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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Economic risk quantification of toll highway projects Hatakama, Toshiaki 1994
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Title | Economic risk quantification of toll highway projects |
Creator |
Hatakama, Toshiaki |
Date Issued | 1994 |
Description | 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 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. |
Extent | 9271985 bytes |
Genre |
Thesis/Dissertation |
Type |
Text |
File Format | application/pdf |
Language | eng |
Date Available | 2009-03-02 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0050408 |
URI | http://hdl.handle.net/2429/5335 |
Degree |
Master of Applied Science - MASc |
Program |
Civil Engineering |
Affiliation |
Applied Science, Faculty of Civil Engineering, Department of |
Degree Grantor | University of British Columbia |
Graduation Date | 1994-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
Aggregated Source Repository | DSpace |
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