA (1) < TSTART) TSTART = TSTART - TSTEP END DO C duration cycle to develop the CDF for EST J=l 53 0  JNUM = J JJ = J-1 TM(J) = TSTART +  (FLOAT(JJ)*TSTEP)  C probability of achieving the duration for each path C FORTRAN doesn't know how to deal with a REAL*4 valued CASE statement so this is the closest that we can come, this could be re-written to use a table to pull out these two values.... O.ODO 0.0025D0, 0.0025DO 0.0050D0, 0.0050D0 O.OIOODO, 0.0150D0 0.0250D0, 0.0250D0 0.0500D0, 0.0500D0 O.IOOODO, 0.1500D0 0.2500D0, 0.2500D0 0.5000D0, 2500D0 1500D0 0 .7500D0, 0500D0 0.9000D0, 0250D0 0.9500D0, 0150D0 0.9750DO, 0050D0 0.9900D0, 0025D0 0.9950D0, l.ODO DO 700 K=1,MREP IF (TM(J) <= VA(K)) THEN PTE(J K) = O.ODO < TM(J) .AND. VB(K) >= TM{J)) THEN ELSE IF (VA(K PTE(J K) = 0.0025D0 + (TM(J) - VA(K)) * 0. 0025D0 / (VB(K) VA(K))) < TM(J) .AND. VC(K) >= TM(J)) THEN ELSE IF (VB (K PTE(J K) = 0.0050D0 + VB(K))) (TM(J) - VB(K)) * 0. 0050D0 / (VC(K) < TM(J) .AND. VD(K) >= TM(J)) THEN ELSE IF (VC(K PTE(J K) = O.OIOODO + (TM(J) - VC{K)) • 0. 0150D0 / {VD(K) VC(K)) ) < TM(J) .AND. VE(K) >= TM(J)) THEN ELSE IF (VD (K PTE(J K) = 0.0250D0 + (TM(J) - VD(K)) • 0. 0250D0 / (VE(K) - VD(K))) < TM(J) .AND. VF(K) >= TM(J)) THEN ELSE IF (VE(K PTE(J K) = 0.0500D0 + (TM(J) - VE(K)) * 0. 0500D0 / (VF(K) VE(K) ) ) < TM(J) .AND. VG(K) >= TM(J)) THEN ELSE IF (VF (K PTE(J K) = O.IOOODO + (TM(J) - VF(K) ) * 0. 1500D0 / (VG(K) VF(K))) < TM(J) .AND. VM(K) >= TM(J)) THEN ELSE IF (VG(K  Appendix  D: Source  Code of  the Model  PTE(J,K) = 0.2500D0 + (TM{J) - VG(K)) * 0.2500D0 / (VM{K) ELSE IF (VM(K < TM(J) .AND. VT(K >= TM(J)) THEN PTE (J K) = 0.5000D0 + (TM(J) - VM{K)) * 0 2500D0 / (VT(K) ELSE IF (VT(K < TM{J) .AND. VU(K >= TM(J)) THEN PTE (J K) = 0.7500D0 + (TM(J) - VT(K)) * 0 1500D0 / (VU{K) ELSE IF (VU(K < TM(J) .AND. VV(K >= TM{J)) THEN PTE (J K) = 0.9000D0 + (TM(J) - VU(K)) * 0 0500D0 / (VV(K) ELSE IF (VV(K < TM(J) .AND. VW(K >= TM(J)) THEN PTE (J K) = 0.9500D0 + (TM(J) - VV(K)) • 0 0250D0 / (VW(K) ELSE IF (VW(K < TM(J) .AND. VX{K >= TM(J)) THEN PTE (J K) = 0.9750D0 + (TM(J) - VW(K)) * 0 0150D0 / (VX(K) ELSE IF {VX{K < TM(J) .AND. VY{K >= TM(J)) THEN PTE (J K) = 0.9900D0 + {TM(J) - VX(K)) * 0 0050D0 / (VY(K) ELSE IF (Vy{K < TM(J) .AND, VZ(K >= TM(J)) THEN PTE (J K) = 0.9950D0 + (TM(J) - VY(K)) * 0.0025D0 / (VZ(K) ELSE IF (VZ(K < TM(J)) THEN PTE(J,K) = l.ODO ENDIF CONTINUE  700  25 7 - VG(K)))  - VM(K)))  - VT(K)))  - VU(K)))  - VV(K)))  - VW(K)))  - VX(K)))  VY(K)))  C cumulative probability of the duration being EST PT{J) = l.ODO DO 710 K = 1,MREP PT(J) = PT(J)*PTE(J,K)  710  IF  (PT(J) < l.ODO)  THEN  J =J+1  GO TO 530 ENDIF C C C C C  re-check this CAREFULLY with the original source to make sure that all the tests come out correctly. this is very messy, but I gather that it has a point. notice the interchanging of K & J throughout. fractile values of the CDF for work package EST DO 800 J = 2, JNUM K = J-1 IF IF  + +  {PT{J) < 0.025D0) GOTO 800 (PT(K) < 0,025D0 .AND. PT{J) >= 0.025D0) THEN ED (INWP) = TM(K)+(0.02 5D0-PT{K))*(TM(J)-TM{K))/(PT(J)-PT(K)) IF (TM(J) >= 0.050D0) EE (INWP) = TM(K)+(0.05 0D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) ENDIF IF  (PT(J) < 0.050D0) GOTO 800  Appendix  D: Source  Code of  the  Model  25 8  IF  + +  {PT{K) < 0.050D0 .AND. PT(J) >= 0.050D0) THEN EE (INWP) = TM(K)+(0.05 0D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) IF (TM(J) >= 0.250D0) EG (INWP) = TM(K)+(0.25 0D0-PT(K))*(TM{J)-TM(K))/(PT(J)-PT(K)) ENDIF IF IF  + +  (PT(J) < 0.250D0) GOTO 800 (PT(K) < 0.250D0 .AND. PT(J) >= 0.250D0) THEN EG (INWP) = TM(K)+(0.250D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) IF (TM(J) >= 0.500D0) EM (INWP) = TM(K)+(0.5 0 0D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) ENDIF IF IF  + +  (PT(J) < 0.500D0) GOTO 800 (PT(K) < 0.500D0 .AND. PT(J) >= 0.500D0) THEN EM (INWP) = TM(K)+(0.50 0D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) IF (TM(J) >= 0.750D0) ET (INWP) = TM(K)+(0.75 0D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) ENDIF IF IF  + +  (PT(J) < 0.750D0) GOTO 800 (PT(K) < 0.750D0 .AND. PT(J) >= 0.750D0) THEN ET (INWP) = TM(K)+(0.750D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) IF (TM(J) >= 0.950D0) EV (INWP) = TM(K)+(0.95 0D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) ENDIF IF IF  + +  (PT(J) < 0.950D0) GOTO 800 (PT(K) < 0.950D0 .AND. PT(J) >= 0.950D0) THEN EV (INWP) = TM(K)+(0.95 0D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) IF (TM(J) >= 0.975D0) EW (INWP) = TM(K)+(0.97 5D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) ENDIF IF IF  +  800  (PT(J) < 0.975D0) GOTO 800 (PT(K) < 0.975D0 .AND. PT(J) >= 0.975D0) THEN EW (INWP) = TM(K)+(0.97 5D0-PT(K))*(TM(J)-TM(K))/(PT(J)-PT(K)) ENDIF CONTINUE  C first four moments of work package Estart CALL ESTMMT -t+  (INWP, PEARSN, ED,EE,EG,EM,ET,EV,EW, ESTART)  GO TO 9 90 C when there is only one representative path  time  Appendix 900  D: Source  Code of  the  259  Model  LN = MREP LPP(LN) = LPREP(LN)+1 LP = I.PREP(LN} DO 920 K = 1, LP LIST(LN,K) = LISREP(LN,K)  920  C first four moments when only one PATH to the work package 950  ESTART ESTART ESTART ESTART  (1, (2, (3, (4,  INWP) INWP) INWP) INWP)  = = = =  O.ODO O.ODO O.ODO O.ODO  LP = LPP(LN)-1 C deal with the special case of only one WORK IF (1 < LP) THEN CALL EARLY (INWP, 1,, LP, 1, WPTIME, CORRD, ESTART, LIST, LISREP) IF (0 < lERR) GO TO 1000 ELSE DO 970 K=1,LP Jl = LIST(LN,K) ESTART (1, INWP) = ESTART ESTART (2, INWP) = ESTART ESTART (3, INWP) = ESTART ESTART (4, INWP) = ESTART ENDIF  + + +  970  9 90  (1, (2, (3, (4,  CONTINUE  1000  CALL TRACE RETURN  9901 9902 9903  FORMAT(F6.3) FORMAT(2I3,3A10) FORMAT(30I3) END  (1, •NETWRK•,  'exiting.')  PACKAGE.  INWP) INWP) INWP) INWP)  + + + +  WPTIME WPTIME WPTIME WPTIME  (1, (2, (3, (4,  Jl) Jl) Jl) Jl)  Appendix  D: Source  Code of  the Model  2 60  C WpCmmt.FOR C modified by Toshiaki Hatakama in July, 1994 C ROUTINE TO EVALUATE THE FIRST FOUR MOMENTS OF THE WORK C PACKAGE COST FOR DIFFERENT DISCOUNT RATES. C= SUBROUTINE WPCMMT + + +  (I,DR,FRA, NWPCF, NDVR, XUCOST, TRIWPC, COST, STFO)  C= IMPLICIT REAL*4(A-H,0-Z) INCLUDE •DEBUG.CMN' INTEGER NWPCF (*), NDVR (*) REAL*4 XUCOST (4, NWP, * ) , TRIWPC REAL*4 COST (4, *)  (NWP, NWP, *)  REAL*4 X {:), Z (:), SZ (:), GZS (:), GZL (:) REAL*4 PWPCl (:),PWPC2{:) ALLOCATABLE X, Z, SZ, GZS, GZL, PWPCl, PWPC2 CALL TRACE  (3, 'WPCMMT',  'starting.')  NNVR = NDVR(I) ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE  (X (NNVR)) (Z (NNVR)) (SZ (NNVR)) (GZS (NNVR)) (GZL (NNVR)) (PWPCl (NNVR)) (PWPC2 (NNVR))  C estimate G(Z) from the g(X) given by the user at the mean C values of Z (the transformed variables) and the partial C deratives with respect to the transformed variables.  10  DO 10 J=1,NNVR Z(J) = XUCOST  20  DO 2 0 J=1,NNVR X{J) = O.ODO DO 2 0 K=1,NNVR X(J) = X{J) + T R I W P C d , J,K) * Z(K)  (1, I, J)  C the value of 6(Z) at the mean values of Z CALL WPCFF  (NWPCF  (I), DR, FRA, X, GZ)  C the partial deravatives of the transformed  variables  Appendix  D: Source  Code of  the Model  2 61  DO 100 J=1,NNVR Z(J) = XUCOST (1, 1, J) * 0.99D0 SZ{J) = XUCOST (1, I, J) * O.OIDO DO 5 0 K=1,NNVR X{K) = O.ODO DO 5 0 L=1,NNVR X(K) = X(K) + TRIWPC(I,K,L) * Z(L)  50  C the value for 6(Z) when Z(J) is less than the mean value C (negative increment)  CALL WPCFF  (NWPCF  ( I ) , DR, FRA, X, GZS  (J))  Z(J) = XUCOST (1, I, J) * I.OIDO DO 60 K=1,NNVR X(K) = O.ODO DO 60 L=1,NNVR X(K) = X(K) + TRIWPC(I,K,L) * Z(L)  60  C the value for G(Z) when Z(J) is more than the mean value C (positive increment)  CALL WPCFF  (NWPCF  ( I ) , DR, FRA, X, GZL  (J))  C the first partial deravative with respect to Z(J) PWPCl(J) = (GZL(J) - GZS(J)) / (2.0D0 * SZ(J)) C the second partial deravative with respect to Z(J) PWPC2(J) = (GZL(J)+GZS(J)-2.ODO*GZ) Z(J) = XUCOST (1, I, J)  C C  PRINT*,'I,J,PWPC2,XUCOST +  / (SZ(J)**2)  (2, I, J)=•,I,J,PWPC2(J), XUCOST (2, I, J)  100 CONTINUE C the first four moments for the work package cost  CALL MMTWPL + + +  DEALLOCATE CALL TRACE RETURN END  (I,NNVR, NWP, XUCOST, GZ,PWPC1,PWPC2, COST, STFO)  (X, Z, SZ, GZS, GZL, PWPCl, PWPC2: (3, 'WPCMMT', 'exiting.')  Appendix  D: Source  Code of  the Model  2 62  C WpCff.FOR C modified by Toshiaki Hatakama in July, 1994. C Routine to check the type of functional form for work package C cost and to estimate the function at the mean values of the C transformed variables. 0============================================================= SUBROUTINE WPCFF (IFF, DR, FRA, X, EVY) 0============================================================= IMPLICIT REAL*4(A-H,0-Z) INTEGER IFF REAL*4 EVY, X (*) REAL*4 Z (5), AZ (5) EVY = O.ODO GO TO (100,200,200,200,200,200,200,200,900,1000,1100),IFF C Type 1 functional form 100 Z(l) = X(13)-DR IF (DABS{Z (1)) .GT.O.OOIDO) GO TO 110 AZ(1) = X(l) GO TO 12 0 110 AZ(1) = (DEXP(Z (1)*X(2) ) - DEXP(Z(1) * (X(2) -X(l) ) ) ) / Z(l) 120 Z(2) = X(14)-DR IF (DABS(Z(2)).GT.O.OOIDO) AZ(2) = X(l) GO TO 140 130 AZ(2) = {DEXP(Z(2)*X(2))  - DEXP(Z(2)*{X(2)-X{1))))  140 Z(3) = X(15)-DR IF (DABS(Z(3)).GT.O.OOIDO) AZ(3) = X{1) GO TO 160 150 AZ(3) = (DEXP(Z{3)*X(2))  190 AZ(5) = (DEXP(Z{5)*X(2))  / Z(3)  GO TO 170  - DEXP(Z(4)*(X(2)-X{1))))  180 Z(5) = X(17)-DR IF (DABS(Z(5)).GT.O.OOIDO) AZ(5) = X(l) GO TO 191  / Z(2)  GO TO 150  - DEXP(Z(3)*(X(2)-X(1))))  160 Z(4) = X(16)-DR IF (DABS(Z(4)).GT.O.OOIDO) AZ(4) = X(l) GO TO 180 170 AZ(4) = (DEXP(Z(4)*X(2))  GO TO 130  / Z(4)  GO TO 190  - DEXP(Z(5)*(X(2)-X(1))))  / Z(5)  Appendix  D: Source  Code of  the Model  2 63  191 Yl = + +  X{9) • X(5) * AZ(1) + X(10) * X(4) * X(5) * AZ{2) + X(ll) • X(6) * AZ(3) + (X(7)/X(l)) * AZ(4) + X(8) * AZ(5)  Y2 =  X(9) * X(5) * (DEXP((X{13)-X(12))*X(2)) - DEXP((X(13)-X(12))*(X{2)-X(l)))) / {X(13) - X(12)) + X(10) * X(4) * X{5) * (DEXP((X(14)-X(12))*X(2)) - DEXP((X(14)-X(12))*(X(2)-X(l)))) / (X(14) - X(12)) + X(ll) * X(6) * {DEXP({X{15)-X{12))*X(2)) - DEXP({X(15)-X(12))*{X{2)-X(l)))) / (X(15) - X(12)) + (X{7)/X(l)) * (DEXP((X{16)-X(12))*X(2)) - DEXP((X(16)-X(12))*(X(2)-X(l)))) / (X(16) - X(12)) + X(8) * (DEXP((X(17)-X{12))*X{2)) - DEXP((X(17)-X(12))*(X(2)-X(l)))) / (X(17) - X{12))  + + + + + + + + +  EVY = FRA * Yl + (1-FRA) * DEXP((X(12)-DR)*X(3)) * Y2 GO TO 9999 C Type 2, 3, 4, 5, 6, 7, and 8 functional forms. 2 00 EVY = X(l) / (X(2) * X{3)) GO TO 999 9 C Type 9 functional form, just constant dollar cost 900 EVY = X(4) GO TO 99 99 C Type 10 functional form. 1000 Z (1) = X(6)-DR IF (O.OOIDO < DABS (Z (1))) GO TO 1010 AZ(1) = X(l) GO TO 1020 1010 AZ(1) = (DEXP(Z(1)*X{2) ) - DEXP(Z(1) * {X(2) -X(l) ) ) ) / Z(l) 1020 Yl = Y2 = C  (X(4)/X(l)) * AZ(1) (X(4)/X(l)) * (DEXP(X{6)*(X(2) -X(l) ) + (X(6) -X(5) )*X(1)) - DEXP(X{6)*(X(2)-X(l)))) / (X(6) - X(5))  EVY = FRA * Yl + (1-FRA) • DEXP((X(5)-DR)*X(3)) GO TO 9999  C Type 11 functional form  * Y2  (toll h i g h w a y ) .  1100 Z(1) = X(7)-DR IF (DABS(Z(1)).GT.O.OOIDO) GO TO 1110 AZ(1) = X(l) GO TO 1120 1110 AZ(1) = (DEXP(Z(1)*X(2))  - DEXP(Z(1)*(X(2)-X(l))))  1120 Z(2) = X(7)-X(6) IF (DABS(Z(2)).GT.O.OOIDO) GO TO 1130 AZ(2) = +  (DEXP(X(7)*(X(2)-X(l))+X(6)*X(3)))*X(1) /(DEXP(-X(6)*X(4))-1) GO TO 1140  / Z(l)  Appendix D: Source 1130 AZ(2) = + +  Code of the Model  (DEXP(X(7)*(X(2)-X(l))+X(6)*(X(3)-(X(2)-X(l))))) *(DEXP((X(7)-X(6))*X(1))-1) /(DEXP(-X(6)*X(4) ) -1)/(X(7) -X(6) )  1140 IF (DABS(DR).GT.O.OOIDO) GO TO 1150 AZ(3) = X(4) GO TO 1160 1150 AZ(3) =  (DEXP(-DR*(X(3)+X(4)))-DEXP(-DR*X{3)))/DR  1160 Yl = (X(5)/X(l)) * AZ(1) Y2 = X(6) * (X(5)/X(l) ) * AZ(2) • AZ(3) EVY = PRA * Yl + (1-FRA) * Y2 9999 RETURN END  2 64  Appendix  D: Source  Code of  the Model  C RvsMMT.FOR C modified by Toshiaki Hatakama in July, 1994. C ROUTINE TO EVALUATE THE FIRST FOUR MOMENTS OF THE REVENUE C STREAMS FOR DIFFERENT DISCOUNT RATES. C C C C C C  DR is passed unchanged thru to RVSFF. pass X, our beloved carrier variable, to RVSMMT as well. let RVSFll & 12 take their parameters from there. everyone else is doing it.... EXCEPT FRJIRR! all values in X beyond NNVR are not modified by this routine. NNVR is N D R V d ) , the maximum value of which is MAXDV. . .  C calls RVSFF, MMTWPL C called by REVSTR, PRJIRR 0================================================================ SUBROUTINE RVSMMT (I, DR, BOTTLE, + NRVSF, NDRV, + XUREV, TRIRVS, + REV, + STFO)  C if you have 16M Ram C if not  enough = 1 =\ 1  $DEFINE enough = 0 INCLUDE •DEBUG.CMN' IMPLICIT REAL*4{A-H,0-Z) INTEGER NRVSF (*), NDRV (*) REAL*4 XUREV (4, NRS, *) $IF enough .EQ. 1 REAL*4 TRIRVS (NRS, MAXDVR, *) $ELSE REAL*4 TRIRVS {*), TEMPRVS (:,:) ALLOCATABLE TEMPRVS $ENDIF REAL*4 REV (4, * ) , BOTTLE (NRS, *) REAL*4 X {:), Z (:), PRVSl (:), PRVS2 (:) ALLOCATABLE X, Z, PRVSl, PRVS2 CALL TRACE  (3, 'RVSMMT',  NNVR = NDRV (I) ALLOCATE ALLOCATE ALLOCATE ALLOCATE  (X (NNVR)) (Z (NNVR)) (PRVSl (NNVR)) (PRVS2 (NNVR))  'starting.')  2 65  Appendix D: Source  Code of the Model  $IF enough .NE. 1 ALLOCATE (TEMPRVS $ENDIF  2 66  (NNVR, NNVR))  C estimate 6(Z} from the g(X) given by the user at the mean C values of Z (the transformed variables) and the partial C deratives with respect to the transformed variables.  10  DO 10 J = 1, NNVR Z (J) = XUREV (1, I, J) CONTINUE  DO 20 J = 1, NNVR X (J) = O.ODO DO 20 K = 1, NNVR $IF enough  .EQ. 1 X (J) = X (J) + TRIRVS  (I, J, K) * Z (K)  $ELSE TEMPRVS (J, K) = SPA_GET3 (TRIRVS, I, J, K) X (J) = X (J) + TEMPRVS (J, K) * Z (K) $ENDIF 20  CONTINUE  PRINT *, 'shakin tree #', I CALL RVSFF (NRVSF (I), 0, 2, DR, BOTTLE, I, X, GZ) meanVal of Z(J) PRINT*,'mean value  ! G(Z)  finished'  DO 100 J = 1, NNVR SZ = XUREV (1, I, J) * O.OIDO  Z  (J)  = XUREV  (1, I, J) * 0.99D0  ! G(Z) when Z(J) < ! meanVal  DO 50 K = 1, NNVR X (K) = O.ODO DO 50 L = 1, NNVR $IF enough  .EQ. 1 X (K) = X (K) + TRIRVS  (I, K, L) * Z (L)  $ELSE X (K) = X (K) + TEMPRVS  (K, L) * Z (L)  $ENDIF 50  CONTINUE CALL RVSFF  Z  (J)  (NRVSF  = XUREV  (I), J, 1, DR, BOTTLE, I, X, GZS)  (1, I, J) * I.OIDO  ! G(Z) when Z(J) > ! meanVal  at  Appendix  D:  Source  Code  of  the  Model  2 67  DO 70 K = 1 , NNVR X (K) = O.ODO DO 7 0 L = 1 , NNVR $IF enough  .EQ. 1 X (K) = X (K) + TRIRVS  (I, K, L) * Z (L)  $ELSE X  (K) = X  (K) + TEMPRVS  (K, L) * Z (L)  $ENDIF 70  CONTINUE CALL RVSFF  (NRVSF  (I), J, 3, DR, BOTTLE, I, X, GZL)  C the first and second partial deravative with respect to Z(J)  PRVSl PRVS2 Z  (J) = (GZL - GZS) / {2.0D0 * SZ) (J) = (GZL + GZS - 2.0D0 * GZ) / (SZ ** 2) (J) = XUREV (1, I, J)  SENSITIVE = PRVSl (J) * Z (J) / GZ WRITE (121, *) 'Sensitivity coefficientl DY = sensitive * 0.02 WRITE (122, *) 'Sensitivity coefficient2 10 0  for',J,'=•,SENSITIVE for',J,'=•,DY  CONTINUE  C the first four moments for the revenue stream CALL MMTWPL DEALLOCATE  (I, NNVR, NRS, XUREV, G Z , PRVSl, PRVS2, REV, STFO) (X, Z, PRVSl, PRVS2)  $IF enough .NE. 1 DEALLOCATE (TEMPRVS) $ENDIF CALL TRACE RETURN END  (3, 'RVSMMT•,  'exiting,')  Appendix  D: Source  Code of  the Model  2 68  C RvSff.for C modified by Toshiaki Hatakama in July, 1994. C Routine to check the type of functional form for revenue C streams and to estimate the function at the mean values of C the transformed variables. C includes calls to RVSFll, RVSF12 C called by RVSMMT 0================================================================ SUBROUTINE RVSFF (IFF, KP, KT, DR, BOTTLE, I, X, EVY) C================================================================ IMPLICIT REAL*4{A-H,0-Z) INCLUDE 'DEBUG.CMN' REAL*4 X (*), BOTTLE (NRS, *) REAL*4 Z ( 5 ) , AZ (5)  + +  GO TO (100,200,200,200,200,200,200,200,200,1000,1100,1200,1300), IFF  C Type 1 functional  form.  100 Z (1) = X (5) - DR IF (O.OOIDO < DABS (Z (1))) THEN AZ (1) = + ( DEXP (Z (1) * X (4) - DR * X (1)) + - DEXP ( - DR * X (1)) ) / Z(l) ELSE AZ (1) = X (4) END IF Z (2) = X (6) - DR IF (O.OOIDO < DABS (Z (2))) THEN AZ (2) = + ( DEXP (Z (2) * (X (1) + X (4))) + - DEXP (Z (2) • X (1) ) ) / Z(2) ELSE AZ (2) = X(4) ENDIF EVY = (X (2) • AZ (1)) - (X (3) * A Z GO TO 9 999  C Type 2 , 3, 4, 5, 6, 7, 8, and 9 functional 2 00 EVY = X(l) / (X(2) * X(3)) GO TO 9999  C Type 10 functional form  (2))  forms  Appendix  D: Source  Code of  the Model  2 69  1000 Z(l) = X(5)-DR IF (DABS(Z(1)).GT.O.OOIDO) GO TO 1010 AZ(1) = X(4) GO TO 1020 1010 AZ(1) = (DEXP(Z(1)*(X(l)+X(4)))  - DEXP(Z(1)*X{1))) / Z(l)  1020 Z(2) = X(6)-DR IF (DABS(Z (2) ) .GT.O.OOIDO) GO TO 1030 AZ(2) = X(4) GO TO 1040 1030 AZ(2) = (DEXP(Z(2)*(X(l)+X(4)))  - DEXP(Z(2)*X(1))) / Z(2)  1040 EVY = (X(2) * AZ(1)) - (X(3) * AZ(2)) GO TO 9999  C Type 11 functional form 1100 CALL RVSFll GOTO 9 999  (KP, K T , DR, BOTTLE, I, X,  C Type 12 functional form 1200 CALL RVSF12 GOTO 999 9  INCLUDE INCLUDE INCLUDE  'RVSFll. I N C 'RVSF12.INC' 'RVSF13.INC'  EVY)  ('Closed' Toll Highway: fixed toll)  (KP, K T , DR, BOTTLE, I, X,  9999 RETURN END  EVY)  ('Open' Toll Highway)  (KP, K T , DR, BOTTLE, I, X,  C Type 13 functional form 1300 CALL RVSF13 GOTO 9999  (Closed Toll Highway)  EVY)  Appendix  D: Source  Code of  the Model  2 70  C TanSp.POR C modified by Toshiaki Hatakama in July, 1994. C ROUTINE TO TRANSFORM CORRELATED WORK PACKAGE COSTS OR REVENUE C STREAMS TO UNCORRELATED WORK PACKAGE COSTS / REVENUE STREAMS. C this should take some sort of an offset into X to reduce the work C of copying arrays that are slightly non-standard into tempVars...  + + + +  SUBROUTINE TANSP (NM, X, Z, COR, TRI)  IMPLICIT REAL*4(A-H,0-Z) INCLUDE •DEBUG.CMN' REAL*4 X (4, *) REAL*4 Z (4, *) REAL*4 COR (NM, NM) REAL*4 TRI (NM, NM) INTEGER IPERM (300) ! just in case this is used on MAXDVR vars REAL*4 SCOR ( ) , CORR {:) REAL*4 ADIG ( , : ) , ADIGI (:,:) REAL*4 TR (:, ) REAL*4 CORRL (:,:), CORLI (:,:) ALLOCATABLE SCOR, CORR, ADIG, ADIGI, TR, CORRL, CORLI CALL TRACE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE  (3, 'TANSP',  'starting.')  (SCOR (NM)) (CORR (NM * NM)) (ADIG (NM, N M ) ) (ADIGI (NM, NM)) (TR (NM, NM)) (CORRL (NM, NM)) (CORLI (NM, NM))  DRATIO = l.OD-7 C diagonal matrix of the standard  deviations  DO 10 J=l, NM DO 10 K=l, NM IF (J == K) THEN ADIG (J, K) = X (2, J) ** 0.5D0 ELSE ADIG (J, K) = O.ODO ENDIP 10 CONTINUE  Appendix  D: Source  Code of  the Model  C correlation matrix as a 1-D array for Cholesky  2 71 decomposition  4 0 LL = NM * NM  50  DO 50 J = 1, LL CORR (J) = O.ODO LLN = NM DO 100 J DO 90 IF  -1 = 1, NM K = 1, NM (J <= K) GO TO 60  L = (LLN * K) + J - LLN CORR (L) = COR (K, J) 60 TO 9 0 60  IF (J < K) GO TO 90 L = (LLN * K) + J - LLN CORR(L) = l.ODO 90 CONTINUE 100 CONTINUE C the inverse of the diagonal matrix of standard  deviations  CALL INV (NM, NM, ADIG, IPERM, NM, ADIGI, DDET, JEXP, DCOND) IF (DDET == O.ODO) THEN WRITE (7, 9901) lERR = 1 GO TO 100 0 ENDIF C Cholesky decomposition of the correlation matrix  CALL DECOMP (CORR, NM, NM, DRATIO) IF (DRATIO <= O.ODO) THEN DO 160 J = 1, NM KK = J + 1 IF (KK <= NM) THEN DO 15 0 K = KK, NM COR (J, K) = O.ODO 150 COR (K, J) = O.ODO ENDIF 16 0 CONTINUE GO TO 4 0 ENDIF C the lower triangular matrix from the Cholesky DO 2 00 J = 1, NM DO 2 00 K = 1, NM IF (J < K) THEN CORRL (J, K) = O.ODO ELSE L = (LLN * K) + J - LLN CORRL (J, K) = CORR (L)  decomposition  Appendix  D: Source  Code of  the Model  2 72  ENDIF 2 00 CONTINUE C the inverse of the lower triangular matrix from the decomposition  CALL INV (NM, NM, CORRL, IPERM, NM, CORLI, DDET,JEXP,DCOND) IF (DDET == O.ODO) THEN WRITE (7, 9902) lERR = 1 GO TO 1000 ENDIF C the transformation matrix  CALL D6MULT  (CORLI, ADI6I, TR, NM, NM, NM)  C the inverse of the transformation matrix  CALL INV (NM, NM, TR, IPERM, NM, TRI, DDET,JEXP,DCOND) IF (DDET == O.ODO) THEN WRITE (7, 9903) lERR = 1 60 TO 1000 ENDIF C C C C C  moments of the transformed W.P costs / revenue st : Z = X (1, K) Z : transformed W.P.C/R.S X : correlated W.P.C/R.S A : the transformation matrix Z : expected value of the transformed W.P.cost or rev. str. DO 3 00 J = 1, NM Z (1, J) = O.ODO DO 3 00 K = 1, NM 300 Z (1, J) = Z (1, J) + TR (J, K) * X (1, K)  C Z (2, : second central moment of the transformed W.P.C or R.S DO 4 00 J = 1, NM SCOR (J) = O.ODO DO 400 K = 1, NM KK = K + 1 IF (KK <= NM) THEN DO 3 90 L = KK, NM 390 SCOR (J) = SCOR (J) + TR (J, K) * TR (J, L) * + COR (K, L) * + (X (2, K) * X (2, L)) ** 0.5D0 ENDIF 400 CONTINUE DO 410 J=1,NM Z (2, J) = 2.0D0 * SCOR (J) DO 410 K=1,NM 410 Z (2, J) = Z (2, J) + TR (J, K) *• 2 * X (2, K)  Appendix  D: Source  Code of  the Model  C Z (3, : third central moment of the transformed W.P.C or R.S DO 5 00 J=1,NM Z (3, J) = O.ODO DO 500 K=1,NM 500 Z (3, J) = Z (3, J) + TR (J, K) ** 3 • X (3, K) C Z (4, : fourth central moment of the transformed W.P.C or R.S DO 600 J=1,NM Z (4, J) = O.ODO DO 600 K=1,NM 600 Z (4, J) = Z (4, J) + TR (J, K) ** 4 * X (4, K) 1000 DEALLOCATE (SCOR, CORR, ADIG, ADIGI, TR, CORRL, CORLI) CALL TRACE (3, 'TANSP', 'exiting.') RETURN 9901 FORMAT{/,'INVERSION OP DIAG. MTX OF STD. DEV. FAILED.',//) 9902 FORMAT(/,'INVERSION OF LOWER TRIANGULAR MTX FAILED.',//) 9903 FORMAT(/,'INVERSION OF THE TRANSFORMATION MTX FAILED.',//) END  2 73  Appendix  D: Source  Code of  the Model  2 74  C CdFunc.FOR C modified by Toshiaki Hatakama in July 1994  C ROUTINE TO OBTAIN VALUES OF THE CUMULATIVE DISTRIBUTION C FUNCTION OF A DEPENDENT VARIABLE APPROXIMATED BY A PEARSON C TYPE DISTRIBUTION. 0============================================================ SUBROUTINE CDPUNC (PEARSN, + AM,SD,SK,AK, + VA,VB,VC,VD,VE,VF,VG, + VM, + VT,VU,VV,VW,VX,VY,VZ) C============================================================ IMPLICIT REAL*4(A-H,0-Z) INCLUDE "DEBUG.CMN' REAL*4 PEARSN (NPEARS,*) CALL TRACE  (3, •CDFUNC•,  'starting.')  C select the pearson distribution that best approximates the C shape characteristics of the dependent variable. C the beta2 values for the lower bound of betal DO 40 YS YK IF  40  PINDEX = 1,NPEARS = SK - PEARSN (PINDEX, 16) = AK - PEARSN (PINDEX, 17) (O.ODO <= YS .AND. YS < O.IDO) THEN IP (O.ODO <= YK .AND. YK < O.IDO) GO TO 5 0 ENDIF CONTINUE GO TO 200  C lower bound of betal fits a pearson type 50  distribution  RSKW = YS RKRT = YK  C is the lower bound of betal the last value YCHK = PEARSN (PINDEX + 1, 16) - PEARSN IF (O.OOOIDO < YCHK) GO TO 200 lYl = PINDEX IY2 = PINDEX + 1  (PINDEX, 16)  C the beta2 values for the upper bound of the betal DO 90 ZS ZK IF  PINDEX = 1,NPEARS = PEARSN (PINDEX,16) - SK = AK - PEARSN (PINDEX,17) (O.ODO <= ZS .AND. ZS < O.IDO) THEN IF (O.ODO <= ZK .AND. ZK < O.IDO) GO TO 100  Appendix 90  D: Source  Code of  the  275  Model  ENDIF CONTINUE GO TO 2 00  C upper bound of betal fits a pearson type distribution C redo with arrays, then this becomes a simple loop C is the upper bound of betal the last value 100  ZCHK = PEARSN (PINDEX+1, 16) - PEARSN IP (O.OOOIDO < ZCHK) GO TO 200 IZl = PINDEX IZ2 = PINDEX + 1  (PINDEX, 16)  C interpolate the percentage points and evaluate values of the C cumulative distribution function of the dependent variable. C redo with arrays, then this becomes a simple loop. Call IntPol  (Pearsn,RSKW,RKRT,lYl,IY2,IZ1,IZ2,<n>,SD,AM,V<n>) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 , 1,SD,AM,VA) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 , 2 ,SD,AM,VB) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 , 3 ,SD,AM,VC) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 , 4,SD,AM,VD) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 , 5 ,SD,AM,VE) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 , 6,SD,AM,VF) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 , 7 ,SD,AM,VG) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 , 8,SD,AM,VM) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 , 9,SD,AM,VT) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 ,10 ,SD,AM,VU) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 ,11 ,SD,AM,VV) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 ,12 ,SD,AM,VW) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 ,13 ,SD,AM,VX) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 ,14 ,SD,AM,VY) INTPOL (PEARSN, RSKW, RKRT, lYl, IY2, IZl, IZ2 ,15 ,SD,AM,VZ)  CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL CALL  GO TO 3 00 C the normal distribution is used as the default 200  VA VB VC VD VE VF VG VM VT VU VV VW VX VY VZ  = = = = = = = = = = = = = = =  AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM  -  (2.8070D0 (2.5758D0 (2.3263D0 (1.9600D0 (1.6449D0 (1.2816D0 (0.6745D0  * * * * * * *  SD) SD) SD) SD) SD) SD) SD)  + + + + + + +  (0.6745D0 (1.2816D0 (1.6449D0 (1.9600D0 (2.3263D0 (2.5758D0 (2.8070D0  * * * * * * *  SD) SD) SD) SD) SD) SD) SD)  distribution  Appendix D: Source Code of the Model 300 CALL TRACE (3, 'CDFUNC•, 'exiting,') RETURN END INCLUDE  'INTPOL.INC  21S  Appendix  D: Source  Code of  the  Model  C Inv.MJW C modified by Toshiaki Hatakama in July, 1994. C this optimized version tests for the special case of a diagonal C matrix. C A can be as large as it likes, we only access up to [N,N]... 0================================================================= SUBROUTINE INV (N, NDIMT, Tl, IP, NDIMA, A, DET, lEXP, COND) 0================================================================= IMPLICIT REAL*4 (A-H,0-Z) REAL*4 A (NDIMA, NDIMA), Tl INTEGER IP (*) C copy T1[N,N]  (NDIMT, NDIMT)  into A  DET = l.DO lEXP = 0 COND = O.ODO ISDIAG = 1 DO 30 J=1,N DO 30 1=1,N A (I, J) = Tl  (I, J)  IF  (I == J .AND. A (I, J) == O.ODO) THEN ISDIAG = 0 ELSE IF (I .NE. J .AND. A (I, J) .NE. O.ODO) THEN ISDIAG = 0 ENDIF ENDIF 3 0 CONTINUE IF IF  (N == 1) GO TO 1991 (ISDIAG == 1) GOTO 1993  C first part of Cond CSUMA=0.D0 DO 45 J=1,N DO 45 1=1,N 45 CSUMA = CSUMA + A(I,J) ** 2 C inversion  starts  DO 199 K=1,N C find maximum element in K*th AMAX=DABS(A(K,K)) IMAX=K  column  111  Appendix D: Source Code of the Model IF(K.EQ.N) GO TO 65 50 KP=K+1 DO 60 I=KP,N AIK=DABS{A(I,K)) IF (AIK.LE.AMAX) GO TO 60 55 AMAX=AIK IMAX=I 60 CONTINUE C test for singularity 65  IP (AMAX == O.DO) GO TO 300  C interchange rows K and IMAX IP (K) = IMAX IF (K.EQ.IMAX) GO TO 100 DET=-DET C compute the determinant, and scale as appropriate. 100  DET = DET * A (IMAX, K) IP  (1,0D15 < DABS (DET)) THEN DET = DET * l.OD-15 lEXP = lEXP + 15 ENDIF IP  (DABS (DET) < l.OD-15) DET = DET * 1.0D15 lEXP = lEXP - 15 ENDIF  THEN  C divide K*th row by A(K,K) 750  T=1./A(IMAX,K) A(IMAX,K)=A(K,K) A(K,K)=-1.0D0  DO 1999 1=1,N A(I,K)=-A(I,K)*T 19 9 9 CONTINUE DO 144 J=1,N IF (J == K) GO TO 144 C interchange rows K and IMAX TEMP=A(IMAX,J) IF (K.EQ.IMAX) GO TO 140 A(IMAX,J)=A(K,J) 75 A(K,J)=TEMP C divide K*th row by A(K,K) 140  A(K,J)=TEMP*T  C subtract A(I,K) times K*th row from other rows  2 78  Appendix  D: Source  Code of  the Model  DO 109 I = 1, N IF (I .NE. K) THEN A (I, J) = A (I, J) + TEMP * A (I, K) ENDIF 10 9 CONTINUE 144 CONTINUE 19 9 CONTINUE C restore proper column order in the inverse NM1=N-1 DO 250 KK=1,NM1 C column now in K*th position actually column  210  K=N-KK J=IP(K)  C ... of the inverse. Therefore... IF  (J == K) GO TO 250  C relocate column K to position J 220  DO 225 1=1,N T=A(I,J) A ( I , J)=A{I,K) A(I,K)=T 225 CONTINUE 2 50 CONTINUE  C calculate COND 260 CSUMB = O.ODO DO 270 J = 1, N DO 270 I = 1, N 2 70 CSUMB = CSUMB + A (I, J) ** 2 275 COND = DSQRT RETURN  (CSUMA * CSUMB) / FLOAT (N)  C procedure for singular or nearly singular matrix. 300 WRITE(6,310) K,AMAX 310 FORMAT (IHO,'STEP•,13,' PIVOT =',D18.8,', is singular?') DET=0.ODO IEXP=0 COND=0.0D0 RETURN C *** CODE FOR ORDER 1 1991 IF (A (1, 1) == O.ODO) GO TO 1992 DET=A(1,1) A(l,l)=1.D0/A{1,1) COND=1.0D0 RETURN  2 79  Appendix  D: Source  Code of  the Model  1992 K=l AMAX=0.ODO GO TO 3 00  C the INV of a DIAGonal matrix is trivial... I think. 1993 SUMA = O.ODO SUMB = O.ODO DO 1994 J = 1, N A (J, J) = l.ODO / Tl (J, J) DET = DET * Tl (J, J) SUMA = SUMA + Tl (J, J) *• 2 SUMB = SUMB + A (J, J) ** 2 IF  (1.D15 < DABS (DET)) THEN DET = DET * l.OD-15 lEXF = lEXP + 15 END IF IF  (DABS (DET) < l.OD-15) DET = DET * 1.0D15 lEXP = lEXP - 15 ENDIF 1994 CONTINUE COND = DSQRT RETURN END  THEN  (SUMA * SUMB) / FLOAT (N)  2 80  Appendix  V: Source  Code of  the Model  2 81  C Decomp.FOR C modified by Toshiaki Hatakama in July, 1994. C THIS ROUTINE DECOMPOSES A TO A=L*LTRANSPOSE VIA CHOLESKI METHOD. C============================================================ SUBROUTINE DECOMP (A, N, M, RATIO) C============================================================ IMPLICIT REAL*4 (A-H,0-Z) REAL*4 A(*) CALL TRACE  (3, 'DECOMP',  'starting.')  MM=M-1 NM=N*M NM1=NM-MM 3001 MP=M+1 C C C C C  transformation of A. A is transformed into a lower triangular matrix L such that A=L.LT (LT=transpose of L . ) . error return taken if RATI0<l.E-7 KK = 2 NCN=0 DET=1.D0 FAC=RATIO BIGL=DSQRT(A(1)) SML=BIGL IF IF  15  (M == 1) GO TO 101 (O.ODO < A(l)) GO TO 15  NR0W=1 RATI0=A(1) GO TO 6 0 DET=A(1) A(l)=SML A(2)=A{2)/A(1) TEMP=A(MP)-A(2)*A(2) IF (TEMP <= O.ODO) RATIO=TEMP IF (O.ODO < TEMP) GO TO 21 NR0W=2 GO TO 6 0  101  DO 102 1=1,N TEMP=A(I) DET=TEMP*DET IF IF  (TEMP <= O.ODO) GO TO 104 (DET < 1.D15) GO TO 1144  Appendix  D: Source  Code of  the Model  DET=DET*1.D-15 NCN=NCN+15 GO TO 1145 1144  IF (l.OD-15 < DET) GO TO 1145 DET=DET*1.D15 NCN=NCN-15  1145  CONTINUE A(I)=DSQRT(TEMP) IF (BIGL < A(I)) BIGI.=A(I) IF (A(I) < SML) SML=A(I) CONTINUE  102  GO TO 52 104 10 3  RATIO=TEMP NROW=I GO TO 6 0  21  A(MP)=DSQRT(TEMP) DET=DET*TEMP IF (BIGL < A(MP)) BIGL=A(MP) IF (A(MP) < SML) SML=A(MP) IF (N == 2) GO TO 52 MP=MP+M DO 62 J=MP,NM1,M JP=J-MM MZC = 0 IF(M <= KK) GO TO 1 KK=KK+1 11 = 1 JC = 1 GO TO 2  1  KK=KK+M II=KK-MM JC=KK-MM  2  DO 65 I=KK,JP,MM IF (A(I) == O.ODO) GO TO 64 GO TO 6 6 JC=JC+M MZC=MZC+1  64 65  66  ASUM1=0.DO GO TO 61 MMZC=MM*MZC 1I=II+MZC KM=KK+MMZC A(KM)=A(KM)/A(JC) IF(JP <= KM) GO TO 6 KJ=KM+MM DO 5 I=KJ,JP,MM  2 82  Appendix  7 5 6 4 61  D: Source  Code of  the Model  ASUM2=0.DO IM=I-MM 11=11+1 KI=II+MMZC DO 7 K=KM,IM,MM ASUM2=ASUM2+A(KI)*A(K) KI=KI+MM A(I)=(A(I)-ASUM2)/A(KI) ASUM1=0.D0 DO 4 K=KM,JP,MM ASUM1=ASUM1+A(K)*A(K) S=A(J)-ASUMl IF (S < O.ODO) RATIO=S IF (O.DO < S) GO TO 63 NROW=(J+MM)/M GO TO 6 0 63 A(J)=DSQRT(S) DET=DET*S IF (l.D-15 < DET) GO TO 144 DET=DET*1.D+15 NCN=NCN-15 GO TO 145 144 IF (DET < l.D+15) GO TO 145 DET=DET*1.D-15 NCN=NCN+15 145 CONTINUE IF (BIGL < A(J)) BIGL=A(J) IF (A(J) < SML) SML=A(J) 62 CONTINUE 52 IF (SML <= FAC*BIGL) GO TO 54 GO TO 53 54 RATIO=0.D0 GOTO 1000 60 PRINT *, "System is NOT POSITIVE DEFINITE in row", NROW GOTO 1000  53 RATIO=SML/BIGL 1000 CALL TRACE (3, 'DECOMP', RETURN END  'exiting.')  2 83  Appendix  D: Source  Code of  the Model  2 84  C DgMMJW.FOR C modified by Toshiaki Hatakama in July, 1994.  SUBROUTINE DGMULT (A, B, C, lAROWS, IBROWS, IBCOLS) 0============================================================ REAL*4 A (lAROWS, IBROWS) REAL*4 B (IBROWS, IBCOLS) REAL*4 C (lAROWS, IBCOLS) INTEGER I, J, K, lAO, IBO lAO = 0 ! this will contain the number of zero entries in A DO 2 I = 1, lAROWS DO 1 K = 1, IBROWS IF (A (I, K) == O.ODO) lAO = lAO + 1 1 CONTINUE DO 2 J = 1, IBCOLS C (I, J) = O.ODO 2 CONTINUE IBO = 0 ! this will contain the number of zero entries in B DO 3 J = 1, IBCOLS DO 3 K = 1, IBROWS IF (B (K, J) == O.ODO) IBO = IBO + 1 3 CONTINUE  C C C C  we have a decision to make, which order should we do the calcs in? it is possible (probable) that it won't make any difference, but it could. so, which path will result in the most savings...? IF  {(IBO * lAROWS) <= (lAO * IBCOLS)) THEN  C there are more  (or just as many) zero-product-reductions  in A.  DO 5 I = 1, lAROWS DO 5 K = 1, IBROWS TEMP = A (I, K) IF (TEMP .NE. O.ODO) THEN DO 4 J = 1, IBCOLS 4 C (I, J) = C (I, J) + (TEMP * B (K, J) ) ENDIF 5 CONTINUE ELSE C there are more zero-product-reductions C stead. DO 7 J = 1, IBCOLS DO 7 K = 1, IBROWS TEMP = B (K, J) IF (TEMP .NE. O.ODO) THEN  in B, so use that way in  Appendix  D: Source Code of the Model DO 6 I = 1, lAROWS 6 C (I, J) = C (I, J) + (A {I, K) * TEMP ) ENDIF 7 CONTINUE ENDIF RETURN END  2 85  Appendix D: Source  Code of  the  Model  C Early.FOR C modified by Toshiaki Hatakama in July,  C C C C C C C  2 86  1994.  ROUTINE TO EVALUATE THE FIRST FOUR MOMENTS OF A PATH EARLY START TIME BY UNCORRELATING THE WORK PACKAGE DURATIONS. 'Suggested' enhancement, redo the defs of LIST & LISREP so that they can be passed interchangeably to EARLY, then forget LID, cause then it's useless. It's only function is to choose between the two. That's it. If one is used, the other is ignored.  0==============================================================:== SUBROUTINE EARLY (J, + LN, + LP, + LID, ! choose between LIST or LISREP + WPTIME, CORRD, + ESTART, + LIST, LISREP) ! two tables with similar information.... 0================================================================= IMPLICIT REAL*4{A-H,0-Z) INCLUDE 'DEBUG.CMN' INTEGER LN, LP, LID REAL*4 WPTIME (4, * ) , CORRD (NWP, *) REAL*4 ESTART (4, *) INTEGER LIST (200, 4 0 ) , LISREP (101, 40) REAL*4 COR (:,:), TRI (:,:), PD (:), X (:,:), Z (:,:) ALLOCATABLE COR, TRI, PD, X, Z CALL TRACE ALLOCATE ALLOCATE  31  32  (3, 'EARLY',  'starting.')  (COR (LP, L P ) , TRI (LP, L P ) , PD (X (4, L P ) , Z (4, LP))  DO 32 K = 1, LP DO 31 L = 1, 4 Z (L, K) = O.ODO DO 32 L = 1, LP IF (K == L) THEN COR (K, K) = l.ODO ELSE COR (L, K) = O.ODO ENDIF TRI (L, K) = O.ODO DO 120 K = 1, LP IF (LID == 1) THEN Jl = LIST (LN, K) ELSE Jl = LISREP (LN, K) ENDIF  (LP))  Appendix  D: Source  Code of  X (1, K) = WPTIME X (2, K) = WPTIME X (3, K) = WPTIME X (4, K) = WPTIME MM = K + 1 IF (MM <= LP) DO 110 M = IF (LID J2 = ELSE J2 = ENDIF  the Model  2 87  (1, Jl) (2, Jl) (3, Jl) (4, Jl)  THEN MM,LP == 1) THEN LIST (LN, M) LISREP  (LN, M)  COR (K, M) = CORRD (Jl, J2) COR (M, K) = COR (K, M) CONTINUE ENDIF CONTINUE  110 12 0  C transform correlated W . P . durations to uncorrelated  durations  CALL TANSP (LP, X, Z, COR,TRI) IF (0 < lERR) GOTO 500 C first partial deravatives of the transformed W.P durations. DO 150 K = 1, LP PD (K) = O.ODO DO 150 M = 1, LP 150 PD (K) = PD (K) + TRI (M, K) C first four moments of a path early start DO 190 K = 1, ESTART (1, ESTART (2, ESTART (3,  LP J) = ESTART J) = ESTART J) = ESTART  time  (1, J) + PD (K) * Z (1, K) (2, J) + PD (K) ** 2 * Z (2, K) (3, J) + PD (K) ** 3 • Z (3, K)  FC = O.ODO MM = K + 1 IF  180 +  190  (MM <= LP) THEN DO 180 M = MM, LP FC = FC + 6.0D0 * (PD (K) * PD (M) ) ** 2 * Z (2, K) * Z (2, M) ENDIF ESTART  500 DEALLOCATE CALL TRACE RETURN END  (4, J) = ESTART  (4, J) + FC + PD (K) ** 4 * Z (4, K)  (TRI, COR, PD, X, Z) (3, 'EARLY', 'exiting.')  Appendix  D: Source  Code of  the Model  2 88  C EstMMT.FOR C modified by Toshlakl Hatakama In July, 1994  C ROUTINE TO APPROXIMATE THE FIRST FOUR MOMENTS FOR EARLY START C TIME WHEN THE MODIFIED PNET ALGORITHM IS USED.  + +  SUBROUTINE ESTMMT{JPV, PEARSN, D,E,G,M,T,V,W, ESTART)  IMPLICIT REAL*4{A-H,0-Z) INCLUDE •DEBUG.CMN' REAL*4 PEARSN (NPEARS, *) REAL*4 D ( * ) , E ( * ) , G ( * ) , M ( * ) , T { * ) , V { * ) , W(*) REAL*4 ESTART (4,*) C expected value of early start CALL TRACE DEL ESTART  (3, "ESTMMT',  time 'starting')  = V (JPV) + E (JPV) - 2.0D0 * M (JPV) (1, JPV) = M (JPV) + 0.185D0 * DEL  C Standard deviation of elements V & E C parameters 3.25D0, O.OOOIDO, 3.29D0, O.IOODO,  3.08D0  K =2 SIGML = O.ODO SIGMl = (V (JPV) - E (JPV)) / 3.25D0 50  IF (590 < K) GO TO 9999 XSI6M1 = SIGMl - SIGML XCHEKl = SIGML * O.OOOIDO IF (DABS(XSIGMl) < DABS(XCHEKl)) GOTO 70 K = K+1 SIGML = SIGMl SIGMl = (V (JPV) - E (JPV)) / + DMAXl (3.29D0 - O.IOODO * (DEL / SIGML) ** 2, 3.08D0) GO TO 5 0  70  ASIGMl = SIGMl  C standard deviation of elements W & D C parameters 3.92D0, O.OOOIDO, 3.98D0, 0.138D0, K =2 SIGML = O.ODO SIGM2 = (W (JPV) - D (JPV)) / 3.92D0  3.66D0  Appendix 80  D: Source  Code of  the Model  2 89  IF (590 < K) GO TO 9999 XSIGM2 = SI6M2 - SI6ML XCHEK2 = SIGML * O.OOOlDO IF (DABS (XSIGM2) < DABS (XCHEK2)) GO TO 100 K = K+1 SIGML = SI6M2 SIGM2 = (W (JPV) - D (JPV)) / + DMAXl (3.98D0 - 0.138D0 GO TO 8 0  100  * (DEL / SIGML) ** 2, 3.66D0)  ASIGM2 = SI6M2  C OK, which SD is greater??? SIGMAD  = DMAXl  (ASIGMl, ASIGM2}  C use that one to scale the vector for the pearson ESTART  (2, JPV)  comparison  = SIGMAD ** 2  X4 X5  = (D (JPV) - ESTART = (E (JPV) - ESTART  (1, JPV)) / SIGMAD (1, JPV)) / SIGMAD  X7 X8 X9  = (G (JPV) - ESTART = (M (JPV) - ESTART = (T (JPV) - ESTART  (1, JPV)) / SIGMAD (1, JPV)) / SIGMAD (1, JPV)) / SIGMAD  Xll X12  = (V (JPV) - ESTART = (W (JPV) - ESTART  (1, JPV)) / SIGMAD (1, JPV)) / SIGMAD  C compare standardized values to those from the pearson RLOW = 10.0 DO 150 K = 1, SUMSQR = ( + + + + + + + + + + + +  NPEARS (PEARSN (PEARSN (PEARSN (PEARSN (PEARSN (PEARSN (PEARSN  (K, 4) (K, 5) (K, 7) (K, 8) (K, 9) (K,ll) (K,12)  -  X4 ) X5 ) X7 ) X8 ) X9 ) Xll) X12)  ** 2 ** 2 ** 2 ** 2 ** 2 ** 2 *• 2) ! ** 0.5  IF  150  (SUMSQR < RLOW) THEN RLOW = SUMSQR BETAl = PEARSN (K, 16) BETA2 = PEARSN (K, 17) ENDIF CONTINUE IP  table  (0.0225D0 < RLOW) GO TO 9999  C third and fourth moments for work package EST  Appendix  D: Source  ESTART ESTART  Code of  the  Model  (3, JPV) = BETAl * (ESTART (2, JPV) ** 1.5) (4, JPV) = BETA2 * (ESTART (2, JPV) ** 2)  25 0 CONTINUE CALL TRACE RETURN  (3, 'ESTMMT',  'exiting.')  C default to a normal distribut ion 9999  ESTART (3, JPV) = O.ODO ESTART (4, JPV) = 3 . ODO * (ESTART (2, JPV) ** 2) GO TO 2 50 END  290  Appendix C C C C C C  D: Source  Code of  the  Model  RvSfll.INC 07mar94 MJW rationalization of the functions Closed System (Manual Collection) we ask nicely for the money from the motorist!  SUBROUTINE RVSFll (KP, KT, DR, BOTTLE, I, X, Y) IMPLICIT REAL*4(A-H,0-Z) INCLUDE 'DEBUG.CMN' REAL*4 BOTTLE  (NRS, * ) ,  X  (*)  REAL*4 Y,AY,AZ,BZ,Z REAL*4 mcbpl(50),mcoll(50),ots(50) REAL*4 ooo(50),oom(50),reve(50) REAL*4 tcmt(50),tccc(50),tccm(50),brco{50),obo(50),ho(50) REAL*4 malnt(50),oper(50),aoper(50) REAL*4 XI(200),X2(200) REAL*4 cost (:,:,:,:), traf (:,s,:,:) REAL*4 tec (:,:), tcm (:,:), Cts (:,:) ALLOCATABLE cost, traf, tcc, tcm, cts  CALL TRACE nAL nP nWC nOL nBR  = = = = =  rlBY IRD  BOTTLE BOTTLE BOTTLE BOTTLE BOTTLE  (2, 'RVSFll', (I, (I, (I, (I, (I,  'starting,')  1) 2) 3) 4) 5)  = X (1) = NINT (X (2))  ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE  (cost (traf (tcc (tcm (cts  DISCI RATEl  X (3) X (4)  DISC2 RATE2  X (5) X (6]  perKM entFee  X (7) X (8)  (IRD, (IRD, (IRD, (IRD, (IRD,  DO 90 11=1,IRD DO 90 J=l,nAL-l travld = 0  nAL, nAL, nP)) nAL, nAL, nP)) nAL)) nAL)) nAL))  291  Appendix  D: Source  Code of  the Model  2 92  DO 90 K=J+l,nAL travld = travld + X(7+K) breakl = 0 break2 = 0 IP (DISCI < travld) THEN breakl = travld - DISCI travld = DISCI ENDIF IF (DISC2 < (travld + breakl)) THEN break2 = (travld + breakl) - DISC2 breakl = (DISC2 - DISCI) ENDIF  90 + +  DO 90 L=l,nP cost(II,J,K,L) = ((travld + (breakl * RATEl) + (break2 * RATE2)) * perKM * X(7+nAL+L) + entFee) * X(7+nAL+nP+II)  CALL TRACE  (3, 'RVSFll',  'traffic volume  calculation.')  DO 1150 11=1,IRD M=0 DO 1150 J=l,nAL-l DO 1150 K=J+l,nAL DO 1150 L=l,nP M=M+1 1150 traf (II,J,K,L)= + X(7+nAL+nP+ 2 * IRD+M ) * + X(7+nAL+nP+ IRD+II) / + X(8+nAL+nP+ IRD ) CALL TRACE  (3, 'RVSFll',  'annual toll revenue...')  DO 1470 11=1,IRD reve (II) = 0.00 DO 1470 J=l,nAL DO 1470 K=J+l,nAL DO 1470 L=l,nP 1470 reve (II) = reve (I) + traf (II,J,K,L)*cost  + (II,J,K,L)*365  LI = 7 + nAL + nP + 2*IRD + nAL*(nAL-1)/2*nP CALL TRACE  + +  (3, 'RVSFll',  'fixed  costs...')  mere = ! road cleaning costs X(L1+13)*(X(L1+1) + X(Ll+4) + X(Ll+7)) + X(Ll+14)*(X(Ll+2) + X(Ll+5) + X(Ll+8) + X(Ll+3) + X(Ll+6) + X(Ll+9))  mcrm = ! road maintenance + X(L1+15)*X(Ll+7) + X(L1+16)*X(Ll+8)  + X(Ll+17)*X(Ll+9)  mcl = ! lighting + X(L1+18)*(X(L1+1) + X(Ll+7)) + + X(L1+19)*( (X(Ll+2) + X(Ll+3)) + (X(Ll+8) + X(Ll+9)))  Appendix  D: Source  Code of  the Model  2 93  mcbr = ! bridge repair + X(Ll+20)*X(L1+1) + X(L1+21)*X(Ll+2)  + X(Ll+22)*X(Ll+3)  mcbp = ! bridge painting X(Ll+23)*X(L1+1) + X(Ll+24)*X(Ll+2)  + X(Ll+25)*X(Ll+3)  +  mctm = ! tunnel maintenance + X(L1+10)*X(Ll+26) + X(L1+11)*X(Ll+27)  + X(Ll+12)*X(Ll+28)  SELECT CASE (nWC) ! snow and ice control based on nWC CASE (1) mcsc = + X(Ll+29)*( (X(L1+1) + X(Ll+4) + X(Ll+7)) + +2*(X(Ll+2) + X(Ll+5) + X(Ll+8)) + +3*(X(Ll+3) + X(Ll+6) + X(Ll+9)) ) CASE (2) mcsc = + X(Ll+30)*( (X(L1+1) + X(Ll+4) + X(Ll+7)) + +2*(X(Ll+2) + X(Ll+5) + X(Ll+8)) + +3*(X(Ll+3) + X(Ll+6) + X(Ll+9)) ) CASE DEFAULT mcsc = 0.00 END SELECT  mcol = ! overlay + X(L1+31)*( X(L1+1) + X(Ll+4) + X(Ll+7) ) + + X(Ll+32)*( X(Ll+2) + X(Ll+5) + X(Ll+8) ) + + X(Ll+33)*( X(Ll+3) + X(Ll+6) + X(Ll+9) ) moot = X (LI + 34) * (mere + mcrm + mcl + mcbr + mctm + mcsc) DO 2295 11=1,IRD IF (lI.EQ.nBR .OR. II.EQ.(nBR+7) .OR. II.EQ.(nBR+14) + .OR. lI.EQ. (nBR + 21) .OR. II.EQ. (nBR + 28) .OR. + lI.EQ. (nBR + 35) .OR. II.EQ. (nBR + 42) .OR. + lI.EQ. (nBR + 49) ) THEN mcbpl(II) = mcbp ELSE mcbpl(II) = 0.00 END IF IF (lI.EQ.nOL .OR, lI.EQ.(nOL+12) .OR. II.EQ.(nOL+24) + .OR, lI.EQ.(nOL+36) ,OR. II,EQ.(nOL+48)) THEN mcoll(II) = mcol ELSE mcoll(II) = 0.00 END IF 2295 CONTINUE C OPERATION  COSTS  CALL TRACE  (3, 'RVSFll',  C C Operation office  overhead  'operation  costs...')  Appendix  D: Source  Code of  the Model  2 94  C DO 2500 11=1,IRD M=0 X2(II) = X(7+nAL+nP+IRD+II) XOO = 7+nAL+nP+IRD+II DO 2500 J=l,nAL-l DO 2500 K=J+l,nAL DO 2500 L=l,nP M=M+1 XO = 7+nAL+nP+2*IRD+M XI(M) = X(X0) IF (KP == XO) THEN IF (KT == 1) THEN XI(M) = X(X0)/0.99 ELSE IF (KT == 3) THEN X1(M) = X{X0)/1.01 END IF ELSE IF (KP == XOO) THEN IF (KT == 1) THEN X2 (II) = X(X00)/0.99 ELSE IF (KT == 3) THEN X2 (II) = X(X00)/1.01 END IF END IF 2500  3420 343 0 3440 3450  traf  (II,J,K,L)= XI(M) * X2(II) / X2(l)  DO 3450 11=1,IRD Ots (II)=0.00 DO 3440 J=l,nAL-l DO 3430 K=J+l,nAL DO 3420 L=l,nP ots(II)=ots{II)+traf(II,J,K,L) CONTINUE CONTINUE CONTINUE CONTINUE  DO 3485 11=1,IRD o o o d i ) =0 C treated traffic is half of through ots(II)=ots(II)*0.5 X3 X4 X5 X6 X7  = = = = =  X(L1 X(L1 X(L1 X(L1 X(L1  + + + + +  40) 46) 52) 58) 64)  IF  (KP == Ll+40) THEN IF (KT == 1) THEN X3 = X(Ll+40)/0.99 ELSE IF (KT == 3) THEN X3 = X(Ll+40)/1.01 END IF  traffic  Appendix  D: Source  Code of  the Model  ELSE IF (KF == Ll+46) THEN IF (KT == 1) THEN X4 = X(Ll+46)/0.99 ELSE IF (KT == 3) THEN X4 = X(Ll+46)/l.Ol END IF ELSE IF (KP == Ll+52) THEN IF (KT == 1) THEN X5 = X(Ll+52)/O.99 ELSE IF (KT == 3) THEN X5 = X(Ll+52)/l.Ol END IF ELSE IF (KP == Ll+58) THEN IF (KT == 1) THEN X6 = X(Ll+58)/0.99 ELSE IF (KT == 3) THEN X6 = X(Ll+58)/l.Ol END IF ELSE IF (KP == Ll+64) THEN IF (KT == 1) THEN X7 = X(Ll+64)/0.99 ELSE IF (KT == 3) THEN X7 = X(Ll+64)/l,01 END IF END IF  1  1  1  1  1  1  3485  IF (ots(II) .LE.X3) THEN ooo(ll)=X(L1+41)*X(Ll+3 5)+X(Ll+4 2)*X(Ll+3 6)+X(Ll+43) *X(Ll+37)+X(Ll+44)*X(Ll+38)+X(Ll+4 5)*X(Ll+39) O o m d l ) =X(L1 + 41) +X(Ll + 42) +X(Ll + 43) +X(Ll+44) +X(Ll + 45} ELSE IF(otS(II).LE.X4) THEN ooo(II)=X(Ll+47)*X(Ll+3 5)+X(Ll+4 8)*X(Ll+3 6)+X(Ll+4 9) *X(Ll+37)+X(Ll+50)*X(Ll+38)+X(Ll+51)*X(Ll+39) oom(ll)=X(Ll+47)+X(Ll+4 8)+X(Ll+4 9)+X(Ll+50)+X(Ll+51) ELSE IF(otS(II).LE.X5) THEN ooo(ll)=X(Ll+53)*X(Ll+35)+X(Ll+54)*X(Ll+36)+X(Ll+55) *X(Ll+37)+X(Ll+56)*X(Ll+38)+X(Ll+57)*X(Ll+39) o o m d l ) =X(Ll + 53)+X(Ll + 54)+X(Ll + 55)+X(Ll + 56)+X(Ll + 57) ELSE IF(otS(II).LE.X6) THEN ooo(ll)=X(Ll+59)*X(Ll+35)+X(Ll+60)*X(Ll+36)+X(Ll+61) *X(Ll+3 7)+X(Ll+6 2)*X(Ll+38)+X(Ll+63)*X(Ll+39) o o m d l ) =X(Ll + 59)+X(Ll + 60)+X(Ll + 61)+X(Ll + 62)+X(Ll + 63) ELSE IF(otS (II) .LE.X7) THEN ooo(ll)=X(Ll+65)•X(Ll+3 5)+X(Ll+66)*X(Ll+3 6)+X(Ll+67) *X(Ll+37)+X(Ll+68)*X(Ll+3 8)+X(Ll+6 9)*X(Ll+3 9) o o m d l ) =X(Ll + 65)+X(Ll + 66)+X(Ll + 67)+X(Ll + 68)+X(Ll + 69) ELSE ooo(ll)=X(Ll+70)*X(Ll+35)+X(Ll+71)*X(Ll+36)+X(Ll+72) *X(Ll+3 7)+X(Ll+7 3)*X(Ll+3 8)+X(Ll+74)*X(Ll+3 9) oom(II)=X(Ll+70)+X(Ll+71)+X(Ll+72)+X(Ll+73)+X(Ll+74) END IF CONTINUE  C C CONSIGNMENT COSTS OF TOLL COLLECTION  2 95  Appendix D: Source  Code of the Model  C  3510 3520 353 0 3540 3550  DO 3550 11=1,IRD DO 3540 M=l,nAL cts(II,M)=0,00 DO 3530 J=l,nAL-l DO 3520 K=J+l,nAL DO 3510 L=l,nP IF(J.EQ.M .OR. K.EQ.M) THEN cts(II,M)=cts(II,M)+traf(II,J,K,L) ELSE Cts(II,M)=Cts (II,M) END IF CONTINUE CONTINUE CONTINUE CONTINUE CONTINUE DO 3790 11=1,IRD DO 3780 M=l,nAL tec(II,M)=0 X8 X9 XIO Xll X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X21 X21 X21 IF  = = = = = = = = = = = = = = = = =  X(L1 + 76) X(L1 + 78) X(L1 + 80) X{L1 + 82) X(L1 + 84) X(L1 + 86) X(L1 + 88) X(L1 + 90) X(L1 + 92) X(L1 + 94) X(L1 + 96) X(L1 + 98) X(L1 + 100) X(L1 + 102) X(L1 + 104) X(L1 + 106) X(L1 + 108)  (KP == Ll+76) THEN IF (KT == 1) THEN X8 = X(Ll+76)/0.99 ELSE IF (KT == 3) THEN X8 = X{Ll+76)/1.01 END IF ELSE IF (KP == Ll+78) THEN IF (KT == 1) THEN X9 = X(Ll+78)/0.99 ELSE IF (KT == 3) THEN X9 = X(Ll+78)/l.Ol END IF ELSE IF (KP == Ll+80) THEN IF (KT == 1) THEN XIO = X(Ll+80)/0.99 ELSE IF (KT == 3) THEN  2 96  Appendix D: Source  Code of  the Model  XIO = X(Ll+80)/l.Ol END IF ELSE IF (KP == Ll+82) THEN IF (KT == 1) THEN Xll = X(Ll+82)/0.99 ELSE IF (KT == 3} THEN Xll = X(Ll+82)/l.Ol END IF ELSE IF (KP == Ll+84) THEN IF (KT == 1) THEN X12 = X(Ll+84)/0.99 ELSE IF (KT == 3) THEN X12 = X(Ll+84)/1.01 END IF ELSE IF (KP == Ll+86) THEN IF (KT == 1) THEN X13 = X(Ll+86)/O,99 ELSE IF (KT == 3) THEN X13 = X(Ll+86)/l.Ol END IF ELSE IF (KP == Ll-)-88) THEN IF (KT == 1) THEN X14 = X(Ll+88)/0.99 ELSE IF (KT == 3) THEN X14 = X(Ll+88)/l.Ol END IF ELSE IF (KP == Ll+90) THEN IF (KT == 1) THEN X15 = X(Ll+90)/0.99 ELSE IF (KT == 3) THEN X15 = X(Ll+90)/1.01 END IF ELSE IF (KP == LlH-92) THEN IF (KT == 1) THEN X16 = X(Ll+92)/0.99 ELSE IF (KT == 3) THEN X16 = X{Ll+92)/1.01 END IF ELSE IF (KP == Ll+94) THEN IF (KT == 1) THEN X17 = X{Ll+94)/0.99 ELSE IF (KT == 3) THEN X17 = X(Ll+94)/l.Ol END IF ELSE IF (KP == Ll+96) THEN IF (KT == 1) THEN X18 = X(Ll+96)/0.99 ELSE IF (KT == 3) THEN X18 = X(Ll+96)/l.Ol END IF ELSE IF (KP == Ll+98) THEN IF (KT == 1) THEN X19 = X(Ll+98)/0.99 ELSE IF (KT == 3) THEN X19 = X(Ll+98)/1.01 END IF ELSE IF (KP == Ll+lOO) THEN  2 97  Appendix  D: Source  Code of  the Model  IF  (KT == 1) THEN X20 = X(Ll+100)/0.99 ELSE IF (KT == 3) THEN X20 = X(L1+100)/l.Ol END IF ELSE IF (KP == Ll+102) THEN IF (KT == 1) THEN X21 = X(L1+102)/0.99 ELSE IF (KT == 3) THEN X21 = X(L1+102)/l.Ol END IF ELSE IF (KP == Ll+104) THEN IF (KT == 1) THEN X22 = X(L1+104)/0.99 ELSE IF (KT == 3) THEN X22 = X(L1+104)/l.Ol END IF ELSE IF (KP == Ll+106) THEN IF (KT == 1) THEN X23 = X(L1+106)/0.99 ELSE IF (KT == 3) THEN X23 = X(L1+106)/l.Ol END IF ELSE IF (KP == Ll+108) THEN IF (KT == 1) THEN X24 = X(L1+108)/0.99 ELSE IF (KT == 3) THEN X24 = X(L1+108)/l.Ol END IF END IF  IF(ctS (II,M) .LE.X8) THEN tCC(II,M)=X(Ll+77)*X(Ll+75)*X(Ll+lll) tcm(II,M)=X(Ll+77) ELSE IF(ctS(II,M).LE.X9) THEN tcc(II,M)=X(Ll+7 9)*X(L1+7 5)*X(L1+111) tcm(II,M)=X(Ll+79) ELSE IF(ctS (II,M) .LE.XIO) THEN tCc(II,M)=X(Ll+81)*X(Ll+75)*X(Ll+lll) tcm(II,M)=X(L1+81) ELSE IF(cts(II,M).LE.Xll) THEN tcc(II,M)=X(Ll+83)*X(Ll+75)*X(Ll+lll) tCin(II,M) =X(Ll + 83) ELSE IF(ctS(II,M).LE.X12) THEN tcc(II,M)=X(Ll+85)*X(Ll+75)*X(Ll+lll) tCiii(II,M) =X(Ll + 85) ELSE IF(ctS(II,M).LE.X13) THEN tcc(II,M)=X(Ll+87)*X(Ll+75)*X(Ll+lll) tcm(II,M)=X(Ll+87) ELSE IF(cts(II,M).LE.X14) THEN tcc(II,M)=X(Ll+89)*X(Ll+75)*X(Ll+lll) tcm(II,M)=X(Ll+89) ELSE IF(ctS(II,M).LE.X15) THEN tcc(II,M)=X(L1+91)*X(Ll+75)*X(L1+111) tcm(II,M)=X(L1+91) ELSE IF(ctS(II,M).LE.X16) THEN  2 98  Appendix  D: Source  Code of  the  Model  299  tCc(II,M)=X(Ll+93)*X(Ll+75)*X(Ll+lll) tcm{II,M)=X{Ll+93) ELSE IF(ctS(II,M).LE.X17) THEN tcc(II,M)=X(Ll+95)*X(L1+75)*X(L1+111) tcm{II,M)=X(Ll+95) ELSE IF(ctS(II,M).LE.X18) THEN tcc(II,M)=X{Ll+97)*X(Ll+75)*X(Ll+lll) tcm{II,M)=X(Ll+97) ELSE IF(ctS(II,M).LE.X19) THEN tCC(II,M)=X(Ll+99)*X{Ll+75)*X(Ll+lll) tcni{II,M) =X(Ll + 99) ELSE I F ( c t S ( I I , M ) . L E . X 2 0 ) THEN tcc(II,M)=X(Ll+101)*X(Ll+75)*X(Ll+lll)  tcin{II,M)=X(Ll + 101) ELSE IF(ctS(II,M).LE.X21) THEN tcc(II,M)=X(Ll+103)*X(Ll+75)*X(Ll+lll) tcin(II,M)=X(Ll + 103) ELSE IF(ctS(II,M).LE.X22) THEN tcc(II,M)=X{Ll+105)*X(Ll+75)*X{Ll+lll) tcm(II,M)=X(L1+105) ELSE IF(ctS(II,M).LE.X23) THEN tCc(II,M)=X(Ll+107)*X(Ll+75)*X(Ll+lll) tcm(II,M)=X(Ll+107) ELSE IF(ctS(II,M).LE.X24) THEN tCc(II,M)=X(Ll+109)*X(Ll+75)*X(Ll+lll) tcm(II,M)=X(Ll+109) ELSE tCc(II,M)=X(Ll+110)*X{Ll+75)*X{Ll+lll) tcin(II,M) =X{L1 + 110) END IF 37 80 CONTINUE 37 90 CONTINUE DO 3797 11=1,IRD tcmt(II)=0 DO 3794 M=l,nAL tcmt(11)=tcmt(II)+tcm(II,M) 37 94 CONTINUE 37 97 CONTINUE  C  •  C TOLL COLLECTION MACHINE MAINTENANCE C DO 3820  3812  COSTS  11=1,IRD  tccc(II)=0 DO 3812 J=l,nAL tccc(II)=tccc(II)+tcc(II,J) CONTINUE  tccm(lI)=tccc(II)*X{Ll+112) 3 82 0 CONTINUE C C BUILDING AND REPAINTING  EXPENSES  Appendix  D: Source  Code of  the Model  300  C RELEVANT EXPENSES TO OPERATION C COST FOR MACHINE AND EQUIPMENT C OTHERS C DO 3860 11=1,IRD brco(II) =X(L1 + 1 1 3 ) * ( o o m d l ) +tcmt (II) ) +X (Ll + 114) 3 860 CONTINUE C-C OPERATION BUREAU OVERHEAD C DO 3890 11=1,IRD obo(II) = reve(II) *X(L1+115) 3 8 90 CONTINUE C C HEADQUARTERS C  OVERHEAD  --  DO 3930 11=1,IRD ho(II)=reve(II)"X(LI+116) 3 93 0 CONTINUE C C REVENUE C C This calculate annual revenue C and C maintenance and operation costs. C CALL TRACE  (3, 'RVSPll', 'total costs  CC Calculate annual maintenance C CALL TRACE  calculation.')  costs  (3, 'RVSFll', 'annual maintenance  costs.')  DO 4200 11=1,IRD 4200 maint (II) = mere + mcrm + mcl + mcbr + mcbpl + + mcsc + mcoll (II) + moot  (II) + mctm  C C Calculate annual operation costs. C CALL TRACE  (3, 'RVSFll', 'annual operation  costs.')  DO 4300 11=1,IRD oper(II)=ooo(II)+tccc(II)+tccm(II)+brco(II)+obo(II)+ho(II) aoper(II)=malnt(II)+oper(II) 4300 CONTINUE  Appendix  D: Source  Code of  the Model  3 01  C C Calculate discounted net revenue. C C -C DO 4500 1 = 1 , 177 C 4500 PRINT * , ' X C , I , ' ) C CALL TRACE  -  -  =  ',X{1)  -  --  (3, 'RVSFll', 'discount NP.')  Y=0.00 DO 5100 11=1,IRD CALL TRACE  (3, 'RVSFll', 'calculating AZ,')  AZ=(DEXP(-DR*(rlBY+II))-DEXP{-DR*(rIBY+II-1)))/(-DR) CALL TRACE C C C C C  (3, 'RVSFll', 'calculating Z.')  PRINT *,'X(L1+117)= PRINT *, 'DR= ' ,DR PRINT *,'Z= ',Z  ',X(L1+117)  Z=X(L1+117)-DR IF(DABS(Z).GT.O.OOIDO) GO TO 5020 BZ=1.00 GO TO 503 0 C  CALL TRACE 5 02 0  (3, 'RVSFll', 'calculating BZ.')  BZ={DEXP{Z*(rIBY+II))-DEXP(Z*(rIBY+II-1)))/Z CALL TRACE  5 03 0  (3, 'RVSFll', 'calculating AY.')  AY=(reve(II)*AZ)-(aoper(II)*BZ) CALL TRACE  (3, 'RVSFll', 'calculating Y.')  Y=Y+AY 5100 CONTINUE C  CALL TRACE (2, 'RVSFll', 'finishing.') DEALLOCATE (cost, traf, tec, tcm, cts) RETURN END  Appendix  C C C C C C  D: Source  Code of  the Model  3 02  RvSfl2.INC 16mar94 TH Open System (Manual Collection) we ask nicely for the money from the motorist!  SUBROUTINE RVSF12 (KP, KT, DR, BOTTLE, I, X, Y) IMPLICIT REAL*4 {A-H,0-Z) INCLUDE •DEBUG.CMN' REAL*4 X {*), BOTTLE  (NRS, *)  REAL*4 Y,AY,AZ,BZ,Z(5) REAL*4 mcbpl(50),mcoll(50),ots(50) REAL*4 000(50),oom(50),reve(50) REAL*4 tcmt(50),tccc(50),tccm(50),brco(50),obo(50),ho(50) REAL*4 maint(50),aoper(50) REAL*4 XI(200),X2(200) REAL*4 cost (:,:,:), traf (:,:,:,:) , ttraf(:,:,:) REAL*4 tec (:,:), t c m ( : , : ) , cts(:,:) REAL*4 tgl (:) ALLOCATABLE cost, traf, ttraf, tec, tcm, cts, TGL  CALL TRACE nAL nP nWC nTG nOL nBR  = = = = = =  ALLOCATE  10  BOTTLE BOTTLE BOTTLE BOTTLE BOTTLE BOTTLE  (I, 1) (I, 2) (I, 3) (I, 6) (I, 4) (I, 5)  DO 10 J = 1, nTG tgl (J) = BOTTLE  ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE  starting.")  (tgl (nTG))  IRD = NINT  100  (3, 'RVSF12', 'toll rate calculation  (I, 6 + J)  (X (2))  (cost (traf (ttraf (tcc (tcm (ctS  (IRD, (IRD, (IRD, (IRD, (IRD, (IRD,  nTG, nP)) nAL, nAL, nP)) nTG, nP)) nTG)) nTG)) nTG))  DO 100 11=1,IRD DO 100 J=l,nTG DO 100 K=l,nP cost(II,J,K)=X(2+J)*X(2+nTG+K)*X(2+nTG+nP+II)  Appendix  D: Source  Code of  the Model  3 03  DO 1150 11=1,IRD M=:0 DO 1150 J=l,nAL-l DO 1150 K=J+l,nAL DO 1150 L=l,nP M=MH-1  1150  traf + + +  (II,J,K,I.) = X (2 + nTG + nP + 2 * IRD + M) * X (2 + nTG + nP + IRD + II) / X (3 + nTG + nP + IRD)  DO 1500 11=1,IRD DO 1500 J=l,nTG DO 1500 K=l,nP ttraf(II,J,K)=0.0 DO 1500 JJ=l,nAL XJJ=FLOAT(JJ) IF (TGL (J) == XJJ) THEN DO 1430 L=l,nAL-l DO 1430 LL=L+l,nAL IF (L == JJ .OR. LL == JJ) THEN ttraf(II,J,K)=ttraf(II,J,K)+traf(II,L,LL,K) END IF 143 0 CONTINUE ELSE IF (JJ < TGL(J) .AND. TGL(J) < (JJ + 1)) THEN DO 1450 L=l,nAL-l DO 1450 LL=L+l,nAL IF (L <= JJ .AND. JJ < LL) THEN ttraf(II,J,K)=ttraf(II,J,K)+traf(II,L,LL,K) ENDIF 1450 CONTINUE ENDIF 1500 CONTINUE  DO 1510 11=1,IRD reve(II)=0.00 DO 1510 J=l,nTG DO 1510 K=l,nP 1510 reve(II)=reve(II)+ttraf(II,J,K)*cost{II,J,K)*365 C C C C  PRINT PRINT PRINT PRINT  *, *, *, *,  'nTG = ', nTG • IRD = ', IRD • nAL = •, nAL • nP = ', nP  Ll=2+nTG+nP+2*IRD+nAL*(nAL-l)/2*nP C C  PRINT *, • PRINT *,  LI  = •, LI  mere = ! maintenance  (road cleaning) costs...  Appendix D: Source + + + + +  Code of the Model  X (LI + 13) • ( X (LI + 1) + X (LI + 4) + X (LI + 7) ) + X (LI + 14) * ( X (LI + 2) + X (LI + 5) + X (LI + 8) + X (LI + 3) + X (LI + 6) + X (LI + 9) )  mcrm + X + X + X  = ! road (LI + 15) (LI + 16) (LI + 17)  mcl = ! + X (LI + X (LI + ( (X  maintenance • X (LI + 7) + * X (LI + 8) + • X (LI + 9)  lighting + 18) * (X (LI + 1) + X (LI + 7)) + + 19) * (LI + 2) + X (LI + 3)) + (X (LI + 8) + X (LI + 9)) )  mcbr X X X  = ! bridge (LI + 20) * (LI + 21) * (LI + 22) *  repair X (LI + 1) + X (LI + 2) + X (LI + 3)  mcbp + X + X + X  = ! bridge (LI + 23) * (LI + 24) * (LI + 25) *  painting X (LI + 1) + X (LI + 2) + X (LI + 3)  mctm + X + X + X  = ! tunnel (LI + 10) * (LI + 11) * (LI + 12) *  maintenance X (LI + 26) + X (LI + 27) + X (LI + 28)  + + +  3 04  SELECT CASE (nWC) ! CASE (1) mcsc = + X (LI + 29) * ( (X + 2* (X + + + 3* (X CASE (2) mcsc = + X (LI + 30) * ( (X + 2* (X + + + 3* (X CASE DEFAULT mcsc = O.ODO END SELECT  mcol + X + X + X  snow and ice control?  (LI + 1) + X (LI + 4) + X (LI + 7)) (LI + 2) + X (LI + 5) + X (LI + 8)) (LI + 3) + X (LI + 6) + X (LI + 9))  (LI + 1) + X (LI + 4) + X (LI + 2) + X (LI + 5) + X (LI + 3) + X (LI + 6) + X  (LI + 7)) (LI + 8)) (LI + 9)))  = ! overlay (LI + 31) * (X (LI + 1) + X (LI + 4) + X (LI + 7)) + (LI + 32) * (X (LI + 2) + X (LI + 5) + X (LI + 8)) + (LI + 33) • (X (LI + 3) + X (LI + 6) + X (LI + 9))  Appendix  D: Source  Code of  the Model  pcot = X (LI + 34) moot = ! other neat stuff.... + pcot * (mere + mcrm + mcl + mcbr + mctm + mcsc)  DO 2295  11=1,IRD  C bridge painting happens every 7 years. IF + + +  (lI.EQ.nBR .OR. lI.EQ.(nBR+7) .OR. II.EQ.(nBR+14) .OR. lI.EQ. (nBR + 21) .OR. II.EQ. (nBR + 28) .OR. lI.EQ.(nBR+35) .OR. II.EQ.(nBR+42) .OR. lI.EQ. (nBR + 49)) THEN mcbpl  (II) = mcbp  ELSE mcbpl END IF  (II) = 0.00  C overlaying takes place every 12 years IP +  (lI.EQ.nOL .OR. II. EQ. (nOL + 12) .OR. II.EQ. (nOL + 24) .OR. lI.EQ.(nOL+36) .OR. II.EQ.(nOL+48)) THEN mcoll  (II) = mcol  ELSE mcoll END IF 22 95  (II) = 0.00  CONTINUE  C OPERATION  COSTS  C Operation office  overhead  DO 2500 11=1,IRD M=0 X2(II) = X(2+nTG+nP+IRD+II) XOO = 2-t-nTG+nP-t'IRD + II DO 2500 J=l,nAL-l DO 2500 K=J+l,nAL DO 2500 L=l,nP M=M+1 XO = 2+nTG+nP+2*IRD+M XI(M) = X(XO) IF  (KP == XO) THEN IF (KT == 1) THEN X1(M) = X(X0)/0.99 ELSE IF (KT == 3) THEN X1(M) = X(X0)/1.01 END IF ELSE IF (KP == XOO) THEN  3 05  Appendix  D: Source  Code of  the Model  3 06  IF  (KT == 1) THEN X2 (II) = X{X00)/0.99 ELSE IF (KT == 3) THEN X2 (11) = X(XOO)/I.01 END IF END IF 2500  traf  (II,J,K,L) = XI(M) * X2(II) / X2(l)  DO 2700 11=1,IRD DO 2700 J=l,nTG DO 2700 K=l,nP ttraf(II,J,K)=0.0 DO 2700 JJ=l,nAL XJJ=FLOAT(JJ) IF (TGL (J) == XJJ) THEN DO 2600 L=l,nAL-l DO 2600 LL=L+l,nAL IF (L == JJ .OR. LL == JJ) THEN ttraf(II, J,K)=ttraf(II,J,K)+traf{II,L,LL,K) END IF 2 600 CONTINUE ELSE IF (JJ < TGL(J) .AND. TGL(J) < (JJ + 1)) THEN DO 2650 L=l,nAL-l DO 2650 LL=L+l,nAL IF (L <= JJ .AND. JJ < LL) THEN ttraf(II,J,K)=ttraf(II,J,K)+traf(II,L,LL,K) ENDIF 2 650 CONTINUE ENDIF 27 00 CONTINUE  DO 3450 11=1,IRD Ots (II)=0.00 DO 3450 J=l,nTG DO 3450 K=l,nP 3450 ots(II)=ots(II)+ttraf(II,J,K) X3 X4 X5 X6 X7 IP  = = = = =  X(Ll+40) X(Ll+46) X(Ll+52) X(Ll+58) X(Ll+64)  (KP == Ll+40) THEN IF (KT == 1) THEN X3 = X(Ll+40)/0.99 ELSE IF (KT == 3) THEN X3 = X(Ll+40)/1.01 END IF ELSE IF (KP == Ll+46) THEN IF (KT == 1) THEN X4 = X(Ll+46)/0.99 ELSE IF (KT == 3) THEN  Appendix  D: Source  Code of  the Model  3 07  X4 = X(Ll+46)/1.01 END IF ELSE IF (KP == Ll+52) THEN IF (KT == 1) THEN X5 = X(Ll+52)/0.99 ELSE IF (KT == 3) THEN X5 = X{Ll+52)/1.01 END IF ELSE IF (KP == Ll+58) THEN IF (KT == 1) THEN X6 = X{Ll+58)/0.99 ELSE IF (KT == 3) THEN X6 = X(Ll+58)/1.01 END IF ELSE IF (KP == Ll+64) THEN IF (KT == 1) THEN X7 = X(Ll+64)/0.99 ELSE IF (KT == 3) THEN X7 = X(Ll+64)/1.01 END IF END IF  DO 3485  ELSE ELSE ELSE ELSE  11=1,IRD IF (ots (II) CALL FOOl IF (ots (II) CALL FOOl IF (ots (II) CALL FOOl IF (ots (II) CALL FOOl IF (ots (II) CALL FOOl  <= X3) THEN (X, 41, 35, ooo (II), oom (II)) <= X4) THEN (X, 47, 35, ooo (II), oom (II)) <= X5) THEN (X, 53, 35, ooo (II), oom (II)) <= X6) THEN (X, 59, 35, ooo (11), oom (II)) <= X7) THEN (X, 65, 35, ooo (11), oom (II))  ELSE CALL FOOl 3485  (X, 70, 35,  ooo (II), oom (II))  END IF CONTINUE  C CONSIGNMENT COSTS OF TOLL  COLLECTION  C Calculate traffic volume. DO 3550 11=1,IRD DO 3550 M=l,nTG Cts(II,M)=0.00 DO 3550 L=l,nP 3550 cts(II,M)=cts(II,M)+ttraf(II,M,L)  X8 = X (LI + 75) • X (LI + 113) DO 3790 11=1,nTG DO 3780 M=l,nAL X9 = O.ODO XIO = O.ODO  Appendix  D: Source  Code of  Xll X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X2e X27 X28  X(Ll+76) X(Ll+78) X(Ll+80) X(Ll+82) X(Ll+84) X(Ll+86) X(Ll+88) X(Ll+90) X(Ll+92) X(Ll+94) X(Ll+96) X(Ll+98) X(L1+100) X(L1+102) X(L1+104) X(L1+106) X(L1+108) X(L1+110)  = = = = = = = = = = = = = = = = = = IF  the Model  (KP == LI + 76) THEN IF (KT == 1) THEN Xll = X (LI + 76)/0.99 ELSE IF (KT == 3} THEN Xll = X (LI + 76)/1.01 END IF ELSE IF (KP == LI + 78) THEN IF (KT == 1) THEN X12 = X (LI + 78)/0.99 ELSE IF (KT == 3) THEN X12 = X (LI + 78)/1.01 END IF ELSE IF (KP == LI + 80) THEN IF (KT == 1) THEN X13 = X (LI + 80)/0.99 ELSE IF (KT == 3) THEN X13 = X (LI + 80)/1.01 END IF ELSE IF (KP == LI + 82) THEN IF (KT == 1) THEN X14 = X (LI + 82)/0.99 ELSE IF (KT == 3) THEN X14 = X (LI + 82)/1.01 END IF ELSE IF (KP == LI + 84) THEN IF (KT == 1) THEN X15 = X (LI + 84)/0.99 ELSE IF (KT == 3) THEN X15 = X (LI + 84)/1.01 END IF ELSE IF (KP == LI -t- 86) THEN IF (KT == 1) THEN X16 = X (LI + 86)/0.99 ELSE IF (KT == 3) THEN X16 = X (LI + 86)/1.01 END IF ELSE IF (KP == LI + 88) THEN IF (KT == 1) THEN  3 08  Appendix  D: Source  Code of  the Model  X17 = X (LI + 88)/0.99 ELSE IF (KT == 3) THEN X17 = X (LI + 88)/1.01 END IF ELSE IF (KP == Ll + 90) THEN IF (KT == 1) THEN X18 = X (Ll + 90)/0.99 ELSE IF (KT == 3) THEN X18 = X (Ll + 90)/1.01 END IF ELSE IF (KP == Ll + 92) THEN IF (KT == 1) THEN X19 = X (Ll + 92)/0.99 ELSE IF (KT == 3) THEN X19 = X (Ll + 92)/1.01 END IF ELSE IF (KP == Ll + 94) THEN IF (KT == 1) THEN X20 = X (Ll + 94)/0.99 ELSE IF (KT == 3) THEN X20 = X (Ll + 94)/1.01 END IF ELSE IF (KP == Ll + 96) THEN IF (KT == 1) THEN X21 = X (Ll + 96)/0.99 ELSE IF (KT == 3) THEN X21 = X (Ll + 96)/1.01 END IF ELSE IF (KP == Ll + 98) THEN IF (KT == 1) THEN X22 = X (Ll + 98)/0.99 ELSE IF (KT == 3) THEN X22 = X (Ll + 98)/1.01 END IF ELSE IF (KP == Ll + 100) THEN IF (KT == 1) THEN X23 = X (Ll + 100)/0.99 ELSE IF (KT == 3) THEN X23 = X (Ll + l O O / l . O l END IF ELSE IF (KP == Ll + 102) THEN IF (KT == 1) THEN X24 = X (Ll + 102)/0.99 ELSE IF (KT == 3) THEN X24 = X (Ll + 102)/1.01 END IF ELSE IF (KP == Ll + 104) THEN IF (KT == 1) THEN X25 = X (Ll + 104)/0.99 ELSE IF (KT == 3) THEN X25 = X (Ll + 104)/1.01 END IF ELSE IF (KP == Ll + 106) THEN IF (KT == 1) THEN X26 = X (Ll + 106)/0.99 ELSE IF (KT == 3) THEN X26 = X (Ll + 106)/1.01  3 09  Appendix  D: Source  Code of  the  Model  END IF ELSE IF (KP == LI + 108) THEN IF (KT == 1) THEN X27 = X (LI + 108)/0.99 ELSE IF (KT == 3) THEN X27 = X (LI + 108)/1.01 END IF ELSE IF (KP == LI + 110) THEN IF (KT == 1) THEN X28 = X (LI + 110)/0.99 ELSE IF (KT == 3) THEN X28 = X (LI + 110)/1.01 END IF END IF  IF  (cts (II, M) <= Xll) THEN tec (II, M = X(Ll+77) • X(Ll+75) * X(L1+113) tcm (II, M = X{Ll+77) ELSE IF (cts (11, M) <= X12) THEN tec (II, M = X(Ll+79) * X(Ll+75) * X(L1+113) tcm (II, M = X(Ll+79) ELSE IF (cts (II, M) <= X13) THEN tec (II, M = X(L1+81) * X(Ll+75) * X(L1+113) tem (II, M = X(L1+81) ELSE IF (cts (II, M) <= X14) THEN tec (II, M] = X(Ll+83) * X(Ll+75) * X(L1+113) tcm (II, M = X(Ll+83) ELSE IF (cts (II, M) <= X15) THEN tec [II, M] = X(Ll+85) * X(Ll+75) • X(L1+113) tem (II, M] = X(Ll+85) ELSE IF (cts (II, M) <= X16) THEN tee [II, M] = X(Ll+87) * X(Ll+75) • X(L1+113) tcm [II, M] = X{Ll+87) ELSE IF (cts (II, M) <= X17) THEN tec II, M) = X(Ll+89) * X{Ll+75) * X(L1+113) tem II, M) = X(Ll+89) ELSE IF (cts (II, M) <= X18) THEN tee II, M) = X(L1+91) * X(Ll+75) * X(L1+113) tem II, M) = X(L1+91) ELSE IF (cts (II, M) <= X19) THEN tec II, M) = X(Ll+93) * X(Ll+75) * X(L1+113) tem II, M) = X(Ll+93) ELSE IF (cts (II, M) <= X20) THEN tee II, M) = X(Ll+95) * X(Ll+75) * X(L1+113) tem II, M) = X(Ll+95) ELSE IF (cts [II, M) <= X21) THEN tec II, M) = X(Ll+97) * X(Ll+75) * X(L1+113) tcm II, M) = X(Ll+97) ELSE IF (cts [II, M) <= X22) THEN tec 1 II, M) = X{Ll+99) • X(Ll+75) • X(L1+113) tcm 1 II, M) = X(Ll+99) ELSE IF (cts II, M) <= X23) THEN tee 1 II, M) = X(L1+101) * X(Ll+75) * X(L1+113) tem 1 II, M) = X(L1+101) ELSE IF (cts II, M) <= X24) THEN tec I II, M) = X(L1+103) * X(Ll+75) * X(L1+113)  310  Appendix  D: Source  Code  tcm ELSE IF tec tcm ELSE IF tec tcm ELSE IF tec tcm ELSE IF tec tcm ELSE tec tcm END IF CONTINUE 3780 3 7 90 CONTINUE  of  the  311  Model  (II, M) = X(L1+103) (cts (II, M) <= X25; II, M) = X(L1+105) • II, M) = X(L1+105) (cts (II, M) <= X26) II, M) = X(L1+107) * II, M) = X(L1+107) (cts (II, M) <= X27) II, M) = X(L1+109) * II, M) = X(L1+109) (cts (II, M) <= X28) II, M) = X(L1+111) • II, M) = X(L1+111)  THEN X(Ll+75) * X(L1+113) THEN X(Ll+75) * X(L1+113) THEN X(Ll+75) * X(L1+113) THEN X(Ll+75) * X(L1+113)  II, M) = X(L1+112) * X(Ll+75) * X(L1+113) II, M) = X(L1+112)  DO 3794 11=1,IRD tcmt (II) = O.ODO DO 3794 M=l,nTG 3794 tcmt (II) = tcmt  (II) + tcm  C C TOLL COLLECTION MACHINE MAINTENANCE C  (II, M)  COSTS -  DO 3820 11=1,IRD tccc(ll)=0 DO 3812 J=l,nTG 3812 tecc (II)=tcce(II)+tcc(II,J) 3820 teem (II) = tecc (II) * X (LI + 114) C C C C C C  BUILDING AND REPAINTING EXPENSES RELEVANT EXPENSES TO OPERATION COST FOR MACHINE AND EQUIPMENT OTHERS -  3 860  DO 3860 11=1,IRD brco(II)=X(L1+115)*(oom(II)+tcmt(II))+X(L1+116)  C C OPERATION BUREAU C DO 3890 C  OVERHEAD  11=1,IRD  PRINT *, II, reve 3890  --  (II), Ll+117, X(L1+117)  obo(II)=reve(II)*X(L1+117)  Appendix  D: Source  C C HEADQUARTERS C  3930  Code of  the  312  Model  OVERHEAD -  --  DO 3930 11=1,IRD ho(II)=reve(II)*X(L1+118)  C -C REVENUE C C This ealculate annual revenue C and C maintenanee and operation eosts. C ---. PRINT *,  'total eosts ealculation  C Calculate annual maintenanee C  4200  starting."  costs -  DO 4200 11=1,IRD maint (II) = mere + mcrm + mel + mcbr + mebpl + metm + mesc + mcoll (II) + moot  (II) +  C Calculate annual operation costs. C-DO 4300 11=1,IRD aoper (II) = maint (II) + ooo (II) + tccc (II) + teem + maint + brco ((II) + obo (II) + ho (II)  c c c c c c c c c 4300  PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT  * * * * * * • * *  (II) +  II = ', II maint', maint (II) ooo", ooo (II) tcee', tccc (II) teem', teem (II) brco', brco (II) obo', obo (II) ho", ho (II)  CONTINUE  C Calculate discounted net revenue. C C  PRINT *, 'NPV ealculation Y = O.ODO DO 5100 11=1,IRD AZ = (DEXP {-DR + DEXP (-DR  starting.'  * (X (1) + II ) ) • (X (1) + II - 1) ) ) / (- DR)  Appendix D: Source Z  Code of  the  313  Model  (1) = X (LI + 119) - DR  IF  {DABS(Z (1)) <= O.OOIDO) THEN BZ = l.ODO 60 TO 4400 ELSE BZ = (DEXP (Z (1) * {X (1) + II DEXP (Z (1) * (X (1) + II END IF 4400  AY  (reve  PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT  c c c c c c c c c 5100  *, *, *, *, *, *, *, *, *,  (II) * AZ) - (aoper  )) D ) ) / Z (1)  (II) * BZ)  • II = •, II ' AZ = •, AZ • Z (1) = •, Z (1) • X (1) = ', X (1) • BZ = •, BZ • reve (II) = ', reve (II) • aoper (II) = •, aoper (II) • AY = •, AY  Y + AY DEALLOCATE RETURN END  (TGL, cost, traf, ttraf, tec, tcm, cts)  C remove some redundant stuff to make the code nicer, SUBROUTINE FOOl REAL*4 X (*)  (X, OFFl, 0FF2, ooo, oom)  ooo = O.ODO oom = O.ODO  10  DO 10 I = 0, 4 ooo = ooo + (X (OFFl + I) * X (0FF2 + I)) oom = oom + (X (OFFl)) RETURN END  Appendix  D:  Source  Code  of  the  Model  314  C RvSfl3.INC C C Closed System (Manual Collection) : fixed rate C we ask nicely for the money from the motorist! C======================================================== SUBROUTINE RVSF13 (KP, KT, DR, BOTTLE, I, X, Y) C = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =: = = = = = = = = = = = = = = = = = = = = IMPLICIT REAL*4(A-H,0-Z) INCLUDE •DEBUG.CMN' REAL*4 BOTTLE  (NRS, * ) ,  X  (•)  REAL*4 Y,AY,AZ,BZ,Z REAL*4 mcbpl(0:50),mcoll(0:50),ots(0:50) REAL*4 ooo (0:50) ,oom(0:50),reve(0:50) REAL*4 tcmt(0:50),tccc(0:50),teem(0:50),brco(0:50),obo(0:50) REAL*4 ho(0:50),maint(0:50),oper(0:50),aoper(0:50) REAL*4 X l ( 0 : 2 0 0 ) , X2(0:200) REAL*4 cost (:,:,:,:), traf ( • /•/•/ REAL*4 tec (:,:), tcm (:,:), Cts (:,:) ALLOCATABLE cost, traf, tcc, tcm, cts  CALL TRACE rlBY IRD nAL nP nWC nOL nBR  (3, •RVSF13',  'starting.')  = X (1) = NINT (X (2)) BOTTLE BOTTLE BOTTLE BOTTLE BOTTLE  ALLOCATE ALLOCATE ALLOCATE ALLOCATE ALLOCATE  (I, (I, (I, (I, (I,  (cost (traf (tcc (tcm (cts  (0 (0 (0 (0 (0  1) 2) 3) 4) 5) IRD, IRD, IRD, IRD, IRD,  nAL, nAL, nAL) nAL) nAL)  0: nAL, 0:nP)) 0: nAL, 0:nP)) ) ) )  DO 90 II = 1, IRD M = 0 XCONST = X (2 + nAL • (nAL  90  DO 9 0 J = 1 , nAL - 1 D O 9 0 K = J + l , nAL DO 9 0 L = 1 , n P M = M + 1 c o s t ( I I , J , K,  CALL TRACE  (3, •RVSF13  L]  1)  X  /  2  * nP  +  II)  (2 + M) * XCONST  traffic volume  calculation.')  Appendix C tra£  D: Source  Code of  the Model  315  (1, is undefined, but accessed In the next loop.... DO 1150  +  11=1,IRD  M=0 XCO = 2 + nAL * (nAL - 1 ) / 2 * n P + 2 * IRD XCl = X (2 + nAL * (nAL - 1) / 2 * nP + IRD + II) / X (3 + nAL * (nAL - 1) / 2 * nP + IRD) DO 1150 J=l,nAL-l DO 1150 K=J+l,nAL DO 1150 L=l,nP M=M+1 traf (II,J,K,L)= X (XCO + M) * XCl  1150  CALL TRACE  (3, 'RVSF13', 'annual toll  revenue...')  DO 1480 11=1,IRD temp = 0.0 0  + 1470  DO 1470 J=l,nAL DO 1470 K=J+l,nAL DO 1470 L=l,nP temp = temp + traf (II,J,K,L) * cost CONTINUE  (II,J,K,L) * 365  reve (II) = temp 1480 CONTINUE  LI = 2 + 2 * (nAL*(nAL-1)/2*nP)  + 2 * IRD  CALL TRACE  costs...')  (3, •RVSF13',  'fixed  mere = ! road cleaning costs + X(L1+13)*(X(L1+1) + X(Ll+4) + X(Ll+7)) + X(Ll+14)*(X(Ll+2) + + X(Ll+5) + X(Ll+8) + X(Ll+3) + X(Ll+6) + X(Ll+9))  +  mcrm = ! road maintenance X(L1+15)*X(Ll+7) + X(Ll+16)*X(Ll+8) + X(Ll+17)*X(L1+9)  mcl = ! lighting + X(L1+18)*(X(L1+1) + X(Ll+7)) + + X(L1+19)*( (X(Ll+2) + X(Ll+3)) + (X(Ll+8) + X(Ll+9))) mcbr = ! bridge repair X(Ll+20)*X(L1+1) + X(L1+21)*X(Ll+2)  + X(Ll+22)*X(Ll+3)  mcbp = ! bridge painting + X(Ll+23)*X(L1+1) + X(Ll+24)*X(Ll+2)  + X(Ll+25)*X(Ll+3)  +  mctm = ! tunnel maintenance + X(L1+10)*X(Ll+26) + X(Ll+ll)*X(Ll+27)  + X(Ll+12)-X(Ll+28)  Appendix  D: Source  Code of  the Model  316  SELECT CASE (nWC) ! snow and ice control based on nWC CASE (1) mcsc = + X(Ll+29)*{ (X{L1+1) + X(Ll+4) + X(Ll+7)) + +2*(X(Ll+2) + X(Ll+5) + X(Ll+8)) + +3*(X(Ll+3) + X(Ll+6) + X(Ll+9)) ) CASE (2) mcsc = + X(Ll+30)*( (X(L1+1) + X(Ll+4) + X{Ll+7)) + +2*{X(Ll+2) + X(Ll+5) + X(Ll+8)) + +3*(X{Ll+3) + X(Ll+6) + X(Ll+9)) ) CASE DEFAULT mcsc = 0.00 END SELECT  mcol = ! overlay + X(L1+31)*( X(L1+1) + X(Ll+4) + X{Ll+7) ) + + X(Ll+32)*( X{Ll+2) + X(Ll+5) + X(Ll+8) ) + + X{Ll+33)*{ X(Ll+3) + X(Ll+6) + X(Ll+9) ) mcot = X (LI + 34) * (mere + mcrm + mcl + mcbr + mctm + mcsc) DO 2295 11=1,IRD IF (lI.EQ.nBR ,0R. lI.EQ. (nBR + 7) ,OR. II.EQ. (nBR + 14) .OR. + lI.EQ.(nBR+21) .OR. II.EQ.(nBR+28) .OR. + lI.EQ. {nBR + 35) .OR. lI.EQ. (nBR + 42) .OR. + lI.EQ.(nBR+49)) THEN mcbpl(II) = mcbp ELSE mcbpl(II) = 0.00 END IF IF (lI.EQ.nOL .OR. lI.EQ. (nOL + 12) .OR. II.EQ. (nOL + 24) .OR. + lI.EQ.(nOL+36) .OR. II.EQ.(nOL+48)) THEN mcoll(II) = mcol ELSE mcoll(II) = 0.00 END IF 22 95 CONTINUE C OPERATION  COSTS  CALL TRACE  (3, 'RVSF13',  C C Operation office  'operation  costs...')  overhead  C DO 2500  11=1,IRD  M=0 X2 (II) = X (2 + nAL * (nAL - 1) / 2 * nP + IRD + II) XOO = 2 + nAL * (nAL - 1) / 2 * nP + IRD + II DO 2 50 0 J=l,nAL-l DO 2500 K=J+l,nAL DO 2500 L=l,nP  Appendix D: Source  Code of the Model  317  M=M+1 XO = 2 + nAL * (nAL - 1 ) / 2 * n P + 2 * XI (M) = X (XO)  IRD + M  IF  (KP == XO) THEN IF (KT == 1) THEN X1(M) = X (XO) / 0.99 ELSE IF (KT == 3) THEN XI(M) = X (XO) / 1.01 END IF ELSE IF (KP == XOO) THEN IF (KT == 1) THEN X2 (II) = X (XOO) / 0.99 ELSE IF (KT == 3) THEN X2 (II) = X (XOO) / 1.01 END IF END IF traf  (II,J,K,L) = XI (M) * X2 (11) / X2 (1)  2 500 CONTINUE  3420 3430 3440 3450  DO 3450 11=1,IRD temp = O.ODO DO 3440 J=l,nAL-l DO 3430 K=J+l,nAL DO 3420 L=l,nP temp = temp + traf(II,J,K,L) CONTINUE CONTINUE CONTINUE ots(II) = temp CONTINUE  DO 3485 11=1,IRD ooo(II)=0 C treated traffic is half of through ots(II)=ots(II)*0.5 X3 X4 X5 X6 X7 IF  = = = = =  X(Ll+40) X(Ll+46) X{Ll+52) X(Ll+58) X(Ll+64)  (KP == Ll+40) THEN IF (KT == 1) THEN X3 = X(Ll+40)/0.99 ELSE IF (KT == 3) THEN X3 = X(Ll+40)/l.Ol END IF ELSE IF (KP == Ll+4e) THEN IF (KT == 1) THEN X4 = X(Ll+46)/0.99 ELSE IF (KT == 3) THEN  traffic  Appendix  D:  Source  Code  of  the  Model  X4 = X(Ll+46)/1.01 END IF ELSE IF (KP == Ll+52) THEN IF (KT == 1) THEN X5 = X(Ll+52)/0.99 ELSE IF (KT == 3) THEN X5 = X(Ll+52)/l.Ol END IF ELSE IF (KP == Ll+58) THEN IF (KT == 1) THEN X6 = X(Ll+58)/0.99 ELSE IF (KT == 3) THEN X6 = X(Ll+58)/1.01 END IF ELSE IF (KP == Ll+64) THEN IF (KT == 1) THEN X7 = X(Ll+64)/0.99 ELSE IF (KT == 3) THEN X7 = X(Ll+64)/1.01 END IF END IF  1  1  1  1  1  1  3485 C  IF(otS(II).LE.X3) THEN ooo(ll)=X(Ll+41)*X{Ll+3 5)+X(Ll+42)*X(Ll+3 6)+X(Ll+43) *X(Ll + 3 7)+X(Ll + 44)*X(Ll + 3 8)+X(Ll + 4 5)*X(Ll + 39 ) oom(II)=X(L1+41)+X(Ll+42)+X(Ll+43)+X(Ll+44)+X(Ll+45) ELSE IF(otS(II).LE.X4) THEN ooo(ll)=X(Ll+47)*X(Ll+3 5)+X(Ll+4 8)*X(Ll+3 6)+X(Ll+4 9) *X(Ll+3 7)+X(Ll+5 0)*X(Ll+3 8)+X(Ll+51)*X(Ll+3 9) oom(II)=X(Ll+47)+X(Ll+4 8)+X(Ll+4 9)+X(Ll+50)+X(Ll+51) ELSE IF(otS(II).LE.X5) THEN ooo(ll)=X(Ll+53)*X(Ll+35)+X(Ll+54)*X(Ll+36)+X(Ll+55) *X(Ll+3 7)+X(Ll+5 6)*X(Ll+3 8)+X(Ll+5 7)*X{Ll+3 9) oom(II) =:X(Ll + 53)+X(Ll + 54)+X(Ll + 55)+X(Ll + 56)+X(Ll + 57) ELSE IF(otS(II).LE.X6) THEN ooo(II)=X(Ll+5 9)*X(Ll+3 5)+X(Ll+60)*X(Ll+3 6)+X(L1+61) *X(Ll+3 7)+X(Ll+62)*X(Ll+3 8)+X(Ll+63)*X(Ll+3 9) O o m d l ) =X(Ll + 5 9) +X(Ll + 6 0) +X(L1 + 61) +X(Ll + 62) +X(Ll + 63) ELSE IF(otS(II).LE.X7) THEN ooo(II)=X(Ll+65)*X{Ll+35)+X(Ll+66)*X(Ll+3 6)+X(Ll+67) *X(Ll+37)+X(Ll+68)*X(Ll+38)+X(Ll+69)*X(Ll+39) oom(ll)=X(Ll+65)+X(Ll+66)+X(Ll+67)+X(Ll+68)+X(Ll+69) ELSE ooo(ll)=X(Ll+70)*X(Ll+35)+X(Ll+71)*X(Ll+36)+X(Ll+72) * X ( L l + 3 7 ) + X ( L l + 7 3 ) * X ( L l + 3 8 ) + X ( L l + 7 4 ) * X ( L l + 3 9) o o m d l ) =X(Ll +7 0 ) + X ( L l +7 1 ) + X ( L l +7 2 ) + X { L l +7 3 ) + X ( L l + 74) END I F CONTINUE -  -  C CONSIGNMENT COSTS OF TOLL COLLECTION C DO 3 5 5 0 1 1 = 1 , I R D DO 3 5 4 0 M = l , n A L t e i n p = 0 . ODO  318  Appendix  3510 3520  3525 3 53 0 3540 3550  D: Source  Code of  the Model  DO 3530 J=l,nAL-l IF (J == M) THEN DO 3520 K=J+l,nAL DO 3510 L=l,nP temp = temp + traf (II,J,K,L) CONTINUE CONTINUE ELSE DO 3525 L=l,nP temp = temp + traf (II,J,M,L) CONTINUE END IF CONTINUE cts(II,M) = temp CONTINUE CONTINUE  DO 3790 11=1,IRD DO 3780 M=l,nAL tcc{II,M)=0.0D0  C we could realize about a 5% increase in speed C by not ROCKing 'N ROLLing these variables at all X8 X9 XIO Xll X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 IF  = = = = = = = = = = = = = = = = =  X(Ll+76) X(Ll+78) X(Ll+80) X(Ll+82) X(Ll4-84) X{Ll+86) X(Ll-»-88} X{Ll+90) X(Ll+92) X{Ll+94) X(Ll+96) X(Ll+98) X(L1+100) X{L1+102) X(L1+104) X(L1+106) X(L1+108)  (KP == Ll+76) THEN IF (KT == 1) THEN X8 = X(Ll+76)/0.99 ELSE IF (KT == 3) THEN X8 = X(Ll+76)/1.01 END IF ELSE IF (KP == Ll+78) THEN IF (KT == 1) THEN X9 = X(Ll+78)/0.99 ELSE IF (KT == 3) THEN X9 = X(Ll+78)/1.01 END IF  319  Appendix  D: Source  Code of  the Model  ELSE IF (KP == Ll+80) THEN IF (KT == 1) THEN XIO = X(Ll+80)/0.99 ELSE IF (KT == 3) THEN XIO = X(Ll+80)/1.01 END IF ELSE IF (KP == Ll+82) THEN IF (KT == 1) THEN Xll = X(Ll+82)/0.99 ELSE IF (KT == 3) THEN Xll = X(Ll+82)/l.Ol END IF ELSE IF (KP == Ll+84) THEN IF (KT == 1) THEN X12 = X(Ll+84)/0.99 ELSE IF (KT == 3) THEN X12 = X(Ll+84)/l.Ol END IF ELSE IF (KP == Ll+86) THEN IF (KT == 1) THEN X13 = X(Ll+86)/0.99 ELSE IF (KT == 3) THEN X13 = X(Ll+86)/1.01 END IF ELSE IF (KP == Ll+88) THEN IF (KT == 1) THEN X14 = X(Ll+88)/0.99 ELSE IF (KT == 3) THEN X14 = X(Ll+88)/1.01 END IF ELSE IF (KP == Ll+90) THEN IF (KT == 1) THEN X15 = X(Ll+90)/0.99 ELSE IF (KT == 3) THEN X15 = X(Ll+90)/1.01 END IF ELSE IF (KP == Ll+92) THEN IF (KT == 1) THEN X16 = X(Ll+92)/0.99 ELSE IF (KT == 3) THEN X16 = X(Ll+92)/l.Ol END IF ELSE IF (KP == Ll+94) THEN IF (KT == 1) THEN X17 = X(Ll+94)/0.99 ELSE IF (KT == 3) THEN X17 = X(Ll+94)/1.01 END IF ELSE IF (KP == Ll-l-96) THEN IF (KT == 1) THEN X18 = X(Ll+96)/0.99 ELSE IF (KT == 3) THEN X18 = X(Ll+96)/1.01 END IF ELSE IF (KP == Ll+98) THEN IF (KT == 1) THEN X19 = X(Ll+98)/0.99  32 0  Appendix  D: Source  Code of  the Model  ELSE IF (KT == 3) THEN X19 = X(Ll+98)/l.Ol END IF ELSE IF (KP == Ll+lOO) THEN IF (KT == 1) THEN X20 = X(Ll+100)/0.99 ELSE IF (KT == 3) THEN X20 = X(L1+100)/l.Ol END IF ELSE IF (KP == Ll+102) THEN IF (KT == 1) THEN X21 = X{L1+102)/0.99 ELSE IF (KT == 3) THEN X21 = X(L1+102)/l.Ol END IF ELSE IF (KP == Ll+104) THEN IF (KT == 1) THEN X22 = X(Ll+104)/0.99 ELSE IF (KT == 3) THEN X22 = X(L1+104)/1.01 END IF ELSE IF (KP == Ll+lOe) THEN IF (KT == 1) THEN X23 = X(Ll+106)/0.99 ELSE IF (KT == 3) THEN X23 = X(L1+106)/1.01 END IF ELSE IF (KP == Ll+108) THEN IF (KT == 1) THEN X24 = X(L1+108)/0.99 ELSE IF (KT == 3) THEN X24 = X(L1+108)/1.01 END IF END IF IF(ctS(II,M).LE.X8) THEN tCC(II,M)=X(Ll+77)*X(Ll+75)*X(Ll+lll) tCin(II,M) =X(Ll + 77) ELSE IF(ctS(II,M).LE.X9} THEN tcc(II,M)=X(Ll+79)*X{Ll+75)*X(Ll+lll) t c m d l / M ) =X(Ll + 79) ELSE I F ( c t S ( I I , M } . L E . X I O ) THEN tcc(II,M)=X(Ll+81)*X(Ll+75)*X(Ll+lll)  tC]n(II,M) =X(L1 + 81) ELSE IF(ctS(II,M).LE.Xll) THEN tcc(II,M)=X(Ll+83)*X(Ll+75)*X(Ll+lll) tcin(II,M) =X(Ll + 83) ELSE IF(ctS(II,M).LE.X12) THEN tCc(II,M)=X(Ll+85)*X(Ll+75)*X(Ll+lll) tcm(II,M)=X(Ll+85) ELSE IF(ctS(II,M).LE.X13} THEN tCC(II,M)=X(Ll+87)*X(Ll+75)*X(Ll+lll) tcm(II,M)=X(Ll+87) ELSE IF(ctS(II,M}.LE.X14) THEN tcc(II,M)=X(Ll+8 9)*X(Ll+7 5)*X(L1+111) tcm(II,M)=X(Ll+89) ELSE IF(ctS(II,M).LE.X15) THEN  321  Appendix  D: Source  Code of  the Model  322  tcc{II,M)=X(Ll+91)*X(Ll+75)*X(Ll+lll) tcin(II,M) =X{L1 + 91) ELSE IF(ctS(II,M).LE.X16) THEN tCc(II,M)=X(Ll+93)*X{Ll+75)*X(Ll+lll) tcm(II,M)=X{Ll+93) ELSE IF(ctS(II,M).LE.X17) THEN tCC(II,M)=X(Ll+95)*X(Ll+75)*X(Ll+lll) tCin(II,M) =X(Ll + 95) ELSE IF(ctS(II,M).LE.X18) THEN tCc(II,M)=X(Ll+97)*X(Ll+75)*X(Ll+lll) tcm(II,M)=X{Ll+97) ELSE IF(ctS(II,M).LE.X19) THEN tCC(II,M)=X(Ll+99)*X(Ll+75)*X{Ll+lll) tcm{II,M)=X(Ll+99) ELSE IF(ctS(II,M).LE.X20) THEN tCc(II,M)=X(Ll+101)*X{Ll+75)*X(Ll+lll) tcm(II,M)=X(L1+101) ELSE IF(ctS(II,M).LE.X21) THEN tCC(II,M)=X(Ll+103)*X(Ll+75)*X{Ll+lll) tcm(II,M)=X(L1+103) ELSE IF(ctS(II,M).LE.X22) THEN tCc{II,M)=X(L1+105)*X{Ll+7 5)*X(L1+111) tCin(II,M)=X(Ll + 105) ELSE IF(ctS(II,M}.LE.X23) THEN tCC(II,M)=X(Ll+107)*X(Ll+75)*X{Ll+lll) tcm{II,M)=X(Ll+107) ELSE IF(ctS(II,M).LE.X24) THEN tCC{II,M)=X(Ll+109)*X(Ll+75)*X(Ll+lll) tcm(II,M)=X(Ll+109) ELSE tCC(II,M)=X(Ll+110)*X{Ll+75)*X{Ll+lll) tcm{II,M)=X{Ll+110) END IF 3 7 80 CONTINUE 37 90 CONTINUE DO 3797 11=1,IRD temp = O.ODO DO 3794 M=l,nAL temp = temp + tcm (II, M) 3 7 94 CONTINUE tcmt (II) = temp 37 97 CONTINUE  C C TOLL COLLECTION MACHINE MAINTENANCE C-  DO 3820 11=1,IRD temp = O.ODO DO 3812 J=l,nAL temp = temp + tec(II,J) 3812 CONTINUE tccc (II) = temp  -COSTS -  Appendix  D: Source  Code of  the Model  3 23  teem (II) = temp * X(L1+112) 3 82 0 CONTINUE C C C C C C  ---BUILDING AND REPAINTING EXPENSES RELEVANT EXPENSES TO OPERATION COST FOR MACHINE AND EQUIPMENT OTHERS DO 3860  --  -  -  11=1,IRD  brco(II)=X{L1+113)*(oom(II)+tcmt(II))+X(Ll+114) 3 860 CONTINUE C --C OPERATION BUREAU OVERHEAD C -DO 3890 11=1,IRD obo(II) = reve(II) *X(Ll+115) 3 890 CONTINUE C C HEADQUARTERS C  OVERHEAD -  -  --  --  -  -  --  DO 3930 11=1,IRD ho(II) = reve(II)•X(L1+116) 3 93 0 CONTINUE C C REVENUE C C This calculate C C C CALL TRACE  -  annual revenue and maintenance and operation costs. (3, 'RVSP13',  C -C Calculate annual maintenance C CALL TRACE  4200  -  (3, 'RVSF13',  "total costs  calculation.')  costs  'annual maintenance  costs.')  DO 4200 11=1,IRD maint (II) = mere + mcrm + mcl + mcbr + mcbpl + + mese + mcoll (II) + mcot  C -C Calculate annual operation costs. C CALL TRACE  (3, 'RVSF13',  (II) + mctm  --  'annual operation  costs.')  Appendix  D: Source  Code of  the Model  3 24  DO 4300 11=1,IRD oper(II)=ooo(II)+tccc(II)+tccm(II)+brco(II)+obo(II) +ho(II) aoper (II) =inalnt (II) + oper (II) 4300 CONTINUE  C save the values into the array C IF (0 < KP) THEN C DO 4900 II = 1, IRD C VCACHE (I, KT, KP, (II * 2) - 1) = reve (II) C VCACHE (I, KT, KP, (II * 2) ) = aoper (II) C 4 900 CONTINUE C ENDIF C -C Calculate discounted net revenue. C -5000 CALL TRACE Y=0.00 DO 5100  (3, •RVSF13',  'discount NP.')  11=1,IRD  IF  +  (DABS (DR) <= O.OOIDO) THEN AZ = 1.0 0 ELSE AZ = ( DEXP (-DR * (rlBY + 1 1 )) DEXP (-DR * (rlBY + II - 1)) ) / (-DR) END IF Z = X (LI + 117) - DR IF  +  (DABS (Z) <= O.OOIDO) THEN BZ = 1.00 ELSE BZ = ( DEXP (Z * (rlBY + 1 1 )) DEXP (Z * (rlBY + II - 1)) ) / Z END IF AY = (reve (II) * AZ) - (aoper (II) * BZ) Y = Y + AY  5100 CONTINUE CALL TRACE DEALLOCATE RETURN  END  (3, 'RVSF13', 'finishing.') (cost, traf, tec, tcm, cts)  Appendix  D: Source  Code of  the Model  3 25  C IntPol.FOR C modified by Toshiaki Hatakama in July, 1994. C called only by CdFunc.FOR C THIS ROUTINE INTERPOLATES THE BETAl AND BETA2 VALUES OF THE C PEARSON TABLE BY A METHOD OF LINEAR INTERPOLATION 0============================================================== SUBROUTINE INTPOL (PEARSN, RSKW, RKRT, + lYl, IY2, + IZl, IZ2, + IPEARS, + SD, AM, RES)  IMPLICIT REAL*4(A-H,0-Z) INCLUDE •DEBUG.CMN' REAL*4 PEARSN (NPEARS, *) RYDIF = PEARSN RZDIF = PEARSN  (IY2, IPEARS) - PEARSN (IZ2, IPEARS) - PEARSN  (lYl, IPEARS) (IZl, IPEARS)  RES = PEARSN (lYl, IPEARS) + (RKRT / O.IDO) * RYDIF RES = AM + SD * + ( RES + (RSKW / O.IDO) * + (PEARSN (IZl, IPEARS) + (RKRT / O.IDO) * RZDIF - RES)) RETURN END  Appendix  D: Source  Code of  the Model  32 6  C SPARSE.FOR C "Sparse-Array" technology for super-large C  arrays  C initialize the size data (the first cell), C and the dimension list (cell 2 and the rest), C and the rest of the cells, just to be safe.... SUBROUTINE SPA_INIT3 (THEARY, NSIZE, NDl, ND2, ND3) REAL*4 THEARY (*) INTE6ER*4 NSIZE, NDl, ND2, ND3 THEARY THEARY THEARY THEARY THEARY  (1) = (2) = (3) = (4) = (5) =  NSIZE 3 NDl ND2 ND3  ! ! ! ! !  how many elements in the array, the number of dimensions. the 1st virtual dimension. the 2nd virtual dimension. the 3rd virtual dimension.  really.  DO 100 X = 6, NSIZE THEARY (X) = 0.0  100  RETURN END  C for a given cell, set the value referenced by (x,y,z) to theVal C I wish FORTRAN supported Variable # of Parameters... SUBROUTINE SPA_SET3 (THEARY, THEVAL, NDl, ND2, ND3) REAL*4 THEARY {*), THEVAL INTEGER*4 NDl, ND2, ND3, KEY, HASH  +  KEY = ( (NDl - 1) * INT (THEARY * INT (THEARY  (4)) + (ND2 - 1) ) (5)) + ND3  HASH = 6 + (MOD (KEY, INT ((THEARY  (1) - 5) / 2)) * 2)  100 IF (THEARY (HASH) == KEY) THEN THEARY (HASH + 1 ) = THEVAL RETURN ENDIF IF (THEARY (HASH) == 0.0) THEN IF (THEVAL == 0.0) THEN C Never store a zero when just leaving it will d o ! ELSE THEARY (HASH) = KEY THEARY (HASH + 1) = THEVAL ENDIF RETURN ENDIF HASH = HASH + 2 IF (INT (THEARY (1)) <= HASH) THEN HASH = 6 END IF  Appendix  D: Source  Code of  the Model  32 7  GOTO 100 END  C get a value from the sparse array.... REAL*4 FUNCTION SPA_GET3 (THEARY, NDl, ND2, ND3) REAL*4 THEARY (*) INTEGER*4 NDl, ND2, ND3, KEY, HASH  +  KEY = { (NDl - 1) * INT (THEARY * INT (THEARY  (4)) + (ND2 - 1) ) (5)) + ND3  HASH = 6 + (MOD (KEY, INT ((THEARY  (1) - 5) / 2)) * 2)  100 IF (THEARY (HASH) == KEY) THEN SPA_GET3 = THEARY (HASH + 1) RETURN END IF IF (THEARY (HASH) == 0.0) THEN SPA_GET3 = 0 . 0 RETURN ENDIF HASH = HASH + 2 IF (INT (THEARY (1)) <= HASH) THEN HASH = 6 END IF GOTO 100 END  C get a check-sum of a sparse array... just to be sure. REAL*4 FUNCTION S P A S U M (THEARY, NSIZE) REAL*4 THEARY (*) S P A S U M = O.ODO IF (THEARY (1) == NSIZE) THEN DO 100 1 = 1 , NSIZE S P A S U M = ( S P A S U M + THEARY (I)) * 2 IF (1.0D15 < S P A S U M ) THEN S P A S U M = S P A S U M / 1.0D14 ENDIF 100 CONTINUE ELSE PRINT *, 'Array size is different than defined!' ENDIF RETURN END  Appendix  C C C C C C  D: Source  Code of  the Model  32 8  Trace.MJW 23mar94 MJW TRACE checks whether or not this particular call contains data which is desirable at this debug level, which is set in AMMA.INI If it is, then it displays the data on the console SUBROUTINE TRACE (NDEBUG, CPROC, MSG) CHARACTER C P R O C * ( * ) , MSG*{*) CHARACTER*8 THEDATE CHARACTER*11 THETIME INCLUDE  •DEBUG.CMN'  CALL DATE CALL TIME IF  C  (THEDATE) (THETIME)  (IDEBUG .GE. NDEBUG) THEN WRITE (6, *) THEDATE, ' ', THETIME(1:5), ' ', CPROC, ': ', + MSG WRITE (7, *) THEDATE, • ', THETIME(1:5), ' ', CPROC, ': •, + MSG END IF RETURN END  Appendix  D-. Source  Code of  C DEBUG.CMN C 25mar94 MJW C this is a blank common program  the Model  32 9  for keeping crucial info regarding the  C NWP is Number of Work Packages C NRS is Number of Revenue Streams C MAXDV is the MAXimum number of Discrete Variables for certain arrays C NPEARS is how many types of Pearson Distributions we know about C IDEBU6 is what level of debug output we want generated C lERR is the system state, 0=ok, l+=error->exit COMMON NWP, NRS, MAXDVC, MAXDVR, NPEARS, IDEBUG,  lERR  

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