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Designing air transport networks that serve sparse demands Khayat, Abdulaziz A. 1993

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DESIGNING AIR TRANSPORTNETWORKS THAT SERVESPARSE DEMANDSBYAbdulaziz A. KhayatB. S., The University of Wisconsin-Milwaukee, 1983M.S., The University of Wisconsin-Milwaukee, 1985A thesis submitted in partial fulfilment ofthe requirements for the degree ofDoctor of PhilosophyinThe Faculty of Graduate StudiesDepartment of Civil Engineeringwe accept this thesis as conforming to the required standard.The University of British ColumbiaDecember, 1993© Abdulaziz A. Khayat, 1993In presenting this thesisin partial fulfilmentof the requirementsfor an advanceddegree at the Universityof British Columbia,I agree that theLibrary shall makeitfreely available forreference and study.I further agree thatpermission for extensivecopying of this thesisfor scholarly purposesmay be granted bythe head of mydepartment or byhis or her representatives.It is understoodthat copying orpublication of thisthesis for financialgain shall not beallowed withoutmy writtenpermission.(Signature)_____________________________Department ofCThe University of BritishColumbiaVancouver, CanadaDate Jo\,‘4DE-6 (2188)ABSTRACTThe aim of this thesis is to formulate a balancedrouting strategy for constructingefficient airline networks in situations where travel demand issparse. The strategy must strike abalance between the various objectives of both the airline operatorand the passengers. Integerprogramming was used to develop three routing algorithms. Thealgorithms were then used tocreate three efficient air networks. The networks were designed to attainspecific objectives.The first network minimized the total cost of airline operations. Thiswas accomplished byconsolidating the traffic demands at a few efficient hub locations toreduce the unit cost ofoperations, and by reducing the minimum number of required flights that meet all trafficdemands. The second network minimized the cost of travel of the passengersby reducing theirtravel and schedule delay times. The third network was designed to minimize the totalcombined cost of both the airline and the passengers. This was done by minimizing the airlineunit costs of operations, schedule delays, and travel times.As a case study, the domestic air transportation network of the Kingdom of Saudi Arabiawere examined. The routes and links between the different airports in the network wererestructured. The study showed that the algorithms were successful in achieving their designgoals. The study also showed that the attributes of air transport networks influence both thepassengers’ travel cost and the airline operating cost. The total cost and network structure arenot independent. Hence, air transport networks must be developed in sucha fashion that totalcosts are minimized and travel service within the network maximized.11TABLE OF CONTENTSAbstract iiTable Of Contents iiiList Of Figures viList Of Tables viiiAcknowledgements ix1. INTRODUCTION1.1.0 Background11.2.0 Routing Strategies31.2.1 Hub and Spoke Strategy 41.2.2 Point to Point Connection Strategy1.3.0 Problem Definition81.4.0 Thesis Objectives81.5.0 Description of The Study101.6.0 Case Study102. LITERATURE REVIEW 122.1.0 The Split Routing Strategy 152.1.1 Discussion of The Model 172.2.0 Heuristic Frequency Planning Model 182.2.1 Discussion of The Model 252.3.0 The Hierarchical-Hub (Hierhub) Model For Airline Networks 22.3.1 Discussion of The Model 332.4.0 Other Work 342.5.0 Summary 353. METHODOLOGY373.1.0 Linear And Integer Programming 373.1.1 Assumptions 33.1.2 Graphical Presentation of Linear Programming 413.1.3 Solution Concept 433.1.4 Integer Programming 483.2.0 Formulation of The Problem. 4c1113.2.1 Airline’s Network Design523.2.2 Passenger’s Network Design533.2.3 Combined Airline & Passenger Network Design593.2.4 Discussion And Validation of The Formulations6C3.3.0 Discussion of The Methodology 6€3.4.0 Computerizing The Formulation 684. THE COMPUTER PROGRAM 694.1.0 The Program694.1.1 Input Data, And Create Data And Problem Formulation Files714.1.2 View And Edit Existing Data File744.1.3 Read Existing Data File And Create Problem Formulation File 754.1.4 Analyse Network Designs 754.1.5 Performance Indicators And Analysis Data7€4.1.6 Sample Output795. The CASE STUDY815.1.0 Existing Network Conditions 815.1.1 The Structural Shape of The Existing Network 825.1.2 Operational Characteristics of The Existing Network 845.2.0 Case study Results 885.3.0 Analysis of Results 885.3.1 Efficient Airline’s Cost Network 925.3.2 Efficient Passenger’s Cost Network 975.3.3 Efficient Combined Cost Network 1035.4.0 Summary 1076. COCNCLUSIONS1097. FURTHER RESEARCH113REFERENCES115APPENDIX (A)119ivAPPENDIX (B)127APPENDIX (C)179APPENDIX (D)189VLIST OF FIGURES1.1 Airline Routing Strategies22.1 Illustration of Split Routing162.2 Flowchart of The Frequency Planning Model202.3 Patterns of Hub And Spoke Network272.4 Example of The B Matrices313.1 Graphical Presentation of Linear Programming433.2 Convex And Nonconvex Feasible Regions 453.3 The Two Convex Parts of The Feasible Region 463.4 Beesley’s Method For Estimating The Value of Time 553.5 Finding The Optimal Economic Cost of Travel 603.6 Example 1, Network Problem 623.7 The Traditional Urban Planning Solution 633.8 The Loop Solution 643.9 The Third & Fourth Possible Solutions 653.10 The Optimal Solution For Example 1 653.11 Example 2, Network Problem 663.12 The Optimal Solution For Example 2 664.1 Program Flowchart 704.2 Input Screen, Typical Example 735.1 The Existing Domestic Air Transport Network of The Kingdom of Saudi Arabia 835.2 Estimated Load Factors Distribution In Existing Network 845.3 Estimated Number of Flights Distribution In The Existing Network 855.4 Estimated Schedule Delay Distribution In The Existing Network 865.5 Estimated Cost Per Passenger-Mile Distribution In Existing Network 875.6 Efficient Airline’s Cost Network 895.7 Efficient Passengers’ Cost Network 905.8 Efficient Combined Cost Network 915.9 Estimated Load Factors Distribution In Efficient Airline Network 925.10 Estimated Number of Flights Distribution In Efficient Airline Network 935.11 Estimated Schedule Delay Distribution In Efficient Airline Network 955.12 Estimated Cost Per Passenger-Mile Distribution In Efficient Airline Network 96vi5.13 Estimated Load Factors Distribution In Efficient PassengerNetwork 995.14 Estimated Number of Flights Distribution In EfficientPassenger Network 1005.15 Estimated Schedule Delay Distribution In Efficient Passenger Network1015.16 Estimated Cost Per Passenger-Mile Distribution In Efficient Passenger Network1025.17 Estimated Load Factors Distribution In Efficient Combined Network1035.18 Estimated Number of Flights Distribution In Efficient Combined Network1045.19 Estimated Schedule Delay Distribution In Efficient Combined Network1055.20 Estimated Cost Per Passenger-Mile Distribution In Efficient CombinedNetwork 1076.1 Cancelled Links From The Existing Network In The Efficient Networks1127.1 Required Models For Efficient Airline Operations 113viiLIST OF TABLES5.1 Attributes of Existing And Design Networks108viiiACKNOWLEDGEMENTSI would like to express my deep appreciation to General Said Yousif Amin and Dr.Waddah K. Alem for giving me the opportunity to pursue my academic goals. I am alsograteful to the members of my examining committee and in particular to Dr. Frank Navin forhis guidance, helpfhl insights, and patience during the course of this study.Special thanks are also extended to my dear friend Dr. Abdulaziz Al-Madi, my familyspecially my wife, and all my good friends specially those at the Bechtel corporation, I.A.P.,and U.B.C. for their support of my search for knowledge.ix1. INTRODUCTION1.1.0 BackgroundTransportation networks are developed to move people andgoods. The total cost oftravel around a network depends on the capital costs of the fixed facilities and the operating costwithin the network. The attributes of the network influence both the capital cost and operatingcost. The total cost and network structure are not independent but mustbe developed in such afashion that total costs are minimized and travel service within the network maximized. Thegeneral problem addressed in this study is that of developing an efficient network when demandis sparse and spread over a large geographical area. The problem reduces to that of sparsenetworks. Such a problem is interesting to study because as will be seen later in the literaturereview chapter of this thesis, no research has been specifically published dealing with sparsedemand levels. Most of the published work on optimizing airlines operations has concentratedon making existing routes more profitable by optimizing crew and flights scheduling.Air transport services are characterized by high fixed costs at airports and operatingcosts that depend on the routing structure and travel demand. In networks with low demand fortravel, operating costs are thought to become even more critical and the shape of the networkhas greater impact on the final per unit cost of travel. The network’s structural shape is dictatedby the airline routing strategy. The most commonly used strategies are shown in Figure 1.1.These strategies are : the Linear Point to Point Connection Strategy and the Hub and SpokeStrategy.14Figure 1. 1 Airline Routing StrategiesLinear Point to Point Connection StrategyHub and Spoke Routing Strategy2As it will be shown later, airline routing strategies fallinto two categories, they arePoint to Point Connection or Hub and Spoke. Air transport networkshaving high degree ofdirect point to point connectivity and sparse travel demands are oftencostly to operate. Huband spoke networks tend to increase travel time and its associated cost.Yaw Jeng1 has shownthat a sound routing strategy can increase the air carrier’s operational efficiency and providemore convenience for the air travellers. Therefore, in sparse travel demands situationsabalanced routing strategy must be formulated to simultaneously consolidate travel demand andreduce travel time in order to minimize the total unit cost of travel. The importance of a goodrouting strategy is more evident when dealing with large geographical areas with sparse traveldemand levels. The air routes that develop in such situations are normally characterized by lowlevels of demands and low load factors on the aircraft. In addition, the frequency of service islow and the size of the aircraft used on such networks tend to be small. Smaller aircraft havebeen found by Schwieterman2to be less cost effective per seat mile supplied relative to largeraircraft as flight distance increases. On short routes however, smaller aircraft have a relativeadvantage over larger ones. To provide a better understanding of the two strategies, thefollowing will be a detailed discussion of their evolution, attributes, advantages, anddisadvantages.1.2.0 Routing StrategiesThrough the years different routing strategies have been developed to fulfil somespecific needs of moving people and goods between demand locations. In the U.S., the earliestroutes were determined by airmail requirements. The early airmail routes were established3between large cities and areas of high populationconcentrations. Not long after,transcontinental routes were developed to link the entirecountry. Prior to the airlineDeregulation Act of 1978 in the U.S., routes were regulatedby the government and the airline’srouting strategy was accordingly dictated. A common strategy in mostpublic transportationsystems at that time was to establish linear route structures withrelatively closely spaced stops.This strategy has also been used in air transportation, where it iscalled “hedgehopping”.However, the costs and passengers inconvenience entailed in making stops along the routeismuch greater in air transportation than it is in other modes3.Also the preference ofpassengersfor a minimum number of stops along the way is very strong4. These preferences combinedwith deregulation has caused the U.S. route system to be mostly shapedby competition betweenthe airlines and the new hub and spoke routing strategy has come to existence. Carriers havetaken deregulation as an opportunity to redeploy their resources and to make major changes intheir route networks5.1.2.1 Hub And Spoke StrategyA hub and spoke network can be thought of as a radial system of roads such as existedin older cities. The central city is equivalent to the hub of a wheel and the routes radiatingfrom it are the spokes that serve the outlying suburbs. In this type of network, the hubs act ascollection and dissemination points where the traffic demands are consolidated and an indirectconnection through the hub city between many city pairs that by themselves cannot generateenough traffic to justify direct flights is permitted6.Flights converge on a hub at approximatelythe same time, this convergence of flights is referred to as “bank” or “complex”. Each bank4lasts from the time the first inbound flight arrives at the hub until the lastoutbound flight hasdeparted7. Flights are normally scheduled in such a way that passengerscan transfer betweenflights on a bank after an adequate time to allow passengers and baggage tobe exchanged.Wheeler8listed the advantages and disadvantages for hub and spoke networks. Themain advantages are as follows:•A hub and spoke network provides high frequency service to a large number of lowdensity city pairs. This type of network allows a carrier to market many origin and destinationpossibilities to each spoke city. This strategy allows the carrier to compete in many marketswhile using relatively few resources. The resulting high frequency service is more desirablebecause it is attractive to business passengers and also it increases the carrier’s chance ofachieving top line display in the computer reservation system (CRS)9.• If there is high demand for non-stop service, a hub and spoke operator can realize higherthan average fares on a non-stop route that it monopolizes.• The large number of origin and destination markets that are normally served by this typeof network allows a hub and spoke operator to be less dependent on any particular market orgroup of markets. Hence, the economic effects of traffic demand fluctuations in a particularmarket will be minimized by this type of network due to the large number of other markets itusually serves.•A hub and spoke operator can normally market a large number of possible itinerariesand thereby increase the number of passengers that he can serve. Also passengers tend to likeusing the same carrier for the entire trip if the trip involves a transfer. Hence, because of thelarge possible itineraries, the operator will be most likely able to serve these transfer passengers.5This is highly desirable because the carrier can then keepa connecting passenger’s full fare,rather than a portion of it.• The large number of possible routing of aircraft and crew athubs permits greater use ofequipments and labour, as well as increased operational flexibility.According to Wheeler’° the main disadvantages of using hub and spokenetworks are asfollows:• A hub and spoke network contributes to congestion and delay at major airportsand inthe traffic sectors that serve these airports. Although in most countries specially inthe UnitedStates these problems are largely the result of the narrowing gap between systemcapacity andthe volume of aircraft movements, they are exacerbatedby the self imposed delay that resultsfrom the “banking” of flight schedules by hub carriers for the purpose of connecting flights.•The consolidation of a carriers operations at its hub results in over use of terminal staff,and equipments. This network type consequently has higher departure cost than lineargates,networks.• Finally, poor weather conditions at a hub airport can result in increased delays and coststhrough the system because of reaccommodation of misconnected passengers, prevention ofillegal scheduling of crew, and other operational problems.61.2.2 Point To Point Connection StrategyIn this strategy as the name implies, long-haul multistage connectionsbetween largecities are normally provided by the carrier. For example, Figure 1.1shows that passengerstravelling from airport 1 to airport 8 must make three stops along theway. The figure alsoshows that the route system does not have any dominant focus. Almostall airports in thenetwork have the same number of links connected to them. Oum and Tretheway” indicatedthat this route structure is sometimes referred to as a “Linear route system”. The reasonbehindthis name is the original government awards of the components of the route system tended tobestraight line routes. For example, the airline may initially have been awarded the right ofservice from 1 to 2 to 3 to 5. It may have been subsequently awarded the service right from 1 to6 to 7 to 8. The remaining routes were most likely awarded later in time.Long stage lengths require larger aircraft for range, and because of the lack of feedertraffic on this type of network the service frequency and passenger load factors tend to be lowwhich increases the cost per passenger unless the city pairs themselves are high trafficgenerators. The low service frequency tend to increase the average schedule delay ofpassengers. Schedule delay is defined as the difference in time between when a person wouldlike to make a trip and the time he is constrained to make the trip because of the airline’sschedul&2. Long travel distances may require overnight layovers, which reduce aircraftutilization rates. Depending on the size of network, aircraft servicing and apron services mayhave to be performed at various locations. Finally, it is well known thatmajor linear routesbetween important cities tend to suffer from intense competition and significantdiscounting1371.3.0 Problem DefinitionIf properly developed, hub and spoke networks are morecost efficient for the airlineespecially when demand is sparse because they consolidate the traffic at the hubs and reducetheminimum number of required flights. However, they tend to increase travel circuity. Circuityis defined as the extra distance needed to serve an origin destination (OD) pair by hub andspoke rather than point to point operatio&4.As a result of increased circuity, hub and spokenetworks increase both the travel time and its associated cost which is incurred by thepassengers. In contrast, point to point connection networks tend to do the opposite. Theyreduce the travel time and its associated cost because of the direct connections. However, theyare less cost efficient for the airline than the hub and spoke type specially when demand issparse. The lack of feeder traffic on this type of network reduces passenger load factors unlessthe OD pairs themselves are high traffic generators. The reduced load factors increase the costof operations per passenger mile because of the high fixed cost of service that is normallyallocated to airline operations. Also, the increased direct connectivity increases the minimumnumber of required flights which in return increases the operating cost of the airline. Evidently,serving large areas with sparse travel demands constitutes a unique problem. The problem hereis to formulate a balanced routing strategy which will minimize the airlines operating cost byconsolidating the demands at some locations in the network. Also the strategy must minimizethe passengers travel times and satisfy all the service demands.81.4.0 Thesis ObjectivesGiven the two routing strategies, and the complexities ofdemand in large sparsenetworks it becomes important to develop a balanced strategy for routing aircraft throughout thenetwork. Therefore, the objective of this thesis is to develop integerprogramming algorithmsthat will yield efficient routing strategies for sparse demand levels.The strategies will then beused to develop efficient air network structures. The structures must be developed in such away as to minimize the travel unit costs of both the carrier and the passengers. The carrier’scost will be minimized by consolidating the travel demands at some ideal hub locations inthenetwork. These ideal locations will be identified by the algorithms in accordance to the demanddistribution throughout the network and the ability of these locations to generate and attracttraffic. The passengers’ cost will be minimized by routing the traffic on routes that reducetravel times and schedule delays. The number of transfers that a passenger has to go throughwill be limited to one. Limiting the number of transfers to one is practical in two ways. First, itis realistic since in practice the majority of travellers try to limit their transfers. Second, thislimitation greatly reduces the number of possible link combinations between any two airports inthe network. As a result, this limitation reduces the number of variables and constraints andspeeds up the computations. The algorithms must also be flexible enough to allow the user tomodel some real life constraints and needs. For example, a specific link between any given twonodes can be included or excluded in the final network structure for any given reason. Also, thealgorithms must be able to deal with the possibility or impossibility of developing a certainairport as a hub in the final network structure. This is necessary because some airports do nothave the gate capacity that will allow them to be developed as hubs. Finally, the routing9algorithms will be built into a computer package thatwill develop the complete integerprogramming formulations of the efficient air networkstructure. The package will alsoevaluates the network’s effects on the airline operations andpassengers services in terms of loadfactors, operating cost, flight frequencies, and travel times.1.5.0 Description Of The StudySome form of integer programming will be employed. The thesis will develop a modelwhich will link air transportation demand levels to an efficient routing strategy. Generalizedcost functions will be developed and used as disutility measures of all possible routes betweenthe various demand locations to develop the efficient routing strategy. The cost functions willinclude elements of demand levels, passenger cost of travel time and schedule delay, airlinescost per passenger, and elements of the two routing strategies. Assuming that the airline canprovide enough flight capacity to satisfy the demands between all the different origin anddestination pairs, the model constraints will then be limited to providing a route between anypair. All possible links between the different demand locations according to the hub and spokeand point to point connection strategies will be used in the generalized cost function as thedecision variables of the model. However, only links that contain a maximum of one transferpoint connecting any pair of demand locations will be considered. This restriction is used toreduce the large number of possible route combinations if more than one transfer is considered.The model will also be flexible and will allow the user to include or exclude any particular linkin the network according to his/her judgement.101.6.0 Case StudyInitially, this thesis attempted to study the airtransport networks of Australia andnorthern Canada. However, this was not possible dueto the lack of publicly available dataelements of these networks. Alternatively, the domesticair transportation network of SaudiArabia which consist of 25 airports that have sparse demand levelsbetween the majority ofthese airports was selected as a case study. The routes and links betweenthe different airportsin the network were examined and restructured. This particular networkwas selected as a casestudy because it represents a unique opportunity since the network size islarge, demand issparse, and there is no other fast alternative of mass travel modes.During the planning phase of this network, the network plan placed strong emphasis onobjectives such as the country’s political integration, the establishment of direct links betweenall population centres, and the social well-being of the population. Asa result, all theKingdom’s centres of population are directly connected to the air transport system by their ownairports. The majority of these airports are directly connected to one another even thoughdemand levels do not necessarily justify direct connections. This high degree of directconnectivity and the low travel demands resulted in lowering the load factors on the majority offlights.112. LITERATUREREVIEWMost of the published work in the area of optimizing airlinesnetworks has concentratedon developing optimum schedules for a predetermined set ofroutes. This is possibly so becauseairline routes were regulated by the government. Thus, themajority of authors have treatedairline routing and scheduling as one single process. The separation of these processes isimportant since it has been found that the efficient selection of routes leads to moreprofitablescheduling’5.Hence, the determination of the sequence of stops for each aircraft through thenetwork of cities prior to scheduling is a critical function. Efficient routing selectionis evenmore critical when dealing with sparse demand, because it can consolidate passengers fromdifferent origins destined to one city through a hub airport and ultimately increase the overallaircraft load factor. Aircraft load factor is defined as the percentage of occupied seats, which isa measure of capacity utilization of the aircraft. Therefore, this thesis will treat airlines routingand airlines scheduling as a separate but highly related processes. Airlines routing which is themain concern of this thesis is defined as the sequence of cities where one aircraft lands. Aschedule is constructed when the routes are assigned specific departure times for each city andis evaluated for constraints and factors not included in the route construction process such ascrew scheduling, terminal operation requirements, and maintenance requirements of aircraft.Airline scheduling process normally encompasses complicated tasks of, synthesizing a multipleof interrelated political, economic, social, legal, and technical factors, to produce a balancedpattern of flights with a timetable that is consistent with the airline’s objectives and constraints.In practice, route construction, traffic forecasting, and operational evaluntions are the majoractivities that form the nucleus of the scheduling process. Traffic forecasts are normally12prepared by using information on the general economicconditions, competitive schedules, andfare structures. This forecasting process estimates the expected trafficby flight segment as anaverage for a given period. Then, an initial set of routings is constructedby combining theinformation on forecasted traffic with the previously flown timetable androutes to produce apreliminary schedule. A new forecast is then made using the preliminary schedulealong withthe other inputs. Based on identified operational inconsistencies andthe previous demand,another set of routings is constructed. the process continues to iterates throughthese steps untilthe final, operational timetable is produced (Richardson)’6.Prior to the airline deregulation act of 1978 in the U.S. when routes were dictated bythe government, most of the optimization work focused on determining the optimal airlinescheduling scheme for the regulated routes. Gordon and De Neufville’7presented a fleetallocation model that optimizes the level of service of a given air transportation network byminimizing the total delay, D, experienced by passengers being served by a fleet with a givennumber of aircraft over a given set of routes. The concept of schedule delay was introduced inthis model as a measure of the value of a given frequency of service. Schedule delay wasdefined as the difference in time between when a person would like to make a trip and the timehe is constrained to make the trip because of the inflexibility of the airline’s schedule. If the loadfactor is fixed on the given routes, it was assumed that schedule delay could be represented withsufficient accuracy as proportional to:(1—p)’;s113wheres = un determined constant that was assumed to be equal to 1.p = the load factor on link i which is assumed to be fixed by the airlines.Based on the above equation, the total schedule delay which is measured inpassenger hours forall passengers was represented as:D = av1(1.pS)_l/SN1wherea = proportionality constant that is assumed to be the same along every link.V1 the volume of passengers on link i.JV = the number of aircraft on route i.The model then basically minimizes the total schedule delay given by the aboveequation. However, the amount of service provided can not exceed the capability of the aircraftfleet, S, which is measured in units of available seat-hours over a given period of time. Inpractice, S would be calculated form the knowledge of the average utilization, capacity, andcruise speed of the aircraft in the fleet. Hence, the model is subject to the following constraint:N1ct Swherec = the capacity of aircraft= the total gate-to-gate or block time for an aircraft over route i.14The model can be solved for any specific patterns ofdemand, size of aircraft, networkconfiguration and number of aircraft in the fleet. By manipulatingthese variables and solvingthe problem and then comparing the results of the solutions, it becomespossible to determineoptimal values of these factors.Dantzig and Ferguson’8 formulated the original linear programming modelthatdetermine the optimal frequency of flights between each city pair to maximize revenue.Etschmaier’9related the airline demand to its frequency of service and the attractiveness ofdifferent aircraft types as well as to the general competitive position of that airline in themarket. Kushige2°considered the case where flight frequencies are symmetrical on the routesbut the demand is not.After the Deregulation, a new trend in airline’s routing has emerged. Airlines have takenderegulation as an opportunity to redeploy their resources and to allow market competitionforces to shape their networks. Since then more work that specifically deals with airline’routing has been published. The following literature review includes some of the publishedworks on airline routing.2.1.0 The Split Routing StrategyJeng2’proposed what he called the split routing strategy. The strategy is primarily basedon serving passengers demands by providing either a direct point to point connection or aconnection through a hub airport according to the relative locationsof origins and destinations.15The costs to be minimized in this strategy include airline operating costsand passenger traveltime costs. The key network parameters include demand level, networksize, and number ofcities or nodes served by the network. The demand is assumed to be homogeneous and constantthroughout the network. And the airline network is structured in a circular configuration. Thecircular network configuration shown in Figure 2.1 assumes that all non-hub nodes areuniformly located along the circumference of a circle with a hub at the center. To apply thisstrategy, airline networks are approximated as circular network needing only the radius of aFigure 2. 1: Illustration of Split Routingcircle and the number of nodes. The radius of the circle can be calculated by averaging all thedistances between non-hub nodes and the hub. According to the strategy, destinations areserved by splitting them depending on their relative locations to the origin, with either pointto point or hub and spoke operation. The main idea behind split routing is to reduce the circuitywhen serving any origin destination pair (OD). For example, the circuity to serve OD pair AB4BA)16in figure 2.1 by hub and spoke operation is much greater than thecircuity to serve OD pair ACby the same operation. Therefore, it is reasonable and logical to serve the nodes closer to theorigin with point to point and the others with hub and spoke operations.The problem thenbecomes finding the number of neighbouring nodes on each side of a non-hub origin that canbeserved by direct point to point operation such that the total cost of the service is minimized forboth the airline and the passengers. This is solved by finding an optimum value for the splitangle W as shown in figure 2. 1. The optimum value of P as derived by Jeng is presented by thefollowing equation:= O.5itWhere:n = the number of nodes in the systemp = Average demand per O-D pair (Passengers / day)d Radius of circular network (mi)The optimum split angle in radians2.1.1 Discussion Of The ModelJeng’s study may provides good understanding of the trade-offs and cause-effectrelationships among key network components and their impacts on the shape of the network.However, the simplified assumptions used in the study such as; the homogeneity of the demand,the inelasticity of the demand with respect to time and cost, and the circular shape of thenetwork with one single hub are too restrictive for actual applications. Hence, the accuracy ofits results specially those that relate to the optimum shape of the network is questionable.17Also, serving sparse demand requires the consolidation of that demand inorder to increase theload factor to minimize the cost per passenger, the model provided in this studydoes not has themechanism to do so. In this method traffic may be consolidated at the single hubin the networkbut only in accordance to the relative geographical locations of the origin and destination.2.2.0 Heuristic Frequency Planning ModelGhobrial, Balakrishanan, and Kanafani22 developed a two-phase heuristic model forairline frequency planning and aircraft routing for small size airlines. The first phase of themodel which is the most relevant to this thesis yields a frequency plan by using an economicequilibrium model between passenger demand for flying a particular route and airline’s supplyof flights on that route given the operating characteristics of aircraft flown. According to theauthors, a frequency plan specifies the configuration of the network (non-stop or multi stoproutes), frequency of service, and the type of aircraft assigned to each flight. The modelhowever assumes only one aircraft type will be used for all flights. The second phase uses atime-of-day model to develop an assignment algorithm for aircraft routing. Together, bothphases are referred to as the schedule construction process.The model is built on the assumption that airlines tend to compete against each other byproviding more flight frequency. This is so because airline’s traffic share of a given market tendto increase as its frequency share in the market increases. Therefore, while airlines try tominimize their operating cost by flying the minimum number of flights in the market, theirflight frequency competition pushes them to operate at their break-even load factors. Given18individual airlines price and operating cost, market equilibrium isreached when each airlineoperates at its break-even load factor subject to indivisibility of flightsand assuming areasonable return on investment23.Given a set of origin-destination markets,a set of candidateroutes (i.e. possible connecting routes for each origin and destination pair while keepinginmind that a route can be composed of a single or multiple links, and any link in the networkcould serve one or more routes connecting different city-pairs.), aircraft types, yieldandoperating cost functions, the objective of the model is to find a set of supply decisions. Thesedecisions include aircraft type, frequency, and routings which achieves a certain goal such asmaximizing airline profits.Figure 2.2, shows the flowchart of a computer based solution algorithm which wasdeveloped by Ghobrial etal to incorporate a set of modules that constitute the frequencyplanning model. As shown in the figure, a set of candidate routes is defined by the user foreach city-pair in the network. These routes represent the possible ways in which service can beprovided between them (i.e. non-stop and multi-stop). The basic requirement for the networkrepresentation is to ensure a conservation of flow at each node. This can be accomplished bythe following constraints:0 fj=o,d (1)1od =+ D0dfj= d V o, d pair (2)—Dodff=O(3)where:od= 0 - D traffic using link id.D0d = 0 - D traffic (demanded at d)194Origin-DestinationPassengers BetweenEach City-PairIn The NetworkAircraftOperational AndEconomicCharacteristicsParameters Of TheUtility FunctionAnd Break-EvenLoad FactorOn Each LinkA Primary NetworkStructure(Candidate RoutesBetween City Pairs)Initial Solution usingUnit Frequency onEach Link In TheNetwork-‘I’,New NetworkStructurePassenger ChoiceOf The Route ToEstimate Route FlowThen Link Flowt‘illScamiig RoutmeDelete Links WithLoad Factors BelowBreak-Even, AndDelete All RoutesContaining ThemFlight FrequencyOn Each Link1INOYesA Frequency PlanFigure 2.2: Flowchart of The Frequency Planning Model20Another set of constraints is used to ensure the structuralrelationship between link androute frequencies. The frequency of service ona given route must be the minimum offrequencies on all links contained in that routeFrMjfl {F} (4)1] LrWhere:Fr= Service frequency on route r.Lr= Set of links contained in route r.F. Service frequency on link ij.To run the model, unit frequencies are initially assigned to all available routes in thenetwork. The traffic is then distributed to these routes (and then to the links) on the bases of aroute choice model. The route choice model is built on the concept that traffic demand forflying a particular route is dependent on the different levels of service attributes of that route(i.e. travel time, frequency of flights, travel cost, number of transfers, etc.). The traffic betweenany O-D pair will be distributed among the different routes joining that pair according to thedifferent service levels offered on these routes. This traffic distribution process is accomplishedby using the multinomial logit model which relates the flows on different routes joining anycity-pair as follows in equation (5):ev (r)flr(5)keKod21flijflr(6)reRwhere:11r= Passenger flow on the r th route connecting the O-D pairK0d= set of all routes connecting the O-D pairR1 = set of all routes containing link ijV(r) utility function for the rth routefl1 = traffic on link ijEquation (6) is used to ensure that the flow on any link is equal to the sum of all flowson all routes containing that link. The utility function V(r) is used as a measure of the serviceattributes of the route and it is assumed to be linear. Service attributes considered in this modelinclude flight frequency, travel time, and air fare. For example, IfFris the service frequencyon route r,Tris the travel time on route r, andj is the fare on route r, then the utility functionV(r) can be formulated as:V(r) = cx Fr+13Tr+ 4fr+ +6 (7)where cx, f3,4, are the attribute coefficients in the utility function and 6 S the error term ofestimation. A characteristic of the logit model is worthy of noting here is that choice elasticityis not constant but is directly proportional to the value of attributes in the utility function (e.g.flight frequency) and inversely proportional to the probability of choice. This implies that themore likely a particular choice is, the less sensitive it is to changes in the value of the utility22function (e.g. diminishing returns of choice with respect toincreased frequency). The inclusionof both time and frequency in the utility equation (7) will then guaranteethe convergence of thetraffic assignment process.According to the flowchart, new link frequencies are then calculated to satisfy theloadfactor constraints. The following set of equations are used to ensure thatlinks with unprofitableflights are dropped out from the initial route network. The flight frequencyFon link i j isexpressed as:mt-ifjLmt(.L)(8 a)mt <mt(8 b)0 if nil < 24s(8c)= F S if > 1 (9 a)U=UFS1 (9 b)=I(9c)where:fl= initial number of passengers on link ij.fl = actual number of passengers on link ij.= actual load factor on link ij232P = break-even load factor on link ij.S = aircraft capacity in terms of number of seatsAccording to Ghobrial eta!, equations (8 a)and (8 b) ensure that an airline operates atleast at its break-even load factor given indivisibility of flights. Equation(8 c) guarantees thatany link is deleted if its traffic does not justify profitable operation of a single flight whenitsresulting load factor is below the break-even level. This is the main reason for airline hubbingwhere low traffic density markets are served through a hub airport24 to consolidate the trafficdemand and to increase the load factor. Because the indivisibility of flights, the frequenciesobtained from equations (8 a) and (8 b) may result in load factors exceeding 100 %. This cantake place when serving thin traffic market where providing two flights can result in a loadfactor below the break-even level. In such case, the airline will then have to operate only onefull flight carrying fl, passengers. In this case however, the airline will lose (flu-unaccommodated passengers to its competitors. This condition is accounted for in equations(9 a) and (9 b).Finally, The flowchart indicates that, the O-D demands are re allocated to differentroutes to account for the effects of the new frequencies on the route choice. The process isrepeated until network equilibrium is reached when no change in both link frequencies andpassengers flow take place. At this stage the scanning routine is used to delete all links withload factors below the break-even level. Consequently, all routes containing these links will alsobe deleted. According to Ghobrial etal, this entire process is iteratively repeated until networkequilibrium is reached and the resulting load factors on all links are economically feasible.242.2.1 Discussion Of The ModelIn a competitive market with a high level of demand,this model is a good tool fordetermining the optimum flight frequency plan for a given set ofcandidate routes, and as aconsequence it will yield an optimum shape or configuration of the network.This can beaccomplished by deleting links and routes from the initial set that do not meet the load factorconstraints and keeping those that do. However, it can not be used as a stand alone model toprovide an optimum frequency plan when the demand is sparse and airlines competition doesnot exist. This is because of the fact that the model was built mainly onthe concept thatfrequency competition between airlines pushes them to operate at their break-even load factor.Hence, the main objective of the model is to formulate a frequency plan that will allow theairline to operate only on those routes that meet its break-even load factor constraints given theindivisibility of flights. The model does not consolidate the demand and it is not intended to doso. As will be shown later, when demand is sparse a more appropriate objective for the airlinewould be the minimisation of its operating cost by consolidating the demand and operatingthrough a hub airport. In many situations as it will be seen in the case study later on, airlinesare subsidized to provide air transport as a social service when operating uneconomical flightsdue to the lack of demand. In such situations, the airline will operate on some routes that willnot meet its break-even load factor constraints. In such cases the frequency planning model canbe used as a second step to provide a flight frequency plan for a pre optimized set of routes thatconsolidate the demand.252.3.0 The Hierarchical-Hub (Hierhub) Model ForAirline NetworksY.H. Chou25 developed the hierhub model based on the hierarchicalstructure of the huband spoke network which is shown in Figure 2. 3 - D. Four basicpatterns of hub-and-spokenetworks are shown in Figure 2.3. The names clearly indicate theattributes as : the single-hub,the double-hub, and the multiple-hub. Node 5 in Figure 2.3 - A is the only hub that acts as asingle transfer location connecting all the other nodes in the network. In the double-hubpatternnodes 4 and 5 serve as the transfer locations through which all flights have togo. In single anddouble-hubs the number of links is minimal and it is equal to N - 1 where N is the number ofnodes in the network. This will imply the existence of only a single path between any twonodes which will basically eliminates the need for any trip assignment process since all tripswill be assigned to that path. Consequently, traffic demands will be consolidated at the hublocations. In multiple-hub networks however, as hubs are all directly connected, the number oflinks is larger than that for a minimally connected network. Therefore, multiple paths will existand provide greater flexibility in routing, resulting in more convenience to passengers.262. 3 - A. Single-hub Network2. 3 - B. Double-hub Network2. 3 - C. Multiple-hub2. 3 - D. Hierarchical-hub4LocalhubPrincihub10 98Local hubFigure 2.3 Patterns of hub-and-spoke networksWhen sufficient air travel demand exist, multi-hub networks are in general morerealistic because major carriers operate on networks with multiple paths. The provision ofmultiple paths in a network is the result of a balance between the savings in operational costs27and the increased revenues from higher passenger patronage.In a hierarchical-hub networks,hubs may or may not be directly connected. The number of links is minimum,and there is onlyone possible path for each trip. Consequently, once the hubs are identified, links canbeestablished and flows are assigned accordingly eliminating the need fora separate tripassignment process. As can be seen in Figure 2.3 - D, in this type of network pattern,a nodemay be the principal hub, a local hub, or a spoke depending on siting and trip assignment. Thetotal number of hubs is determined by the structure of the optimal hierarchical network. All thenodes that provide any degree of switching are considered hubs.To summarize, the hierarchical-hub network may be considered as an early stage versionof the multi-hub network. At a later stage, as traffic demand increase and the need for multiplepaths emerges, a carrier may increase links and upgrade the network into a multi-hub system.This makes the hierarchical-hub an intermediate network between the double-hub and themulti-hub systems. In addition, both the single-hub and the double-hub networks can beconsidered as special cases of the hierarchical-hub network.According to hierarchical-hub model the following exogenous variables are required formodeling Hierhub networks:N = The number of nodes in the network.= The traffic flow originating from node i.= The traffic flow destinated for node j.= The traffic volume from node i to node j.= The unit transport cost between node i and nodej.28The structure of a hierarchical hub-and-spokenetwork is expressed mathematically byan N X N connectivity matrix26.The first degree connectivitymatrix shows the presence orabsence of a direct link between each origin-destination (O-D)nodes in the network. If a directlink exist, its representing element in the matrix willbe assigned a value of 1; otherwise theelement will be assigned a value of zero. Similarly, the second degree connectivity matrixshows the indirect connectivity between each O-D pair utilizing the combinationof two directlinks.For developing the hierhub model, connectivity matrices are modified into the Ematrices. These E matrices are developed for a minimally connected network. A network isconsidered minimally connected if all of its nodes are connected by N - 1 links. The first degreeE matrix, E’, is similar to the first degree connectivity matrix except that the E1 matrix must beminimally connected. is the ith - row and jth - column element. It is equal to one if there isa direct link between the corresponding nodes; otherwise it is equal to zero. Similarly, Thesecond and the third degree E matrices, E2, E3 , are constructed. The degree of E matricesranges from one to the diameter of the tree which is defined as the minimal number of steps orlinks between the most distant node pair in the network. An important distinction between Ematrices and connectivity matrices is that for each O-D pair only the shortest path is recorded inthe E matrices. And if a path appears in a lower degree E matrix for any O-D pair, the sameO-D pair in all higher degree matrices will be zero. Mathematically, the E matrices are specifiedby Chou as follows:e (0, 1) V i,j,k (1)U29Vi,k (2)(3)kij(4)ii iiiE’=2(N—1) (5)iiii(6)juE’N—1 (7)iUThe above equations were developed to satisfy the following constraints: Equation(1)requires that each element in the E matrix is either 1 or 0 depending on the presence or absenceof connectivity (link) for the corresponding degree k. Equation (2) requires that all path fromone node to itself are non-existent. Equation (3) indicates that only the shortest path for eachO-D is considered. Equation (4) states that each O-D pair has symmetrical paths. Equation (5)ensures the matrix to be minimally connected. Equation (6) ensures that each node to be directlyconnected with at least one other node. Equation (7) requires every node to be directlyconnected to no more than N-i other nodes to guarantee no circuit exists in the network.For illustrative purposes, Figure 2.4 shows an example of a 6-node network which isminimally connected. The largest degree of the E matrices is four since the diameter of thenetwork is equal to four. This is because the longest path which is between nodes 4 and 6 in thenetwork takes four steps; 4 to 3, 3 to 2, 2 to 1, and 1 to 6.30B1123456101000121010103 0101004 00100050100006 10000031234561 0001002 0000003 0000014 1000105 0001016 001010E12345610010102 00010131000104 010000510100060100004E1234561 0000002 00000030000004 00000150000006000100Figure 2. 4 Example Of The E matrices Of A 6-Node NetworkAccording to Chou, the first step of the hierhub modeling is to build a minimal spanningtree for each node as the root of the tree and the node is denoted as r. For each tree at least anE’ matrix is obtained and a new transport cost, can be determined whichis defined as thetotal cost of travel from node i to nodej in the tree such that:a42E31C=+(Cim+Cmj)EmEjEj+(Cim + Cmp++ +(Cim ++ Cqj)Ewhere d is the diameter of the tree.The number of elements in the above equation will be equal to the diameter of the tree. The firstelement is composed of direct links. The second element consists of two steps indirect paths,i.e., when transfer through an intermediate node is necessary to move from origin to destination.Similarly, the third element consists of three steps indirect paths, and so forth. It should benoted here that, for each i-j pair there is one meaningful element only. For example, in therooted spanning tree of figure 2. 4, between nodes 1 and 5 only E215 equals one while all theotherEk15are zero. Accordingly, the defines the actual transport cost for the two stepsindirect path between nodes 1 and 5.The cost (r-cost) can be greater than, equal to, or less than the given transport cost,C, depending on the structure of the tree. It can be greater than C if the direct link of minimalcost between nodes i and j is not included in the tree. In this case the new cost is higher becausean indirect path of higher cost must be used in connecting these nodes. The r-cost is equal to thetransport cost either when the direct link is included in the tree or when the total transport costof the indirect path is identical to C. . The r-cost can be less than C, when there exists anindirect path of which the total transport cost is less than that of the direct link. This situation32can take place due to the scale effects associated with larger traffic volumewhich can result asthe traffic gets consolidated along the indirect path.After determining the cost for each O-D of each tree rooted at each node, the modelsearches for the system which minimizes the total transport cost while satisfying the flowconstraints. This can be mathematically formulated as follows:MinZ=2CWV riisubject to:wu=oiThe final result of the model includes an optimum spanning tree which connects all thenodes in the network, the traffic volume assigned to each link, and the traffic volume goingthrough each node. In the optimal system, any node having traffic volume larger than its O-Dvolume is a hub because it handles connecting traffic. Otherwise it is a spoke. The hierarchicalstructure can be identified from both the linkages of the spanning tree and the assigned trafficvolumes.2.3.1 Discussion Of The ModelOne important feature of this model is its ability to endogenously derive the optimalnumber of hubs and also identify their locations in the network. Models that require this number33to be provided arbitrarily as an exogenous variable havesome difficulty in justifying thatnumber. In order to accept an arbitrary number, one must solve theproblem for differentnumbers of hubs and compare the solutions. Such comparative process canbe time consumingand costly. However, this feature might not be desirable in all situations. Forexample, in someoccasions a carrier might decide for one reason or another to establish a network witha certainnumber of hub facilities. In other occasions, some airports can not be developedas hubs eitherdue to their lack of capacity or due to some other reasons. At the same time some other airportswill be more suitable for that purpose but this model does not have any control mechanism thatwill help in dealing with this problem. Also, the model does not allow its user to add or deleteany specific link in the network. Consequently, travelling between two non-hub airports mightrequire two or even more transfers resulting in longer travel times. This is because the modelwas built to optimize the network for the carrier purposes and completely ignored the traveller.2.4.0 Other WorkTodoroki, Hanzawa, and Fukuda27 proposed an integer programming model thatidentifies the optimum location(s) of hub airport(s) among all airports in the network. Themodel basically assumes that all flights must go through a hub airport. The objective of theoptimization is the minimisation of the total trip-distance. For a single-hub air network theobjective function is:Min{YOi d(p1,H)+D1d(H,p)}I34where:= the amount of trips originated at airport i andterminated at airport j.H = the serial number of an airport which is chosenas the hub.p. = the serial number of an airport i.d(x, y) = the distance between airport x and airporty.In the case of a multiple-hub network, the model assumes that each local airportisserved by only the nearest hub airport. Also two flight patterns exist, onewith flight path thatgoes through one hub only and the other with flight path that goes through two hub airports. Inthis case the model is formulated as follows:MinW,{d(p1,Hi) + d(H1,H2)+ d(H2,p3)}iiFor this model to work the number of hub airports in the network has to be chosenarbitrarily by the user as an exogenous variable and the earlier mentioned comparative approachof different numbers must be taken to determine the optimal number.2.5.0 SummaryTo summarize, It is safe to conclude that prior to the airline deregulation act of 1978 inthe U.S., the majority of the academic work has concentrated on developing models thatprovide optimal solutions for scheduling flights over given sets of pre determinedroutes. The35main concern of those models was to make the existing routes more profitable to operate. Thiswas the case because routes were dictated by the government and the airlines did not have thefreedom to alter them. For example, the previously discussed models that were developed inthat time were created to either produce airline schedules that minimize the schedule delay timeof the passengers, or to provide the optimal frequency of flights that will minimize theoperating cost of the airlines on the given routes. After the deregulation, models weredeveloped to provide optimal network configuration, optimal frequency of service, and optimalhub locations. It is important to remember that these models, as with any mathematical models,can not represent the real world in perfect detail. Also, there is no specific criteria as to whatdetail is sufficient enough. Inescapably, a model will not meet someone’s notions of what is theright level of details because each model has a limited scope and certain objectives to satisfy.However, any model can not generally be judged right or wrong. Every model has a certainvalue, which depends on how important the problem being modelled is, and how much insightthe model provides into the problem. Finally, dealing with networks that serve sparse demandsis unique because such networks have not been specifically addressed in the published literature.363. METHODOLOGYThis chapter outlines the methodology to develop the routingalgorithms. Also a shortreview of linear and integer programming techniques will be given. Apresentation of themechanics, the assumptions, and the implications of the assumptions involved in these twotechniques will be discussed to provide a better understanding of the methodology. The routingalgorithms and the necessary data elements required to optimize sparse networks will also bepresented.3.1.0 Linear And Integer ProgrammingAccording to Wu and Coppins28,linear programming is a mathematical technique that isnormally used as a decision aid tool for selecting the best course of action(the optimumalternative or solution) from a given set of feasible alternatives. It is called linear because therelationships between the variables involved are linear.A typical linear programming problem can be presented as follows: Optimize (eithermaximize or minimize) a dependent variable which is a linear function of some independentvariables subject to a series of linear constraints involving the independent variables. Thedependent variable is known as the “objective function” and usually involves economicconcepts such as; profits, revenues, costs, sales, time, distance, etc. The objective function is anequation that defines the quantity to be optimized. The independent variables in the objectivefunction equation are called “the decision variables” because the decision maker must determine37the values of the variables that optimize the objective in order to solve theproblem. An optimalsolution to any linear program includes a set of values for the decision variablesor sets ofvalues in some cases when the solution is not unique. It also includes the corresponding valuesof the objective function. A standard linear program can be written in symbols as follows:Optimizef=clxl+c2x2+ +CX;1or1=1Subjectto allxl+a12x2++alnxn bia2lxI+a22x2+ +a2x b2a1 Xi +a12x2 + +a1x b1amixl+am2x2+....+amnxn bmor i=11=1X1,X2,XOwherex, , x2 , X, = decision variables= objective functionC, , C2 , C, = coefficients of decision variables in the objective functiona11a2 , a1,, = coefficients of decision variables in the ith constraintb1 = constant (the right hand side of the ith constraint)Since in practice linear programming problems normally deal with a very large numberof variables and constraints29,they are mostly presented in vector and matrix notation. Thus:Max or Mm f=CX38Subject to A X or Bwhere C, X, and B are row and column vectors, andA is the matrix of a1,parameters of thevariables in the system of constraints.3.1.1 AssumptionsAccording to De Neufville30,the power of linear programming isa direct result of theassumptions it makes about a problem. The main assumption of linear programming is that theobjective function and all the constraints are linear. Also, the decision variablesare assumed tobe nonnegative and continuous in the case of linear programming. In the case of integerprogramming the decision variables are assumed to be nonnegative and integers.Linearity. The idea of linearity here is more specific and limited than the general idea that themajority of people have about a linear equation. Generally, a linear equation is thought of asone with all variables contained in the equation are raised to the power of one.Formally, a functionf(X)= f(X , X) is linear if, for all variables X andconstants S1:f(S1X SX)=S1f(X)+ +Sf(X)This definition can be split into two equivalent statements:1. Constant returns. A linear function must have constant returns or economics of scale. Thisimplies that f(SX) Sf(X)39which really means that multiplying every decision variableby a common factor S leads to anS-fold change in the objective function or constraint.2. Additivity. A linear function must be additive which means that thevalue of the functionwith all X simultaneously is equal to the sum of the values of that functionwith eachXibyitself:f(S1X SX)=S1f(X)-F +Sf(X)this implies that the contribution of eachXitof(X) should not depend on the presence orabsence of any others.Continuity. As mentioned previously, linear programming assumes that the decision variablesare both continuous and nonnegative. The continuity assumption means, as a practicalmatter, that the physical realities do not restrict them to integer or discrete values. Thisrestriction can be seen as a difficulty since many systems do indeed consist of design elementsthat can only be integer or discrete. For instance, the number of aircraft in a fleet must be aninteger, as must be the number of warehouses in a distribution system. In practice however, theassumption of continuity dose not constitute a major difficulty. This assumption can be dealtwith in two ways. First, we can simply assume that integer variables are continuous and roundoff our results. In many situations this will be satisfactory if the possible error of a few percentis within the accuracy with which we can formulate any real problem. Second, in somesituations, some people might argue that the rounding off approach might violate some of theconstraints or it might produce a nonoptimal solution. In such situations, integer programmingwhich offers a way to formulate linear programs that can cope with integer values can be used.40Nonnegativity. This assumption which restricts all of the decision variablesto nonnegativevalues is merely a technicality imposed by the way a linear program finds theoptimal solution.In practice, this requirement does not really restrict us since we can alwaysdefine variables sothat they are not negative. Consequently, this assumption just requires thatwe be careful in theway we formulate a linear program.3.1.2 Graphical Presentation Of Linear ProgrammingAs long as the number of decision variables is 2, linear programs can be analysed andsolved graphically. Consequently, a graphical approach is not practical since most real worldproblems involves a large number of decision variables. However, a graphical presentation herefor a hypothetical problem as seen in figure 3. 1 will provide valuable insight into therelationships and solution procedure of linear programming in general.For illustration purposes, the following problem is to be analysed:Maximize f = 12 X1 + 8 X2Subjectto 6X1+2X2l203X+4X 120x1,x2 owhere:the objective function f(X1,X2) can be thought of as the profit from selling two products. Thecoefficients in the function represent the per unit profit from each product. X1,X2 are the twoproducts. The right hand side of the two constraints represent the amount of two resourcesavailable for manufacturing the two products, while the coefficients in the constraints represent41the amount required per each unit of production. The problem here is tofind the most profitablemix of the two products.The above problem is presented graphically in figure 3. 1 by letting the horizontal axisrepresent ( X1) and the vertical axis represent ( X2).The nonnegativity constraints mean thatonly the first quadrant is meaningful. The two constraints are plotted by finding their interceptson each axis and lines were connected through them. Any feasible solution or production mix ofthe two products must satisfy the two constraints simultaneously. Therefore, the set of feasiblesolutions is the intersection of the sets of points which satisfy each constraint. This set is shownin figure 3. 1 by the shaded area in the figure. To find the optimal solution, the objectivefunction(f) must be considered. But since we cannot graph ( f) per se since it does not have afixed value, its “iso line “ for a particular value can be graphed. In this example, its iso linefor f= 120 is drawn. “Iso “means the “ same “, in this case each point on the line f= 120 is acombination of the two products that will yield a profit of 120. Since this problem requires themaximization of the objective function, this means that we must construct the “iso line” whichhas the largest value of the objective function and still passes through the set of feasiblesolutions. Alternatively, the process of finding the optimal solution can be envisioned asdrawing an iso line for the objective function through the set of feasible solution and thenpushing it as far as it can go while still passing through the set. In this example, the optimalsolution occurs at point (A), which is the only point in the feasible region through which themaximum iso line(f ) passes.42Figure 3. 1 Graphical Presentation Of Linear ProgrammingAs mentioned above, the optimal solution to the given example occurred at point (A),which is a corner point in the set of feasible solutions. This did not happen by a chance. It canbe shown by the solution concept discussion which will be presented below, that the solution tolinear programming problem always can be found at a corner point or points of the set offeasible solutions.3.1.3 Solution ConceptThe solution to any linear programming problem no matter how complex orsophisticated the problem is, is entirely based on two important consequences of theassumption4Graphical Presentaton OfLi near Programming7060504030201006 Xl + 2 X2 = 120= 120xl40 50 6043of linearity of the objective function and constraints. In order to presentthe solution concept, itis first essential to present the effects of the linearity assumptions,which provide the basis forall linear programming procedures.Effects Of Linearity Assumptions.The linearity assumption has two effects, they are:1. If it exist, the feasible region is convex.2. The optimum solution is located at an edge of this region, particularly at one of its corners.These two facts greatly reduce the optimization procedure to a search through a limited set ofwell defined possible solution combinations located specifically on the edges of the feasibleregion, which is very small compared to the infinite number of solution possibilities containedin the entire feasible region.To facilitate the following discussion of the effects of linearity assumption, it isimportant to define what is meant by a convex feasible region. Formally, a feasible region isconvex if every straight line between any two points in the region lies entirely in the region.As it can be seen in figure 3. 2 , a convex feasible region is therefore one that has no reentrantboundaries, no edges that intrude or dent into its space. It is worth to mention that, theconvexity of the region does not simply depend on the shape of its boundary. As it can be seenin the same figure, the same boundary can be associated with both convex and nonconvexregions.444NTo explain the two effects of linearity, it is helpful to visualize the feasible region to beconsisting of two parts. As shown in figure 3.3, these two parts are:1. The space defined by the constraints.2. The volume defined by the relationship of the decision variables to the objective function.If the feasible region defined by the linear constraints exist, it must be convex since anytwo points that satisfy any constraint must be on one side of that constraint inside the feasibleregion to satisfy all the other constraints and any line between them will be entirely in thefeasible region. Therefore the operational definition of convexity is met. At this point it isworth mentioning that, a feasible region might not exist at all. This situation can take place ifthe constraints are contradictory and there is no possible set of decision variables that willX2X2NonconvexRegionReentrantACovex FeasibleRegionRegionxlFigure 3. 2 Convex And Nonconvex Feasible Regions45satisfy all constraints simultaneously. In this case the solution isinfeasible. A good example forthis situation in the real world is the possibility of not being able tomeet some environmentalstandard with the available technology or resources.4Feasible RegionFor XxlFigure 3. 3 The Two Convex Parts Of The Feasible RegionBy the same argument as before, the volume defined by the objective function andconstraints is also convex. And since the objective function is linear, it can be concluded thatthe rate of change from any point interior to the region in any direction is constant. Hence, theremust be an edge that has a value of the objective function equal to or greater than any interiorpoint in the region. Only one exception to this can occur if the problem is unbounded so thatfFeasible Region ForObjective Functionf=Cl Xl +C2X2S.X246it is possible by the way the constraints are set to increase theobjective function infinitely.Similarly, since the rate of change of the objective functiona long every edge is constant, thevalue of the objective function must be equal to or greater at one of the corner points to thatedge than anywhere in the middle of the edge. Therefore it can be concluded that the optimalsolution must be located at a corner point. In the example of figure 3.3, when maximizing theobjective function the solution must be at R, 5, or T.It is possible to have multiple optimal solutions for a linear program. This situation cantake place when the rate of change of the objective function along an edge is zero (Theobjective function and a constraint have the same slope). In such case, the entire edge,including its corner points, constitutes a set of optimal solutions.Numerous computer programs are available for solving linear programming problems.They differ in their degree of sophistication and range from smaller routines that run onpersonal computers to very large programs that can deal with thousands of variables. To solvea linear programming problem, all programs are essentially developed to conduct an organizedsearch for the solution through the corner points. The general procedure for finding the optimalsolution can be described as follows:1. Find a corner point as a feasible solution to all constraints.2. Proceed sequentially to other corner points that provide better solutions to the problem.3. The search should stop at the corner point from which no adjacent corner leads to abetter value of the objective function.47In practice, the different computer programs utilize differentmethods to execute theprocedure outlined above. These methods will not be presented in thisthesis since they are notthe main concern.3.1.4 Integer ProgrannningInteger programming is a variation of linear programming which forces the solution tobe integer31.In many real world situations it is necessary for the decision variables to take ononly integer values. For instance, the number of aircraft in a fleet must be an integer, as must bethe number of warehouses in a distribution system. Also as it will be seen later in this thesis,any alternative route between to locations in a given transportation network can either take onthe value of one or zero. One if the route should be included in the final optimal network orzero if it should not. Such situations can be dealt with in two ways. First, we can simplyassume that integer variables are continuous and round off our results. In many situations thiswill be satisfactory if the possible error of a few percent is within the accuracy with which wecan formulate any real problem. Second, in some situations, some people might argue that therounding off approach might violate some of the constraints or it might produce a nonoptimalsolution. In such situations, integer programming which offers a way to formulate linearprograms that can cope with integer values can be used. For this thesis, it is satisfactory toconsider integer programming as only a slight variation of linear programming. The problemsin both techniques are set-up in the same manner and with the exception of the continuityassumption, all other assumptions are the same in both cases.483.2.0 Formulation Of The Problem.Before introducing the formulation designed for the problem itis helpful to presentsome definitions that will be used in the remainder of the thesis.In this thesis, an air transportnetwork consist of nodes, routes, and links. Nodes represent theairports in the network. Eachnode or airport is assigned a specific number. Routes represent the paths that flightsareassigned to and follow between the origin and destination airports. Each route in this thesis canconsist of one or two links. If a route contains one link only, then it is a direct route. If itcontains two links, then it is a transfer route. Links represent direct connections between twoairports. A single link can constitute a direct route.When designing a transport network the interests of both the passenger and the airlineoperator must be considered. It is assumed that passengers are rational and they will try tominimize their travel time and the costs associated with it while maintaining a certain level ofconvenience. For example, a rational passenger will try to minimize the number of transfersand reduce travel circuity. An airline operator however will try to minimize his cost ofoperation. If that operator is monopolizing the transport market as is the case in our case studyor in the majority of areas where demand is sparse and there is only one airline operator servingthe market, then travel circuity and the number of transfers are not as important to the operatoras his cost of operation. Evidently, a conflict of interest might exist between the operator andthe passenger. Therefore, three routing algorithms will be formulated to produce three distinctdesigns of “efficient air transport networks” to satisfy all interests. The algorithms will besimilar in all aspects except that their cost functions will be tailored to reflect the interests of the49passenger, the operator, and the combined interests of the two together. The resulting networkdesigns will provide valuable insight for the decision maker on how to best meet theexpectations and the objectives of both the passenger and the operator. Any resulting designshould not be considered or looked at in isolation as a final design by it self. The three designsmust be evaluated together and used as a decision making tool that helps the decision maker.The objective functions and the constraints of the algorithms can take the general mathematicalform presented below:Minimize:(CjY +CimjYimj)V i,j,m wherepaxjj,paxjm,paxmj>0i=1j=lm=ljimzorjSubject to:1. Yi + Yimj 1 V i&j = 1,2,3 ,n; and ijm=1miorj2.Yim — Yimj0 V i,j, &m = 1,2,3 n; and ij,i m,jm3. Ymj — Yimj0 V i,j,& m = 1,2,3 n; and ij,i m,j m4. Y13 &Yimj 0V i,j, &m = 1,2,3 n; andij, i m,jm5. Y1 = 1 or 0 all i,j e nThe above costraints are only applicable where Fax1,Fax1m’&1Cmj>0Where:i = origin airport index.j= destination airport index.m = hub or transfer airport index wherePaxim&Paxmj0.fl = the total number of airports in the network.C= the unit cost function of transport between airports i andj; where C f(Pax, S. FC,BT, ADT, VT, NF, OFF).C1mj= the unit cost function of transport between airports i andj through airport m;where C=f(Fax, S. FC, BT, CT, ADT, VT, NF, OFF).50= direct link between origin and destination airports. It isa decision variable with avalue of either 1 or 0.mj= transfer link between i andjthrough m. It is a decision variable witha value ofeither 1 or 0.Fax the number of passengers.S = aircraft seating capacity.FC = cost of one flight linking two airports.BT = block time.CT = average flight connection time spent by passengers ata transfer airport = 1.5 hr.ADT = average schedule delay time.VT = value of time.= minimum number of flights required to satisfy all demand = Fax /S.OFF operating period.The objective function as presented above, will compare the unit costs of transport of thetwo routing strategies for each origin-destination pair in the network. The least costly strategyfor any given pair will then be selected. The cost provided by this objective function is not anaccounting cost, but it is a heuristic that provide sensible results in the cases examined. Allairports in the network that has travel demand interaction with both the origin and destinationairports are considered as potential transfer airports. The first constraint of the model isimposed to select only one routing strategy and one route for each origin destination pair in thenetwork. This constraint in effect will constitutes a process similar to the “all or nothing” routeassignment process of the urban transportation planning. The second and third constraints areimposed to only select transfer airports that has direct link with both the origin and destinationairports in the final network design. The fourth constraint is the general none negativityconstraint of linear programming. The fifth constraint is optional side constraint, any additionalside constraint of the form = 1 would specify links (i, j) that are necessarily included in thefinal network’s design. This type of constraint is necessary to model any proposed improvementin the network or to evaluate the development of a particular airport as a hub in the network.513.2.1 Airline’s Network DesignThe first network is designed to meet the operator objectiveby minimizing the airline’stotal operating cost. This can be achieved by consolidating the traveldemands at some idealhub or transfer locations which will be determined by the algorithm in accordance to thedemand distribution throughout the network. Consolidating the travel demands will inevitablyminimize the airline’s operating unit cost of transporting passengers between the differentdemand locations. The unit cost of transporting passengers can be defined as the cost oftransporting one passenger between the origin and destination airports. The following is themathematical formulation of the cost functions that will minimize the operator’s cost ofoperations as can be used in the general algorithm as presented above:C, = FC13*NF1÷ Fax13Cimj = FCim*NF1m÷ (Pax+Paxim)+FCmj *NFmj ÷ (Pax +Paxmj)Where:NF = Pax/S3;= (Pax1+Paxim)imNFmj(Pax3+Paxmj)/SmjThe above cost functions are designed to calculate the airline’s unit cost of transport foreach origin destination pair that must be served according to the two routing strategies.Calculating the cost of direct routes is a straightforward task as indicated above. Calculating thecost of indirect routes for any given origin-destination (OD) pair however, must take account ofthe fact that passengers travelling between the (OD) pair can be flown on the same flights with52passengers who are travelling between the originand transfer airports, and those who aretravelling between the transfer and destination airports.The resulting savings in operational cost can either thenbe passed to the passengers interms of reduced ticket prices, or they can be kept by the airline toimprove its profitability.Passing the savings to passengers might stimulate more traffic which might further reduce theunit cost of operation however, this is a policy decision and calculating the effect of pricereductions on traffic demand is not within in the scope of this thesis.3.2.2 Passenger’s Network DesignThe second network is designed to minimize the passengers’ cost of travel. This can beaccomplished by selecting the routes that minimize both the travel time and the averageschedule delay time required for passenger trips between the origins and destinations airports.It must be noted here that the actual cost of travel in term of ticket prices is not included in thisdesign because it is directly related to the operational cost of the airline operator which is dealtwith in the first design. Also, the third network design which will be presented later, will dealwith this cost element to provide a balanced routing strategy that will provide a balance betweenthe various costs involved. Travel time can be measured in many ways one of which is the doorto door time. However, for reasons that will be explained later, travel time will be assumedequal to the “Block time” which is defined as the time span between the moment when theaircraft leaves the departing terminal and the moment when it stops at the arriving terminal32.Schedule delay time is defined as the difference in time between when a person would like or53desire to make a trip and the time he or she is constrainedto make the trip because of theavailability of a flight according to the airline’s schedule33.By assuming that the desireddeparture time is uniformly distributed over the entire periodof flight operating hours per day,the average schedule delay time per day can be calculatedas:ADT— Length OfOperating Period— OFF— 2*Flight Frequency — 2* NFThis assumption may seems unreasonable in cases where the true distributionis not uniform.However, several studies including Oum’s, and Tretheway’s34 indicated that theassumption isadopted by the airline industry, therefore it will be satisfactory for the purposes of this thesis.Minimizing the travel and schedule delay times is important because when a passengerwants to travel from one place to another he or she, must not only pay a price for it, but mustalso reckon with some other disadvantages including discomfort and must sacrifice a certainamount of time. While transportation costs and their prices are measured in terms of money,travel and schedule delay times are measured in time units. Consequently, these measures cannot be added together because they are based on different criteria. This means that they mustbe grouped under a common denominator: either the common denominator of time or that ofvalue. Traditionally, the common denominator of value has been used in most transportationstudies to group the two elements. Thus, it is assumed that time equals money, and the timespent travelling or waiting to travel can be converted to its monetary equivalence by multiplyingthe time units by the value of travel time. The value of travel time is not an absolute value, thisis so because the value depends not only on the trip circumstances, but also on the calculationmethod35.54Several Methods are available for estimating the valueof travel time, For example,Bruzelius36 presented the “Beesley method”. The method is called afterits originator M. E.Beesley. This method is built on the hypothesis that if a passenger canchoose between twotravel alternatives, e.g. modes, then the passenger will choose alternative 1 if:aoi +pl+ aqi<ao2 +p2 + aq2= Fixed cost of alternative 1.= Price of alternative 1.= Travel time of alternative 1.= The value of time.= Fixed cost of alternative 2.= Price of alternative 2.= Travel time of alternative 2.According to Bruzelius, the method assumes only one value of time exist, so that thepassenger’s willingness to pay to save time is the same for the two travel alternatives. Toestimate this value of time, a sample of observations including data on the chosen alternative,prices, and time are recorded in a coordinate system as shown in Figure 3.4.wherea01P1aa02P2q27- Np1 —p2= Choice of alternative Io= Choice of alternative 2xxx—0Figure 3.4 : Beesley’s Method For Estimating The Value of Time55A straight line is then drawn to separate the pointsrepresenting the choices of the twoalternatives. Bruzelius indicated that a perfectseparation between the points can not beexpected but an effort has to be made to make thenumber of points ending up on the wrongside of the line as small as possible. After the bestline is located, the value of time is inferredfrom the slope of the line, and the difference in the fixed costsas represented by point B. Thefull details of this method is available in Beesley’s paper which was publishedin 1965.Tarski38 presented the “production-based method”. The method is built on thehypothesis that shortening travel time of workers releases an additional amount of labour asaproduction factor that will increase the net and gross output of the society. Thus, a workercould add to the gross or net output during one hour of the time he would save on travelling.Hence, Tarski presented the following equation to estimate the value of time:JrP“P—2000pwhereVP = The value of one hour of travel time.P = The annual amount of the gross or net product (in monetary units).p = The average number of persons employed in material production.The 2000 is the average number of’ effective working hours in one year.Harrison and Quarmby39 presented the “revealed preference method”. In this method, asample of travellers are asked to make a choice between 2 different travel modes with differenttravel times, costs, and other travel characteristics. Their choices are recorded and then used tocalibrate the logit model of the Urban Transportation Planning process as presented below:L(x)L(x) = a1x and Pi (x)= 1 e56whereX = a vector of values of relative characteristics of the twotravel modes (time, cost, etc.).a. = a vector of parameters who’s values are to be determinedby the calibration process.L(x) = the relative disutility of the two modes.P1 (x) = the probability of a traveller or a group of travellers choosing mode 1.After calibrating the model, the value of time can thenbe estimated by dividing the timecoefficients by the cost coefficients.It it clear that there are various methods of calculating the value of travel time,but themost suitable method for the purposes of this thesis in terms of the data availability is the “costsaving method” presented by Harrison and Quarmby40.The method simply estimates thevalueof time by reference to the wage rates. Harrison and Quarmby indicated that this method isbased on the marginal productivity theory of factor rewards which states “Employers hirelabour until it is no longer worth their while to do so”. Thus, the wage rate is a satisfactorymeasure of the value of production gained or lost by changes in labour force. And sincereducing travel time of workers releases an additional amount of labour, then the wage rate isalso a satisfactory measure of the value of time.Due to the lack of data and studies on the value of travel time in Saudi Arabia, thisthesis will utilize the cost saving method as mentioned above, and it will assume that the valueof travel time is equal to the average hourly wage rate. Urban transportation studies traditionallyuse two thirds of the wage rate as an estimate of travel time. This traditional value will not beused in this study because air travellers usually earn more money than travellers using other57modes of travel. Subsequently, air travellers time is morevaluable41,and the full wage rate ismore reasonable to use in this case. Also, the majority of domestic travellersin Saudi Arabiaare business travellers42.Hence, any changes in travel times will greatlyaffect their workproduction, and the full wage rate will provide a better reflection of thesechanges. The valueof the schedule delay time however, is assumed to be equal to half of the averagehourly wagerate since it can be argued that this delay time can be used for accomplishingdifferentproductive tasks other than travelling. The average hourly wage rate in Saudi Arabia isestimated to be 28 Saudi Riyals (SR) per hour which is equivalent to 9$Canadian. Thisestimate was made by pooling a number of people in different types of occupations, and byusing the background knowledge of this author about the country. The following is themathematical formulation of the cost functions that will minimize the passenger’s cost of travelas can be used in the general algorithm as previously presented:C= VT(BTZJ) + 0.5 VT*ADTIJCimj = VT(B Tim + B Tmj + CTmj) + 0.5 VT*ADT; wherexx = i rnf NFim <NFmjxx = mj if NFim NFmjThe above cost functions use the value of time to calculate the passenger’s cost oftravel time for each origin destination pair according to the two routing strategies. For thisthesis, it is assumed that travel time is comprised of the following three components only:block and schedule delay times which were defined previously, and connection time which canbe defined as the time spent in a transfer airport in order to get on a connecting flight to thefinal destination. The minimum connection time is assumed to be 1.5 hr. This assumption wasmade based on information provided by officials of the Saudi Arabian Airlines43.Only these58time components were considered because they are theonly time components that can beaffected by the route choice. Calculating the cost of directroutes is a straightforward task.Calculating the cost of indirect routes however involves determining theconnection time andthe largest possible schedule delay time that a passenger has to experiencebecause of the flightfrequency at either the origin airport or the transfer airport.3.2.3 Combined Airline & Passenger Network DesignThe third network is designed to minimize and provide a balance between both theoperator and passengers’ cost of travel. This can be accomplished by selecting the routes thatminimize passengers’ travel and schedule delay times with their associated costs, as will as theairlines’ unit cost of operation between any given origin and destination airports. Striking abalance between the passenger and the operator costs of travel is important because as can beseen in Figure 3.5 some routes with their travel and schedule delay times might increase thepassenger cost of travel because they either increase travel circuity or because they have lowflight frequency. The same routes however might reduce the operator cost by consolidating thepassenger demands and visa versa. Therefore, the following is the mathematical formulation ofthe cost functions that will provide a balanced routing strategy for both the passenger and theairline by minimizing their total cost of travel:C=FC*NF ÷ Pax3 + VT(BTZJ) + 0.5 VT*ADT13Cimj = FCim*NFim ÷ (Pax + PtlXim) + FCm3*NFmj ÷ (Ptix + PWCm3)+VT(BT1m+BTmj+CTmj)+O.SVT*ADTxx; whereXX im fNFim <NFmjLxx=mj ifNFimNFmj594Costpassenger costairline costoptimal TimeFigure 3.5 Finding The Optimal Economic Cost Of Travel3.2.4 Discussion And Validation Of The FormulationsThe formulations presented above seek to find efficient routing strategies for alldemands between all (OD) pairs in the network. The two routing strategies that were previouslymentioned were embodied in the formulations. The hub and spoke strategy will consolidatepassenger demands on the least costly links in the network by abandoning the more costly ones.This consolidation process is accomplished by comparing the unit cost on the direct routebetween any given origin destination pair and all unit costs on potential routes that include atransfer. The least costly route weather it is a direct or a transfer route is then selected andpassengers are assigned to it. This cost comparison in essence is really then nothing but acomparison between the two airline’ routing strategies. The main advantage of this formulationis the fact that it keeps all options or route combination possibilities thatcan satisfy all travel60demands in the system open for comparison. This advantageenables the formulation to do anexhaustive search for all routes that minimize the total costof operations.Due to the nature of air transportation, comparing unit costs turn out tobe a great idea.This is so because once a flight departs, the airline incurs its costregardless of how manypassengers were flying on that flight. Therefore, the consolidation process reduces the numberof flights required to satisfy all demands throughout the network. Reducing the numberofrequired flights will then eventually reduces the total operating cost of the airline. Also, theusage of unit costs links the demand distribution throughout the network to the process ofcreating the network. This will result in the creation of a network that is “demanddriven”.Hence, if the demand distribution change, the network shape will also change to accommodatethe new demand distribution. This is so because any change in the demand distribution willcause a change in the unit costs.The following two examples will help in demonstrating the consolidation effects andcompare this thesis approach of constructing the transportation network with the traditionalapproach of the urban transportation planning process. The first example will also provenumerically that the results produced by the formulation are the least costly among all otherpossible alternatives. The second example in particular will show that the formulation is robustand it can produce good results for networks with different number of airports and costs ofoperations.61Example 1:Let us assume that we want to find the optimal routing strategy for trips on the simplenetwork shown in figure 3.6. Assuming that we have unit demands between all (OD) pairs inboth directions in the network and the costs of the vehicle or aircraft trips are as indicated in thefigure. To prove the validity of the formulation, all possible solutions to the problem will begenerated at first and then they will be compared with the solution produced by the formulation.Solutions:C= 12Figure 3.6: Example 1, Network ProblemThe traditional approach of the urban transportation planning process was used toproduce the first solution. This problem was solved by constructing the minimum cost trees foreach node at first and then these trees were overlaid together to get to the final shape of thenetwork as shown in figure 3.7.c=1162Mm cost tree for i Mm cost tree for 2 Mm cost tree for 2The complete solution Total cost of operation = 6,,)Figure 3.7 : The Tradditional Urban Planning SolutionAccording to the first solution, three Bi-directional links must be established betweenthe three nodes. This will require a total of six flights to serve the demand. The total cost ofoperating the system will then be 66 units. This solution while it might be suitable for assigningpersonal trips using the automobile it is not suitable for assigning them using the aircraft. Thisis so because of the nature of air travel where personal trips can be consolidated and the numberof required flights can then be reduced as discussed before.A second possible solution is to use the hedgehopping strategy by creating a “loop offlights” to serve the network. This is shown in figure 3.8. This solution will require a total of 4flights. The first flight will depart from 1 to 2 and it will take 2 passengers. One passengerwould be travelling between 1 and 2 and the second passenger will be travelling between 1 and3 through 2. The second flight will depart from 2 to 3 and it will take 3 passengers. The first63passenger is the one travelling to 3 from 1, the second is the one travelling between2 and 3, andthe last passenger is the one travelling between 2 and 1 through3. The third flight will departform 3 to 1 and it will take 3 passengers. The first passenger is the one travelling to 1 from 2,the second is the one travelling between 3 and 1, and the last passenger is the one travellingbetween 3 and 2 through 1. The fourth flight will depart form 1 to 2 and it will take thepassenger travelling from 3 to 2 through 1. The total cost of operating this system will then be43 units. Although, this solution consolidates the demands and reduces the number of the totalflights required it is not the least costly solution that can be found. In fact, the least costlysolution is going to be the one produced by the formulation.Figure 3.8: The Loop SolutionThe third and fourth solutions (as presented in figure 3.9) can be established by usingairports number 1 and 3 as transfer airports respectively. A total of four flights will be requiredfor each solution with a total cost of operations of 44 and 46 units respectively.4c=1oNF 2c=11NF 1Total cost of operation = 4364IFigure 3.9: The Third & Fourth Possible SolutionsFinally, Figure 3.10 presents the last possible solution which is produced by theformulation. The solution is established by using airport number 2 as the transfer airport in amanner similar to the fourth and fifth solutions. This solution however is the optimal one sinceits resulting total cost of operation is only 42 units which is the least cost among all alternatives.Figure 3.10: The optimal Solution For Example 1Example 2:This example is particularly designed to show the robustness of the formulation and itsability to react to and handle different networks. As can be seen in Figure 3.11, the samenetwork of the first example is used with the exception that a fourth airport is added. Also theTotal cost of operation = 44The third solutionc=11NF =2C=12 NF=2L 3Total cost of operation = 46The fourth solution2=1o/Jç0Total cost of operation =4265cost of operations on the new links connecting thefourth airport are less than the operationcosts on other links.4c=1oG13C=8C=9Figure 3.11: Example 2, Network ProblemSolutionThe solution is presented in Figure 3.12. It shows that the formulation has reacted to theintroduction of the fourth airport with its less costly links. Flights were then shifted away fromthe previous links which were identified as least costly in example 1 and assigned to the newlinks.()C=7NF =2Total cost of operations = 48Figure 3.12: The Optimal Solution For Example 2663.3.0 Discussion Of The MethodologyTo summarize, the construction of “an efficient air transport network” willbeaccomplished by conducting an exhaustive search for the least costly routesamong all possibledirect and transfer route alternatives. This search is doneby comparing the total unit cost oftransporting passengers according to the two routing strategies andby selecting the least costlyrouting strategy that can serve the demands between each orign-destination pair in the network.The usage of unit costs links the demand distribution throughout the network tothe process ofcreating the network. This will result in the creation of a network that is “demand driven”.Hence, if the demand distribution change, the network shape will also change to accommodatethe new demand distribution. This is so because any change in the demand distribution willcause a change in the unit costs. Depending on the type of network design required, differentcost elements can be included in the total unit cost. For example, if the network is intended tominimize the airline operating cost then only the airline operating costs are considered.Possible routes are those that offer a direct connection or a connection through a transferairport. The number of transfers for any trip is limited to one merely for the convenience ofpassengers. However, this limitation will definitely eliminate any hedgehopping in the network.Such elimination is reasonable when the network size is relatively small as is the case in thecase study of the thesis, or when the convenience of the passengers in terms of reducing theirtransfer time is among main objectives of creating the network. In larger networks however,hedgehopping may need to be considered for any given reason. In that case, the restriction onthe number of transfer must be relaxed by modifying the model. All airports in the network thathave travel interaction with both the origin-destination pair at hand can be considered as67transfer airports. Assuming that all trips between any two demand locations(origin anddestination) can only be assigned to one path which has the least unit cost. In effecta processsimilar to the “all or nothing trip assignment” of the urban transportation planningprocess willbe used to create the network.One potential advantage of this formulation that is worth to note is the noticeably shortcomputation time. This may be a result of the limited number of sets of constraints imposed onthe objective function.3.4.0 Computerizing The FormulationWriting all the elements of the above objective functions and constraints for a largenetwork with many airports can be a cumbersome task. It is possible to have a huge number ofalternative route combinations that trips can be assigned to between the different demandlocations, hence mistakes can occur. For this reason a computer program written in “C”language was developed to write the complete forms of the objective function and constraintsas presented in appendix (B) . A detailed discussion of the program will be provided in thefollowing chapter.684. THE COMPUTER PROGRAMThis chapter outlines the mentioned computer program developedto formulate therouting algorithms and to analyse the design networks.The program’s data inputs and outputfiles along with its flow chart and the tasks that it issuppose to accomplish will be presented.In addition, network performance measuresare developed. These measures will help analysingthe different network implications on airline operationsand passenger service.4.1.0 The ProgramAs previously mentioned, writing all the elements of the routingalgorithms for a largenetwork with many airports can be a cumbersome task.Also, when dealing with networks thathave large numbers of airports to be served, it is possible to havea huge number of alternativeroute combinations that trips canbe assigned to between the different demand locations. As thenumber of possible combinations increases mistakes in the formulationcan occur. For thisreason a personal computer based program written in “C” languagewas developed to write thecomplete forms of the objective function and constraintsas presented in appendix (B). Theprogram is also designed to help its user in evaluating the performanceof the designed networksagainst the existing network. Figure 4.1 shows the programflowchart which will help inshowing the interrelationships between thevarious tasks involved and it will also help infacilitating a better understanding of the program.69EZZZ2ProblemFormulationFileI Run Integer ProgranmingPackageI?Lindo”-EZ4IMain Menu1. Input Data, And Create Data & Problem Formulation Files2. View & Edit Existing Data File3. Read Existing Data File & Generate Problem Formulation File4. Analize Network Designs5. End Program Execution3. Read Existing Data File2.View && Generate Problem Edit ExistingFormulation File Data FileI. Create Data File &Generate ProblemFormulation FileGenerat ProblemFormulation FileFigure 4.1 : Program Flowchart70Before running the program it is necessary to assign numbers to all airports in thenetwork. Those numbers will be used by the program to identify the different airports and toalso identify the links between them. It is also recommended to prepare the necessaryinformation about traffic demands, flights operating cost, travel times and distances between thedifferent origins and destinations in matrix formats. This is important to ease and speed thedata entry process as required by the program. The program was designed to be user friendlyand to accomplish the following four tasks:1. Input data, and create data and problem formulation files.2. View and edit existing data files.3. Read existing data files and create problem formulation files.4. Analyse the resulting network designsAs seen in the flowchart, the program is designed to start by presenting its main menuwhich will enable the user to select one of the four mentioned tasks or to stop the program. Thefollowing will be a detailed discussion of each task.4.1.1 Input Data. And Create Data And Problem Formulation FilesIf no “Data File” is already in existence, the user must select the first task to create one.In that case, the program will request the user to enter a data file name and a problemformulation file name which the program will create for later use. The names will then beassigned to those files with the extension “DAT” added to the data file name and the extension71“FUN” added to the problem formulation file name. The program will then ask about therequired network design, i.e whether the network design is intended to suit the passenger, theairline, or both. And it will also ask for the total number of airports in the network and thevalue of time or the hourly wage rate. After this, a new screen as presented in Figure 4.2 willappear. On this screen, the airport indices (numbers) are generated automatically and thefollowing information will then be requested for entry as the cursor moves and blinks under theneeded information:1. Passengers flow (Fax) between the given origin destination pair. This is necessary todetermine the demand distribution throughout the network and to calculate the unitcosts of transport. In our case study, weekly demands are used because in some parts ofthe network the daily demands are very low. Weekly demands were obtained bydividing annual demands as given by the airlines by 52.2. The cost of operating a direct single flight (FC) according to the aircraft type usedbetween the given origin destination pair. This is necessary to calculate the total andunit cost of transport. In our case study, actual costs of flying in thousands of SaudiRiyals were provided by the airline.3. The number of seats (5) according to the aircraft type used between the givenorigindestination pair. This is necessary for calculating the number of required flights (NP)which is equal to the number of passengers divided by the number of seats and alwaysrounding up the results in our case study to accommodatellpassengers.4. The average block time in hours (BT) of the flightbetween the given origin destinationpair. This is necessary to minimize the travel times of passengers andto convert timeunits to cost units. In our case study this data element isprovided by the airline.725. The distance in miles (D) between the given origin destination pair. This is necessaryto calculate the costs of operations per passenger mile or seatmile. In our case studythis data element is provided by the airline.Number_of_airports: 25Value_of_time: 28.40From To Flow F.Cost Seats Time Dist From To Flow F. CostPax*1000 hr Mi Pax*10001 2 0 0.00 0 0.00 0 2 1 0 0.001 3 0 0.00 0 0.00 0 3 1 0 0.001 4 0 0.00 0 0.00 0 4 1 0 0.001 5 2 8.33 102 0.49 125 5 1 2 8.331 6 77 66.97 102 1.81 607 6 1 77 66.971 7 0 0.00 0 0.00 0 7 1 0 0.001 8 0 0.00 0 0.00 0 8 1 0 0.001 9 0 0.00 0 0.00 0 9 1 0 0.001 10 0 0.00 0 0.00 0 10 1 0 0.001 11 0 0.00 0 0.00 0 11 1 0 0.001 12 0 0.00 0 0.00 0 12 1 0 0.001 13 0 0.00 0 0.00 0 13 1 0 0.001 14 404 37.13 258 0.79 106 14 1 442 37.241 15 0 0.00 0 0.00 0 15 1 0 0.00Figure 4.2: Input Screen, Typical Example.Upon the completion of the data entry process, the program will then provides its user achance to enter any specific side constraints, i.e, include or exclude any specific link or linksbetween any given pair of origin and destination airports in the final design of the network.Those side constraints are important because they will allow the user to examine the effects ofcreating different situations such as developing a specific airport as a hub on the efficiency of73the network. The program will then create a “Data File” which canbe viewed and edited lateron if necessary (see appendix (A)). After creating the data file, the program will callasubroutine to generate the “Problem Formulation File” which can be seen in the appendix (B).The subroutine embodies in it the general objective function and all constraints equations aswell as all the different cost functions that were mentioned in the methodology chapter. Asshown in the flowchart, the problem formulation file which contains the formulated objectivefunction and constraints has then to be used as an input for a linear optimization package called“Lindo” which is available on the Mainframe computer of the university. Lindo will solve theproblem and will then provide the network design in the “Network Solution File” whichcontains the set of links between the different airports that comprises the final network design.The solution file is presented in appendix (C). As shown in the flowchart, once a selected taskis accomplished, the program reverts back to the main menu. The user will then have thechance to either select another task, or to stop the program.4.1.2 View And Edit Existing Data FileWhen entering a large set of data as required by this program, mistakes can happen. Forthis reason, the program is designed to view and edit any existing data file. Once this option isselected, the program asks the user to enter the name of the data file to be edited. The userresponse will then prompt the program to start a text editor namely “Microsoft DosEdit” andopen the data file for editing. The user must then edit and save the file to return to the mainmenu.744.1.3 Read Existing Data File And Create Problem Formulation FileOnce this option is selected, the program will ask its user to enter the names of the datafile and the problem formulation file. All information in the data file will then be used by thepreviously mentioned subroutine to create the problem formulation file.4.1.4 Analyse Network DesignsIn order to provide a better understanding of the network designs and to evaluate themagainst an existing network, the program is designed to read the network solution files andprovide the analysis results in the “Analysis Result File”(see appendix (D)). To start theanalysis, the program will first read the data file in order to retrieve all information relating tothe traffic demand levels and flight costs. Network analyse will be conducted according to twoanalysis categories, these are:1. Link analysis. This analysis category is used to evaluate the impact of implementingthe new network designs on traffic flows over the different links that make up thenetwork. Airline operating performance and passenger’ services will be evaluated oneach link. In this analysis category, all links that make up the network are scannedform the network solution file. The numbers of passengers using each link either as adirect link or as a transfer link between their origin and destination airports are readfrom the data file and added together to give the total number of passengers assigned toeach link. The required number of flights on each link can then be determined by75dividing the total number of passengers assigned to the linkby the number of seatsaccording to the aircraft type that is going to be used by the airline on that link. It isassumed that the airlines will continue to use the same type of aircraft that it is currentlyusing between the origin and destination airports. The user however can evaluate theimpact of using different aircraft on the shape of the network. Since flights areindivisible, all fractions in the division result are rounded up to accommodate allpassengers. In addition, some performance indicators as will be seen later were createdto evaluate the impact of implementing any new network design on flight operationsand passengers’ services on the different links.2. Entire network as a system. This analysis category is intended to evaluate theperformance of the network as a whole system. The impacts of implementing any newnetwork design on the airline operations and passenger’ service is analysed. In thisanalysis category, information relating to link operations are either added or averagedto quantify network performance. Various performance indicators were utilized toevaluate the different impacts.4.1.5 Performance Indicators And Analysis DataThe airline industry has established a set of performance indicators to evaluate differentaspects of airlines operations and performance. In this thesis however, the main test ofimprovements in airline operations as a result of implementing the new networks is thereduction in the total and unit costs of providing the service. Improvements in passenger76services are mainly measured in terms of flight frequencies, and schedule delays. Theseimprovements will reduce the passenger’s costs of travel. The following will be a presentationof the data items to be analysed and their related performance indicators which were utilized inthis thesis to evaluate the different impacts of implementing all the new design networks:1. Number of passengers (Fax). This is the total number of passengers using eachindividual link including direct and transfer passengers. The number is necessary todetermine the minimum number of flights that can accommodate the demand. It is alsoimportant for calculating unit costs as will be seen later.2. Number of flights (NF). The total minimum number of required flights on each link isimportant for determining schedule delay time of passengers. In this thesis, the numberis calculated as: NF = FAX / S where S being the number of seats on the aircraft.Given the indivisibility of flights, the result must be rounded up to accommodate allpassengers. The number is also used for calculating the total operating cost for eachlink and the entire system. NF is calculated for each link as shown above, and for theentire system by adding up the costs of flights on individual links.3. Average schedule delay time (ADT). As previously defined, this is used as ameasureof the level of service being offered to passengers. In this thesis, passenger’s traveldemand was assumed to be uniformly distributed over the week44,hence, ADT iscalculated as: ADT = total operating hours in the week/2 NF. ADTis calculated foreach link as shown, and for the entire network system by adding the link numbers toget the total system delay time. Average system schedule delay time for all links is alsocalculated by dividing the total system delay by the number of links in the network.4. Total onerating cost (TC). This is the major operation’s improvement measures. Forlink analysis it is calculated as: TC = FC*NF. The total system cost is then obtainedby adding the costs of providing the service on all links.775. Passenger miles flown (Fax Mi). Because not all flights have the same flight distance,passengers on different flights are assigned different “weights”. This number is definedas the sum of the products obtained by multiplying the number of passengers carried oneach flight by the flight distance45.The number can also be used as a measure of thedispersion of the network.6. Available seat miles (ASMi). This is a measure of the capacity provided by the airline.It is defined as the sum of the products obtained by multiplying the number ofpassenger seats available for sale on each flight by the flight distance46.This measure iscalculated for the system analysis category, but it is also used to calculate the cost perseat mile for each link.7. Passenger load factor (LF). This is a measure of the capacity utilization. It is definedas the percentage of passenger miles from the available seat miles. Hub and spokenetworks which usually consolidate passengers demands usually has higher load factorsthan point to point connection networks.8. Cost per seat mile (C / SMi. This is a measure of the airline productivity. It iscalculated as: C / SMi = TC / ASMi . This measure is calculated for both the linkanalysis and the system analysis categories. Network configurations that providesmaller numbers usually indicates better performance. However this can be misleadingbecause as the airline provide more capacity in some segments of the market, thiscapacity might not be fully utilized.9. Cost per passenger mile (C/Fax Mi. This is a measure of the airline productivity.It iscalculated as: C / Fax Mi = TC / Fax Mi. This measure is calculated for both the linkanalysis and the system analysis categories. A network configuration that providesmaller numbers usually indicates better performance.784.1.6 Sample OutputFor illustration purposes, a sample of the outputs of the integer programming package“Lindo” and the “C” program will be presented below. As can be seen below, Lindo’s output isa list of the routes that make-up the designed network. The C program output is comprised oftwo parts. The first part is a list of all the links in the network with the performance indicatorsassociated with each link. The second part is the result of the calculations of all systemperformance indicators. The sample given below is an extract of the analysis result of theexisting airline network in Saudi Arabia.1. Lindo’s Output: “Network Solution File”Y1T5 1.0000 This indicates the presence of a direct route between 1 and 5.Y1T18T6 1.0000 This indicates the presence of a transfer route between 1 and 6 through 18.Y1T14Y1T18Y2T18T6The sample given above is a list of the routes that make up the network. The completenetwork files for the existing network and the proposed new networks are presented in appendix(C).792 The “fl” Proram Oiitrnit “Anlvsi File”Link Total Total Schedule Total Cost per Cost per LoadFr To Flow Flights Delay Cost (SR) Seat Mile Pax Mile Factor1 5 2 1 49.00 8330.00 0.65 33.32 0.021 14 404 2 24.50 74260.00 1.36 1.73 0.781 18 808 5 9.80 216150.00 0.59 0.74 0.802 14 3134 16 3.06 730720.00 0.79 0.82 0.972 18 3596 18 2.72 1057320.00 0.63 0.64 0.992 19 77 1 49.00 15680.00 0.52 0.68 0.75System Flights = 778 System Cost = 32989960.00 System Delay = 3736.87System Seat-Mi Cost = 0.56 System Pax-Mi Cost = 0.60Average Delay = 26.69 System Load Factor = 0.94Average Seat-Mi Cost = 0.66 Average Pax-Mi cost = 2.54Average Load Factor = 0.66Available Seat-Mile = 58683524 Passenger-Mile Flown = 54875896The complete analysis files for the existing network and the proposed new networks arepresented in appendix (D).805. THE CASE STUDYAs a case study, the domestic air transportation network of the Kingdom of Saudi Arabiawhich consists of 25 airports that have sparse demand levels between the majority of theseairports were examined. The routes and links between the different airports in the network wererestructured. This particular network was selected as a case study because as it will be shown inthe discussion of the existing network conditions, this network represents a unique opportunitysince the network size is large, demand is sparse, and there is no other fast alternatives of masstravel modes.5.1.0 Existing Network ConditionsIn general, any transport network plan that matches supply with demand has to begoverned by constraints imposed by the availability of resources and economic efficiency. Inthis regard, the domestic air transport network plan of the Kingdom of Saudi Arabia is noexception. However when planning this network, the national airline (Saudia) was able toconsider aspects that extend beyond economic efficiency. The network plan placed strongemphasis on objectives such as the country’s political integration, the establishment of directlinks between all population centres, and the social well-being of the population47.As a result,all the Kingdom’s centres of population are directly connected to the air transport system bytheir own airports. The majority of these airports are directly connected to one another eventhough demand levels may not necessarily justify direct connections.815.1.1 The Structural Shape Of The Existing NetworkSaudia currently provide air transport services that link 25 airports with direct flights inmost cases48. Figure 5. 1 shows the structural shape of the existing network. The networkcurrently has a total of 172 routes connecting 172 city pairs of origins and destinations. Out ofthe 172 routes, only 32 routes include a transfer. A casual inspection of this network mightmislead the reader into thinking that this is a multi hub and spoke network that has 23 hubs.However, by definition a hub airport is a focal airport that facilitates flights transfer betweenvarious origins and destinations. In this sense, Riyadh(airport number 18),Jeddah (airportnumber 14),and Tabuk(airport number 22) airports are the only hubs in the network. Inreality, the network provides direct point to point service to 140 city pairs and only 32 city pairsare served by transfer routes.82Figure 5. 1: The Existing Domestic Air Transport Networkof The Kingdom of Saudi ArabiaAirports Of’ Saudi ArabiaInternational Airports[]En*e NetworkQDomestic AirportsOrigin Airport #---Existing NetworkAirline’s Cost MinimizationPassengers’ Cost MinimizationCombined Cost Minimization835.1.2 Operational Characteristics Of The Existing NetworkTravel demand throughout the network with the exception of demands to or from Jeddahor Riyadh is sparse. A quick examination of the average weekly travel demand matrixprovided in appendix (A) will show that travel demand between some city pairs is as low as 2passengers per week. Saudia officials indicated that the airline currently provide scheduled airtransport services between such city pairs as social services that are subsidized by thegovernment. Given these low demand levels and the size of the Boeing 737 (102 seats) whichis the smallest aircraft that the airline currently operates for scheduled service, load factorsthroughout the network are low. Figure 5.2 shows the estimated load factor distribution in theexisting network if the airline operates only the minimum number of flights that can satisfyFigure 5. 2: Estimated Load Factors Distribution In Existing Network4100%Load Factor DistributionOn Links Of The Existing Network,. 80%Z60%40%20%0%10 20 30 40 50 60 70 80Load Factor(%)Frequency Distribution Cumulative Distribution90 10084all travel demands. Thefigure indicates thatup to 29 % of links inthe network have loadfactors between 1 and 40percent. According to someSaudia officials, the actualoperating loadfactors which were notavailable for this research areeven less than those presentedin theFigure. This is so because theairline currently operatesmore flights than the requiredminimumfor different policy reasons.These policies include reasons thatrelates to the social wellbeingof the population49.For thisresearch the minimum numberof flights is usedas a base forconducting network analysisthroughout the remainderof this thesis. This will helpinproviding a uniform basis forcomparing the performance ofthe various network structures.Also, since there is no availabledata on how Saudia decides on thenumber of flights scheduledon each link, the minimumnumber is a viable solutionto problems caused by the lackof data.Figure 5. 3 shows the estimatednumber of flights distribution inthe existing network if Saudiaoperates the minimum numberof flights to improve its economicefficiency of operations.Figure 5. 3: EstimatedNumber Of Flights Distribution InExisting Network4100%Number Of Flights DistributionOn Links Of The Existing Network. 80%Z60%40%20%0%1 2 5 10 2030 40 50Mm. Number Of Flights Per weekFrequency Distribution CumulativeDistribution60 7085In this case, Saudia will have to operate a minimum of 778 flights per week to meet all traveldemands. The figure shows that 38 % of the links will only support the operation of one flightper week for maximum economic efficiency. The figure also shows that up to 59 % of all linksin the network have only 1 or 2 flights per week. This will have an implication on the qualityof service that will be offered to passengers. For example, the low number of flights on themajority of links will greatly increase the schedule delay in the entire system. In fact, if theairline only operates the minimum number of flights, the total schedule delay for all links in thenetwork will be 3,736 hours per week. Figure 5.4 indicates that 38 % of the links in thenetwork would have schedule delay of 50 hours per week. The same figure also indicates thatonly 16 % of the links in the existing network have schedule delay up to 5 hours.Figure 5. 4: Estimated Schedule Delay Distribution In Existing NetworkFinally, if Saudia operates the minimum required number of flights on each link, its totaloperating cost is estimated to be 33.0 millions Saudi Riyals (SR) per week. Figure 5.5 shows4Schedule Delay DistributionOn Links Of The Existing Network100%062%Z6040%— 320% —3%4%0%]15 20 25 30 40Schedule Delay On Links (Hr I Week)Frequency Distribution Cumulative Distribution86the estimated distribution of this cost in terms of theoperating cost per passenger-mile. Thefigure shows a wide range of costs per passenger-miles that spreads between0.5 SR to 40 SR onthe different links. 57 % of the links in the existing network havea cost that ranges between 0.5SR to 1.0 SR. This can be explained by Figure 5.2 which indicated that approximately 58 % ofthe links have load factors that ranges between 80% to 100 %.To summarize, The existing network is mostly directly connected. About 81 % of theroutes in the network are direct connection routes. This high degree of direct connectivitycoupled with the low demand levels and the size of the smallest aircraft that is currently beingused by the airline clearly explain the low load factors that characterize the current operations.In return, the low load factors on the majority of flights explains the high cost of operations perpassenger-miles.Per Passenger-Mile Cost DistributionOn Links Of The Existing Network50%40%0Z20%10%0%0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Cost Per Passenger-Mile (SR)10 20 40Figure 5.5 : Estimated Cost Per Passenger-Mile Distribution In Existing Network875.2.0 Case Study ResultsNetwork restructuring was accomplished by applying the developedformulations. As aresult, three new efficient network structures were constructed. Figure 5.6 shows the firstnetwork structure which was designed to minimize the total cost of the airline operationsbyconsolidating travel demands through the usage of the hub and spoke routing strategy. Figure5.7 shows the second network structure which was intended to reduce the cost of travel ofpassengers by reducing their travel time and schedule delay. When designing this network, itwas assumed that ticket prices which passengers have to pay for the trips will remain unchangedregardless of the chosen routes. Figure 5.8 shows the third network structure which wasdeveloped to reduce the combined costs of both passengers and airline. This was done becauseas was seen in Figure 3.5, reducing the sum of the airline’s and passengers’ costs will producethe efficient level of service with its efficient economic cost.5.3.0 Analysis Of ResultsThe following discussion will be a detailed analysis of the three efficient networks. Theimplications of each network structure on airline operations and passengers services will bepresented. Items such as load factor distribution, number of flights distribution, schedule delaydistribution, and operating cost distribution throughout the network will be discussed tocompare the performance of each network structure.88“23—Fabi224Gulf8__________6925771513’Red/ —Sea142024-- -Airports Of Saudi ArabiaIExisting NetworkInternational Airports[]NetworkIx Airline’s Cost MinimizationQDomestic AirportsOrigin Airport #I IPassengers’ Cost MinimizationI I Combined Cost MinimizationFigure 5. 6: Efficient Airline’s Cost Network89Figure 5. 7: Efficient Passengers’ Cost Network90Airports Of Saudi ArabiaInternational AirportsQDomestic Airports[)Entire NetworkOrigin AirportI IExisting NetworkAirlin&s Cost MinimizationIx Passengers’ Cost MinimizationI I CombineciCost MinimizationFigure 5. 8: Efficient CombinedCost NetworkAirports Of Saudi ArabiaHInternational Airports[]Entire NetworkQDomestic AirportsLIOrin Airport #ra.—— --I IExisting NetworkAirline’s Cost MinimizationI IPassengers’ Cost MinimizationIxI Combined Cost Minimization915.3.1. Efficient Airline’s Cost NetworkThis new network has a total of 172 routes connecting 172 city pairs of originsanddestinations. The solution file of this network (see appendix C) indicates that the number ofroutes that include a transfer has increased from 32 routes in the existing network to 66 routesin this network. Consequently, the total number of direct routes has been reduced from 140 inthe existing network to 106 in this network. This happened as a result of the trafficconsolidation process and the abandonment of the most expensive point to point connectionroutes where traffic volumes did not justify direct connections. Consequently, load factors inthis network are higher than those in the existing network. Figure 5.9 shows the estimated loadfactor distribution throughout the network if only the minimum number of flights is operated tomeet all travel demands. The figure indicates that links with load factors under 40% haveFigure 5. 9 : Estimated Load Factor Distribution In Efficient Airline NetworkLoad Factor DistributionOn Links Of The Efficient Airline Network100%80%0Z60%40%20%14%17%100/_0 4/ 4/ 00% 01% 1% 0%1%_0%10 20 30 40 50 60 70 80Load Factor (%)Frequency Distribution Cumulative Distribution35%90 10092decreased from 29% in the existing network to only 4% in this network. Also, the fraction oflinks with load factors higher than 80% has increased from 58% in the existing network to83%in this network.Traffic consolidation has also resulted in reducing the total number of required flights.The analysis file of this network (see appendix D) indicates that a total of 745 flights per weekare required to serve all travel demands. Links with low traffic volumes were removed andtheir flights were cancelled. These low traffic volumes were then re-routed on links that hashigher traffic demands. This re-routing process has increased the frequency of flights on themajority of links in this network. Figure 5.10 shows the estimated number of flightsdistribution throughout the network. The figure shows that the fraction of links with oneFigure 5. 10: Estimated Number Of Flights Distribution In Efficient Airline NetworkNumber Of Flights DistributionOn Links Of The Efficient Airline Network100%CI)Z60%20°%0%2%0%1% 1%0% —1 2 5 10 20 30 40 50 60 70Mm. Number Of Flights Per WeekFrequency Distribution Cumulative Distribution93weekly flight has been reduced from 38% in the existing network to22% in this network. Thefigure also indicates that 38% of the links in this network can be servedby more than 5 weeklyflights. This clearly shows the effects of the shape of the network on airline operations andpassengers service. By adopting this network, the airline can reduce the total number of flightsand simultaneously improve passenger’s service by re-routing low traffic volumes on links thathas higher flight frequency.Higher flight frequencies resulted in reducing the schedule delay in the network. Byadapting this network structure, the total schedule delay can be reduced by 42% from 3736hours per week in the existing network to 2160 hours per week in this network. Figure 5.11shows the estimated schedule delay distribution throughout the network. The figure indicatesthat the fraction of links that have schedule delay of 50 hours per week has been reduced from38% in the existing network to 22% in this network. The figure also indicates that 42% of theroutes in the network can experience schedule delays up to 10 hours per week.944Figure 5. 11: Estimated Schedule Delay Distribution In Efficient Airline NetworkFinally, the abandonment of routes with low traffic volumes, the selection of the leastcostly routes, and the subsequent reduction of the number of required flights can lead toreductions in airline operating cost. By adopting this network, the airline can reduce its currentestimated operating cost from 33.0 millions SR per week to 32.4 millions SR. Figure 5. 12shows the estimated distribution of the estimated cost in terms of the operating cost perpassenger-mile. The figure clearly reflects the abandonment of the most costly routes. Thehighest cost per passenger-mile in this network is 4.5 SR and it can only be found on onepercent of the links in the network.Schedule Delay DistributionOn Links Of The Efficient Airline Network100%80%Z60%40%20%0%5 10 15 20 25 30 40 50Schedule Delay On Links (Hr I Week)Frequency Distribution Cumulative Distribution954Figure 5. 12 Estimated Cost Per Passenger-Mile Distribution In Efficient Airline NetworkTo summarize, the algorithms has produced a network that reduces the airline operatingcost by eliminating the most costly direct connection routes and re-routing low traffic volumesthrough the hub airports. Jeddah and Riyadh airports were identified as the major and mostdominant hubs in this new network because of their huge ability to generate and attract traffic.Consequently, the total number of required flights has been reduced and at the same time flightfrequencies on the remaining transfer routes has increased providing better service to thepassengers by reducing their expected schedule delays. Load factors on the majority of routesare higher in this network than those in the existing network. This fact alone clearly indicatesthat by adopting this network the airline can improves its operational efficiency and reducesitsoperating cost. Hansen and Kanafani5°researched the effects of load factors on the operatingcost and they have clearly stated”If hubbing resulted in higher load factors or higher averageaircraft size, it would also result in lower costs “. Their conclusion is important since it will helpin explaining the changes in airline operation cost according to the changes in load factors.Per Passenger-Mile Cost DistributionOn Links Of The Efficient Airline Network70%60%050%,S30%20%0%0.5 1 1.5j#4:2 2.5 3 4.5 5Cost Per Passenger-Mile (SR)10 20 40965.3.2. Efficient Passenger’s Cost NetworkThis network was particularly designed to minimize the total travel cost of passengers.This travel cost includes elements such as the ticket price, the cost associated with travel time,and the cost associated with schedule delay. The ticket price between any origin and destinationairports was assumed to remain constant regardless of the trip route. Hence only the remainingtwo cost elements were reduced in this network. This was accomplished by selecting the routesthat minimize the total travel time and the schedule delay time. Travel time can be calculated inmany ways. One way is to consider the door to door time. In this study however, only thetravel time components that relate to the air mode is considered. These time components canincludes elements such as check-in time, waiting time, block time, and transfer time. But sincethe first two elements can not be affected by the chosen travel route, only the last two timeelements were used and minimized in this network.The origin destination matrix presented in appendix (A) clearly shows that traveldemand levels have wide variations between the different origin destinations pairs. This cancause wide variations in the required flight frequencies between the different airport pairs. Inreturn, this made the schedule delay time the most dominant time element. Hence this networkis mostly comprised of routes that reduces the schedule delay time. The network has a total of172 routes. 67 of these routes are direct routes and 105 are transfer routes.As indicated by the network solution file presented in appendix (C) and the map of thisnetwork presented in figure 5.7, the majority of these routes are transfer routes that send trafficthrough Jeddah (airport number 14) or Riyadh (airport number 18) airports. These two airports97are the major traffic generators in the network, and therefore they generate the largest flightfrequencies. For this reason the majority of trips are routed through these two airports.Figure 5.13 shows the estimated load factor distribution throughout the network if onlythe minimum number of flights is operated to serve all demands. A comparison betweenfigures 5.2 and 5.13 indicates that this network has higher load factors than the existing networkon approximately 36% of the routes. This fact alone shows that by adopting this network trafficcan be consolidated on some routes. At the same time, the figure indicates that 10% of theroutes have load factors under 20%. Comparing this fact with figure 5. 9 which indicated thatonly 4 % of the routes in the efficient airline network has load factors under 50% clearlyindicates that the degree of traffic consolidation in this network is not as large as that in theefficient airline network. This is observation is expected since this network is intended toreduce the passenger travel cost and not the airline operating cost.984Load Factor DistributionOn Links Of The Efficient Passenger Network100%80% —0%20%18%10%10%10% io°i012%13%0%101%0%fl O% OVo‘°:Load Factor (%)Frequency Distribution Cumulative DistributionFigure 5. 13 : Estimated Load Factor Distribution In The Efficient Passenger NetworkSince this network was designed to minimize the cost of travel of passengers, themajority of its routes has the highest flight frequencies as compared to the previous twonetworks. Figure 5.14 shows the estimated number of flights distribution throughout thenetwork. The figure indicates that the fraction of links with one flight per week is reduced toonly 12% as compared to 39% and 22% in the previous two networks. The figure also indicatesthat 64% of the links in the network can be served by more than 5 weekly flights. To providethese flight frequencies it is estimated that this network would require a minimum of 766flights per week to be operated to serve all traffic demands.90 100994Figure 5. 14: Estimated Number Of Flights Distribution In The Efficient Passenger’s NetworkRouting traffic on links with the highest flight frequencies has resulted in huge reductionin schedule delays in this network. By adapting this network, the total schedule delay can bereduced by 77% from 3736 hours per week in the existing network to 843 hours per week inthis network. Figure 5.15 shows the estimated schedule delay distribution throughout thenetwork. The figure indicates that only 12% of the links in this network are expected toexperience schedule delay that ranges between 25 and 50 hours per week. The figure alsoindicates that 43% of the routes can have schedule delays under 5 hours per week. This clearlyindicates that this network would provide better levels of service to the passenger than the twoprevious networks.Number Of Flights DistributionOn Links Of The Efficient Passenger Network100%80%Z60%2O%0%2 5 10 20 30 40 50 60 70 80Mm. Number Of Flights Per WeekFrequency Distribution Cumulative Distribution100Figure 5. 15 : Estimated Schedule Delay Distribution In The Efficient Passenger’s NetworkFinally, figure 5.16 shows the estimated distribution of the cost of operations in terms ofthe operating cost per passenger-mile. A casual examination of this figure alone can bemisleading because it indicates that the majority of links in this network has lower perpassenger-mile costs than those links in the existing network. This might lead the reader intothinking that this network would be less costly to operate than the existing network. However,operating this network will be more costly to the airline. Airline operating cost is estimated toincrease from 33.0 millions to 34.4 millions SR per week if this network is adapted. Thisincrease in cost can be explained by comparing figures 5.2 and 5.13. The comparison showsthat this network has higher load factors on approximately one third of its routes than theexisting network. However, since these higher load factors were limited to a minority of routesin this network and the routes were selected to minimize the travel cost of the passengers,airline operating cost of this network is higher than that of the existing network. Also, the100%Schedule Delay DistributionOn Links Of The Efficient Passenger Network88% 88%,.s 80%00)Z60%40%20%0%10 15 20 25 30 40 50Schedule Delay On Links (Hr / Week)Frequency Distribution Cumulative Distribution101routes in this network are not necessarily the least costly to operate on, they are howevertheones that provide the least travel and schedule delay times. This isso because the objective ofdeveloping this network is the reduction of the travel cost of the passengers.To summarize, this network provide better service levels to the travellers by routingthem on routes that have high flight frequencies. High flight frequencies minimizes scheduledelays which in return reduces the passengers cost of travel. Traffic is consolidated on someroutes in this network. This is clearly indicated by comparing figure 5.13 with figure 5.2. Thecomparison shows that this network has higher load factors on approximately one third of itsroutes than the existing network. However, since these higher load factors were limited and theroutes were selected to minimize the travel cost of the passengers, airline operating cost of thisnetwork is higher than that of the existing network.Per Pessenger-Mile Cost DistributionOn Links Of The Efficient Passenger Network80%70%6O%50%40%30%20%10%0%JQ.:(, /0.5 1 1.5 2 2.5 3 4.5 5Cost Per Passenger-Mile (SR)10 20 40Figure 5. 16: Estimated Cost Per Passenger-Mile Distribution In EfficientPassenger’ Network1025.3.3. Efficient Combined Cost NetworkThis network was specifically designed to minimize the total cost of both the airline andthe passengers. This has resulted in developing a network that is comprised of a collection oflinks from the efficient airline and passengers networks. The solution file provided in theappendix shows that this network has 76 direct routes and 96 routes that include a transfer eitherthrough Jeddah or Riyadh airports.Load factors in this network are higher than any other network indicating a high level oftraffic consolidation on its routes. Figure 5.17 shows the estimated load factor distributionthroughout the network if only the minimum number of flights are operated to serve all traveldemands. The figure shows that the majority of routes (64%) will have load factors that rangesFigure 5. 17: Estimated Load Factor Distribution In The Efficient Combined Cost Network4Load Factor DistributionOn Links Of The Efficient Airline & Passenger Network100%.. 80%00%40%r.d)20%0%20%flO/0% 0% 0% 0%1% 1%0%0%1%10 20 30 40 50 60 70 80 90 100Load Factor (%)Frequency Distribution Cumulative Distribution103between 90 1 nd 100 percent. The figure also indicates thatonly 1% of the links in the networkhave the lowest load factor of 30%. 95% of the links will haveload factors higher than 60%.Traffic consolidation resulted in reducing the numberof direct links in the network andthe number of required flights. It is estimated that a total of 744flights per week will berequired to serve all travel demands in this network. Figure 5.18shows the estimated numberof flight distribution throughout the network. The figure indicates that the fraction oflinks withone weekly flight has been significantly reduced from 38% in the existingnetwork to 3% in thisnetwork. It is worth to note that flight frequencies of the majority oflinks are higher in thisnetwork than the frequencies of the existing network even though the total numberof requiredflights is lower in this network.Figure 5. 18 : Estimated Number Of Flights Distribution In EfficientCombined Cost Network100%Number Of Flights DistributionOn Links Of The Efficient Airline & Passenger Network,. 80%60%E40%0%2 5 10 20 30 40 50 60 70Mm. Number Of Flights Per WeekFrequency Distribution Cumulative Distribution104Higher flight frequencies resulted in reducing the schedule delays and improved theservice levels. By adapting this network structure, the total schedule delay canbe reduced by76% from 3736 hours per week in the existing network to 881 hours per week in this network.Figure 5.19 shows the estimated schedule delay distribution throughout the network. The figureindicates that the fraction of links that have schedule delay of 50 hours per week has beenreduced from 38% in the existing network to 3%. The figure also indicates that 62% of theroutes in the network can experience an average schedule delays up to 10 hours per week.Figure 5. 19 : Estimated Schedule Delay Distribution In The Efficient Combined Cost NetworkTraffic consolidations and reduction in the number of flights have reduced the total costof airline operations. By adapting this network, the airline can reduce its current estimated costof operations from 33.0 millions SR per week to 32.8 millions SR per week. Although thisnetwork has the highest degree of traffic consolidations as indicated by its load factorsdistribution in figure 5.17, its savings in operation cost is not as high as those of the efficientSchedule Delay DistributionOn Links Of The Efficient Airline & Passenger Network100%,. 80%8)Z60%8)40%20%0%5 10 15 20 25 30 40 50Schedule Delay On Links (Hr / Week)Frequency Distribution Cumulative Distribution)105airline network. This is so because some of the routes in this network are notnecessarily theleast costly to operate on. These routes were included in the network to particularlyreduce thetravel cost of the passengers. In essence a trade off between the two costshave taken place toreduce the total sum of the two costs. To understand this trade off it is helpful to remember thatthe objective of developing this network is to minimize the total costs of both the airline and thepassengers. Figure 5.20 shows the estimated distribution of the airline operating cost in termsof the operating cost per passenger-mile. A casual comparison of this figure with figure 5.12can be misleading. This is so because this figure indicates that the majority of the links in thisnetwork have lower per passenger-mile cost than those links in the efficient airline network.Therefore, this network should have lower total cost of operations than the efficient airlinenetwork. However, this is not the case, this network has higher cost of operations. The highercost can be explained by the absolute numbers of links and their operating costs in eachnetwork. This network has less number of links that have low operating costs than the othernetwork. For example, the efficient airline network has 63 links with an operational cost of 1.0SR per passenger mile. This network has only 52 links that falls in the same cost category.1064Figure 5. 20 : Estimated Cost Per Passenger-Mile DistributionIn The Efficient Combined Cost NetworkTo summarize, the algorithm successfully produced a network that fulfilled its designobjective by reducing the total cost of travel for both the airline and the passenger. By adaptingthis network the airline can save 0.2 million SR per week as compared to their currentoperations. Passengers’ savings are much higher, this network will reduce the total scheduledelays and its associated cost by 76%.5.4.0 SummaryThe above networks analysis clearly indicates that the developed routing algorithmshave successfully created networks that meet their specific design objectives. The newnetworks reduce both the airline operating cost, and passengers’ travel cost. Any of thesePer Passenger-Mile Cost DistributionOn Links Of The Efficient Airline & Passenger Network80%70%60%50%40%30%20%10%0%0.5 1 1.5 2 2.5 3 4.5 5Cost Per Passenger-Mile (SR)/10 20 40I107networks should not be considered or looked at in isolation as a final network design by it self.The three network designs must be viewed as a decision making tool that helps the decisionmaker. To select a network for operations, all network designs must be evaluated against a setof predetermined goals and objectives that relates to airline operations and passengers’ servicelevels. Finally, table 5.1 offers comparisons between key attributes of the different networks.Existing Airline Passengers CombinedNetwork Network Network NetworkNumber of Direct Routes 140 106 67 76Number of Transfer Routes 32 66 105 96Average Load Factor (%)66 83 84 89Number of Flights778 745 766 744Average Sched. Delay (hr/week) 26.96 20.38 12.60 11.60Total Sched. Delay (hr/week) 3736 2160 843 881Average Operating Cost (SRJPassenger - mi) 2.54 0.84 1.58 0.71Total Operating Cost (Million SRI week) 33.0 32.4 34.4 32.8Total Passenger-miles Flown 54,875,896 55,231,064 59,562,624 56,543,592Table 5.1: Attributes of Existing And Design NetworksIt is interesting to note in this table that the average operating cost per passenger-mile of theefficient combined network (0.71 SR) is lower than that of the efficient airline network (0.84SR). Hence, one might think that the combined network is less costly to operate than theefficient airline network but, this is not the case. In fact, the total operating cost of the efficientairline network is estimated to be 32.4 Million SR/week while the total operating cost of thecombined network is estimated to be 32.8 Million SR/week. The lower average operating costper passenger-mile of the combined network can be explained by the fact that the size of thisnetwork in terms of the passenger-miles flown (56,543,592) is larger than the size of theefficient airline network (55,231,064).1086. CONCLUSIONSThis thesis developed efficient routing algorithms for routing air traffic in situationswhere demand levels are sparse and spread over large geographical areas. Three algorithmswere developed and used to create three efficient network structures. The networks weredesigned to attain specific objectives. The first network minimized the total cost of airlineoperations. The minimum airline cost network consolidated traffic demands at a few ideal hublocations, and reduced the minimum number of required flights that meet all traffic demands.The second network minimized the cost of travel of the passengers by reducing their travel andschedule delay times. In this network trips were assigned to the links with the least travel andschedule delay times. The third network minimized the total combined cost of both the airlineand the passengers. This was done by consolidating the traffic at a few ideal hub locations tominimize the airline unit costs of operations, and by assigning the trips to the routes that havethe least schedule delays, and travel times.The case study showed that all algorithms have successfully achieved their designobjectives, and made it possible to explore the influence of the structural shape of air transportnetworks on the operational cost of the airline, the passengers cost of travel, and the level ofservice. Also, in the analysis part of the study, the following conclusions were reached:1. The attributes of air transport networks influence both the passengers’ travel cost andthe airline operating cost. The total cost and network structure are not independent.109Hence, air transport networks must be developed in such a fashion thattotal costs areminimized and travel service within the network maximized.2. In networks with sparse demand for travel, operating costs are greatly influencedby theshape of the network. Increased direct point to point connectivity in such networks willincrease the airline operating cost, reduce load factors, and increase schedule delays.3. In sparse demand networks, the consolidations of traffic demands through the usage ofthe hub and spoke routing strategy will increase load factors, increase the frequency ofservice, reduce schedule delays, and minimize the airline operating cost.4. The usage of unit costs links the demand distribution throughout the network to theprocess of creating the network. This will result in the creation of a network that is“demand driven”. Hence, if the demand distribution change, the network shape will alsochange to accommodate the new demand distribution. This is so because any change inthe demand distribution will cause a change in the unit costs.5. The new passengers’ network design showed that traffic consolidation alone does notautomatically reduces the airline operating cost. In order to do so, the network routesmust be selected in such a fashion that minimizes the unit costs of transport.6. In Saudi Arabia the existing airline network was designed to meet all passengersdemands regardless of the sparse volumes. As a result of government policies, thepolitical integration of the country as well as the social well-being and the comfort of110the population were given greater considerations over the economical operations of theairline. Consequently, all the kingdom’s centres of population are directly connected toone another even though demand levels do not necessarily justify direct connection.7. Figures 6.1 shows the cancelled links of the existing network in the new airline’s,passengers’, and combined networks. The figure also shows the populationconcentrations around the different airports in Saudi Arabia. It is interesting to notethat the majority of the cancelled links provide direct connections between areas withlow population concentrations in the northern part of the country. These low populationconcentrations explain the cancellations of the direct links in the new networks sincesuch population levels can only generate low traffic demands which result in higher unitcosts and low frequency of service on these links. The same figure also shows theadded links to the new networks. These links were added as substitutes for some of thedeleted links.111f/ -- //If \\\J—--=(17)’..\JL\\\ P( N - -Arabian11Gulf8 62/\RedSea‘.20/—10 -Population Centres & Airports Of Saudi Arabia10000<50000 /\iooooo< 150000,/’\200000<500000(Zi1000000<2000000Q____CancelledUnks In Effi. Networks50000< 100000()150000<200000 500000< 1000000Added Links In Effi. NetworksFigure 6.1: Cancelled Links From The Existing Network In The EfficientNetworks1127. FURTHER RESEARCHIn this thesis, demand volumes and distributions were treated as static parameters.However, air traffic demand is dynamic and responds to changes in a wide variety of factorsincluding cost of travel, and frequency of service. As previously mentioned, all designnetworks will improve the frequency of service. These improvements can positively stimulatethe demand levels. And since any changes in the demands can alter the unit costs on the variouslinks in the network, the network configuration may change. If demand levels growsubstantially, more direct links will be created. However, if the growth is marginal, hubbingwill be reinforced. Demand levels do not change quickly, therefore, demand levels anddistribution throughout the network should be periodically monitored. The routing algorithmsdeveloped in this thesis may be linked to a demand forecasting model to revise the networkstructure. Also, to further improve the airline operations in Saudi Arabia, a flight schedulingmodel must be developed and linked to the routing algorithms as can be seen in Figure 7.1.DemandsEedulinModel OutputScheduleModel Feedbackien,JFigure 7.1: Required Models For Efficient Airline Operations113The developed networks must be refined by refining some of the parameters used intheir creation. For example accurate measure of the value of travel time in Saudi Arabia mustbe determined. This is important because the value of travel time is a western concept, itsapplicability and its magnitude in a country like Saudi Arabia must be determined for accuratelyconverting time units of schedule delays and travel times into their equivalent monetary values.Also, the full average hourly wage rate was used in this thesis as a measure of the value oftravel time. It must be noted that the model is not limited to this value, but this value was usedbecause several studies on the value of air travel time including Gronau’s51 suggested justifiablythe usage of the full wage rate. The common justification in these studies is the notion thattravel time is mostly wasted in the sense that it can not be used for conducting any productivework. These studies have also argued that the majority of air travellers earn more money thantravellers using other modes of travel. Therefore, air travellers time is argued to be morevaluable and thus the full wage rate was used. However, with the development of notebookcomputers it can be argued that some portion of the travel time can be used for conductingproductive work. In this case, the full wage rate is not an accurate measure. Therefore, anaccurate measure of the value of air travel time must be determined and used in such a case.The impact of using smaller air craft size on the shape of the network can beinvestigated. In this thesis it was assumed that the airline will use the same type of aircraft thatit is currently using. It must be noted that the model is not limited to the current aircraft size,and any aircraft size can be used as an input to the model. Using smaller aircraft will definitelychange the shape of the design networks simply because different aircraft types have differentoperating costs which will be reflected on the unit costs of operations on the different links.114Also, when using smaller aircrafttraffic may not need to be consolidated asmuch as is the casewhen using larger aircraft.Hence, more direct routes can be establishedin the network with theusage of smaller aircraft size.This model was particularlydeveloped for routing air trafficin situations where traveldemand is sparse andair services are monopolized by one,or a small number of airlines.Itsapplicability in competitiveand large demand situationsis not known at this time, butit can beinvestigated.Finally, while the developednetworks were for SaudiArabia, the applicabilityof thealgorithms to other areas withsimilarly sparse demands suchas Australia, NorthernCanadacould be investigated.115REFERENCESYaw Jeng, Chawn., “An Idealized Modelfor Understanding Impactsof Key NetworkParameters on Airline Routing”., TransportationResearch Record 1158., Transportation Reseach Board., National ResearchCouncil., Wash, D.C., 1988.2Schwieterman, Joseph P., “Airline Routesand Metropolitan Areas: ChangingAccessTo Non-Stop Service Under Deregulation”.,Transportation Research Record 1161.,Transportation Reseach Board, NationalResearch Council, Wash, D.C., 1988.Kanafani, Adib., and Hansen, Mark., “HubbingAnd airline Costs”, Institute OfTransportation Studies., UniversityOf California., Berkeley., Research ReportUCB-ITS-RR-85-12., August 1985.Shaw, Stephen., Airline Marketing And Management.,Pitman Publishing., 1985.Baily, Elizabeth E., Graham, David R.,and Kaplan, Daniel P., Deregulating The Airiins., 1985.6Higgins, R. G., and Toh, R.S., “The Impact of Hub and Spoke Network Centralizationand Route Monopoly on Domestic AirlineProfitability”., Transportation JournalSummer 1985.Wheeler, Cohn F., “Strategies for Maximizing theProfitability of Airline Hub andspoke Networks”., Transportation Research Record 1214.,Transportation Research Record 1158., Transportation Reseach Board., NationalResearch Council., Wash, D.C.,1989.8See Wheeler., Reference 7 Above.Morrison, S., and Winston, C., The EconomicEffects of airline Deregulation,Brookngs Institution., Washington, D. C.,1986., P. 18.10See Wheeler., Reference 7 Above.Oum, Tae., and Tretheway, Michael., “Airline Huband Spoke Systems”., Transportation Research Forum., Vol. XXX, No. 2.,1990.12Gordon, S., and De Neufvill, R., “Design of Air TransportationNetworks”., Transportation Research., Vol. 7., 1973.13See Higgins., and Toh., Reference 6 Above.14See Yaw Jeng., Reference 1 Above.15Richardson, Robert., “An Optimization Approachto Routing Aircraft”., TransportationScience., Vol. 10., P 52 - 71., 1976.16See Richardson.. Reference 15 Above.11617Gordon, Steven., and De Neufville, Richard.,”Design Of Air Transportation Networks”., Transportation Research, Vol. 7, pp. 207-222., 1973.18Ferguson, A., and Dantzig, G. B., “The Problem Of Routing Aircraft, A MathematicalSolution”., Rand Report P-561, Rand Corporation., Santa Monica, California, Sept.,1954.19Etschmaier,M. M.,”Schedule Construction And Evaluation For Short And MediumRange Corporate Planning”., AGIFORS 10., 1970.20Kushige, T., “A Solution Of Most Profitable Aircraft Routing”., AGIFORS 3, 1963.21See Jeng., Reference 1 above.22Ghobrial, Atef., Balakrishnan, Nagraj., and Kanafani, Adib., “A Heuristic Model ForFrequency Planning And Aircraft Routing In Small Size Airlines”., TransportationPlanning And Technology., Vol. 16, PP. 235 - 249., 1992.23Bailey, B., Graham,D., and Kaplan, D.,”Deregulating The Airlines” MIT Press, Cambridge., MA., 1985.24Ghobrial,A.,”Analysis Of The Air Network Structure: The Hubbing Phenomenon”.,Ph.D. Dissertation., University Of California., Berkeley., UCB-ITS-DS-83-2, PP. 138.,1983.25Chou,Y.H.,”The Hierarchical-Hub Model For Airline Networks”., Transportation Planning And Technology., Vol. 14, PP. 243 - 258., 1990.26Taaffe, E.J., and Gauthier, H. L., Geography of Transportation., Prentice-Hall., NewJersey., 1973.27Todoroki, T., Hanzawa, Y., and Fukuda, A., “Analysis Of Domestic Air TransportationNetwork In Indonesia”., The 6th World Conference On Transportation Research., LyonFrance., 1992.28Nesa Wu., and Coppins, Richard., Linear Programming And Extensions., McGraw-Hill., 1981.29De Neufville, Richard., Applied Systems Analysis., McGraw-Hill., 1990.30See De Neuville., Reference 29 Above.31See De Neuville., Reference 29 Above.32Shaw, Stephen., Airline Marketing And Management., Pitman., 1985.Gordon, S., and De Neufville, R., “Design Of Air Transportation Networks”., Transportation Research., Vol.7., 1973.Oum, Tae H., and Tretheway, Michael W., “Airline Hub And Spoke Systems”., Journal Of The Transportation Research Forum., Vol. XXX., No. 2., 1990.117Tarski, I., The Time Factor In Transportation Processes., Elsevier., Warsaw., Poland.,1987.36Bruzelius, Nils., The Value of travel Time., Croom Helm., London.,1979.Beesley, M. E., “ The Value of Time Spent Travelling: some New Evidence”., Economica., Vol. 32, PP. 174-85., 1965.38See Tarski., Reference 35 Above.A. J. Harrison., and D. A. Quarmby., “The Value Of Time”., From Richard Layard(Editor)., Cost Benefit Analysis., Penguin., 1972.A. J. Harrison., and D. A. Quarmby., “The Value Of Time”., From Richard Layard(Editor)., Cost Benefit Analysis., Penguin., 1972.41Gronau, R., “The value of Time In Passenger Transportation: The Demand For AirTravel”., National Bureau of Economic Research., NewYork., 1970.42Personal Interviews With Officials of Saudi Arabian Airlines., Jeddah., Saudi Arabia,August., 1992.Personal Interviews With Saudi Arabian Airline Officials., Jeddah., Saudi Arabia.,Aug., 1992.Oum, Tae H., and Tretheway, Michael., “Airline Hub And Spoke Systems”., JournalOf The Transportation Research Forum., Vol. XXX., No. 2., 1990.International Air Transport Association., World Air Transport Statistics., 1988.46International Air Transport Association., World Air Transport Statistics., 1988.Kocks Consult GMBH., “Saudi Arabian National Transportation Plan”., Vol. 1 Executive Summary., Ministry Of Planning., Kingdom Of Saudi Arabia., 1982.48Saudia., “Timetable”., Saudi Arabian Airline., Jeddah., Saudi Arabia., July 1992.Personal Interviews With Airline Officials, Jeddah., Saudi Arabia., August 1992.50Mark Hansen., And Adib Kanafani., “Hubbing And Airline Costs”., Journal of Transportation Engineering., Volume 115., No. 6., November., 1989.See Gronau, R., Reference 41 Above.118APPENDIX A119w120DDDI—I-C.)xLUU08APPENDIX A:DATA FILEDATA FILENumber of airports: 25Value_of_time: 28.40From To Flow Cost Seats Time Dist From To1 2 00 0.00 0 0.00 0 2 11 3 0 0.00 0 0.00 0 3 11 4 0 0.00 0 0.00 0 4 11 5 2 8.33 102 0.49 125 5 11 6 77 66.97 102 1.81 607 6 11 7 0 0.00 0 0.00 0 7 11 8 0 0.00 0 0.00 0 8 11 9 0 0.00 0 0.00 0 9 11 10 0 0.00 0 0.00 0 10 11 11 0 0.00 0 0.00 0 11 11 12 0 0.00 0 0.00 0 12 11 13 0 0.00 0 0.00 0 13 11 14 404 37.13 258 0.79 106 14 11 15 0 0.00 0 0.00 0 15 11 16 0 0.00 0 0.00 0 16 11 17 0 0.00 0 0.00 0 17 11 18 731 43.23 201 1.31 362 18 11 19 0 0.00 0 0.00 0 19 11 20 0 0.00 0 0.00 0 20 11 21 0 0.00 0 0.00 0 21 11 22 0 0.00 0 0.00 0 22 11 23 0 0.00 0 0.00 0 23 11 24 0 0.00 0 0.00 0 24 11 25 0 0.00 0 0.00 0 25 12 3 0 0.00 0 0.00 0 3 22 4 0 0.00 0 0.00 0 4 22 5 0 0.00 0 0.00 0 5 22 6 577 91.52 244 2.08 734 6 22 7 0 0.00 0 0.00 0 7 22 8 0 0.00 0 0.00 0 8 22 9 0 0.00 0 0.00 0 9 22 10 0 0.00 0 0.00 0 10 22 11 0 0.00 0 0.00 0 11 22 12 0 0.00 0 0.00 0 12 22 13 0 0.00 0 0.00 0 13 22 14 3096 45.67 202 1.10 286 14 22 15 19 54.36 102 1.51 466 15 22 16 0 0.00 0 0.00 0 16 22 17 0 0.00 0 0.00 0 17 22 18 3019 58.74 202 1.54 461 18 22 19 77 15.68 102 0.99 298 19 22 20 212 30.30 202 0.94 229 20 22 21 0 0.00 0 0.00 0 21 22 22 19 73.26 102 2.22 798 22 22 23 0 0.00 0 0.00 0 23 22 24 0 0.00 0 0.00 0 24 22 25 0 0.00 0 0.00 0 25 23 4 0 0.00 0 0.00 0 4 33 5 0 0.00 0 0.00 0 5 33 6 0 0.00 0 0.00 0 6 33 7 0 0.00 0 0.00 0 7 33 8 0 0.00 0 0.00 0 8 33 9 19 24.00 102 1.08 333 9 3Flow Cost0 0.000 0.000 0.002 8.3377 66.970 0.000 0.000 0.000 0.000 0.000 0.000 0.00442 37.240 0.000 0.000 0.00769 52.370 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00538 87.360 0.000 0.000 0.000 0.000 0.000 0.000 0.003058 40.9658 54.360 0.000 0.003192 68.04115 17.68308 33.940 0.0038 73.260 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0019 20.13121APPENDIX A:DATA FILE3 10 0 0.00 0 0.00 0 10 3 0 0.003 11 58 18.75 102 0.80 184 11 3 5815.123 12 0 0.00 0 0.00 0 12 3 00.003 13 0 0.00 0 0.00 0 13 3 00.003 14 173 28.56 102 1.68 548 14 3 17327.543 15 0 0.00 0 0.00 0 15 3 0 0.003 16 0 0.00 0 0.00 0 16 3 0 0.003 17 0 0.00 0 0.00 0 17 3 0 0.003 18 577 32.66 102 1.58 483 18 3 577 25.533 19 0 0.00 0 0.00 0 19 3 0 0.003 20 0 0.00 0 0.00 0 20 3 0 0.003 21 28 9.38 102 0.67 149 21 3 17 14.743 22 0 0.00 0 0.00 0 22 3 0 0.003 23 19 18.04 102 0.78 158 23 3 19 11.253 24 0 0.00 0 0.00 0 24 3 0 0.003 25 0 0.00 0 0.00 0 25 3 0 0.004 5 0 0.00 0 0.00 0 5 4 0 0.004 6 0 0.00 0 0.00 0 6 4 0 0.004 7 0 0.00 0 0.00 0 7 4 0 0.004 8 0 0.00 0 0.00 0 8 4 0 0.004 9 0 0.00 0 0.00 0 9 4 0 0.004 10 0 0.00 0 0.00 0 10 4 0 0.004 11 0 0.00 0 0.00 0 11 4 0 0.004 12 0 0.00 0 0.00 0 12 4 0 0.004 13 0 0.00 0 0.00 0 13 4 0 0.004 14 0 0.00 0 0.00 0 14 4 0 0.004 15 0 0.00 0 0.00 0 15 4 0 0.004 16 0 0.00 0 0.00 0 16 4 0 0.004 17 4 20.16 102 0.84 640 17 4 2 22.564 18 385 22.22 102 0.92 219 18 4 462 16.734 19 0 0.00 0 0.00 0 19 4 0 0.004 20 0 0.00 0 0.00 0 20 4 0 0.004 21 0 0.00 0 0.00 0 21 4 0 0.004 22 0 0.00 0 0.00 0 22 4 0 0.004 23 0 0.00 0 0.00 0 23 4 0 0.004 24 0 0.00 0 0.00 0 24 4 0 0.004 25 0 0.00 0 0.00 0 25 4 0 0.005 6 58 32.64 102 1.92 661 6 5 77 28.805 7 0 0.00 0 0.00 0 7 5 0 0.005 8 0 0.00 0 0.00 0 8 5 0 0.005 9 0 0.00 0 0.00 0 9 5 0 0.005 10 0 0.00 0 0.00 0 10 5 0 0.005 11 0 0.00 0 0.00 0 11 5 0 0.005 12 0 0.00 0 0.00 0 12 5 0 0.005 13 0 0.00 0 0.00 0 13 5 0 0.005 14 385 17.58 102 0.99 227 14 5 404 18.035 15 0 0.00 0 0.00 0 15 5 0 0.005 16 0 0.00 0 0.00 0 16 5 0 0.005 17 0 0.00 0 0.00 0 17 5 0 0.005 18 615 20.44 102 1.34 361 18 5 596 21.325 19 0 0.00 0 0.00 0 19 5 0 0.005 20 0 0.00 0 0.00 0 20 5 0 0.005 21 0 0.00 0 0.00 0 21 5 0 0.005 22 0 0.00 0 0.00 0 22 5 0 0.005 23 0 0.00 0 0.00 0 23 5 0 0.005 24 7 10.98 102 0.61 149 24 5 7 10.725 25 0 0.00 0 0.00 0 25 5 0 0.006 7 96 28.28 102 2.02 704 7 6 96 38.386 8 0 0.00 0 0.00 0 8 6 0 0.006 9 173 21.75 102 1.25 391 9 6 173 30.45122APPENDIX A:DATA FILE6 106 116 126 136 146 156 166 176 186 196 206 216 226 236 246 257 87 97 107 117 127 137 147 157 167 177 187 197 207 217 227 237 247 258 98 108 118 128 138 148 158 168 178 188 198 208 218 228 238 248 259 109 119 129 139 149 159 169 179 18192 32.6238 24.900 0.000 0.004231 96.80346 55.920 0.000 0.007385 38.760 0.00365 89.300 0.000 0.000 0.000 0.000 0.000 0.000 0.0019 12.750 0.000 0.000 0.00577 24.120 0.000 0.000 0.00712 23.9738 12.240 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00115 24.5019 21.160 0.000 0.0019 35.910 0.000 0.000 0.0038 16.030 0.000 0.000 0.000 0.004 12.780 0.000 0.00942 51.1277 49.9519 19.800 0.001115 21.59102 2.14 808102 1.66 5380 0.00 00 0.00 0253 2.01 763180 1.82 6200 0.00 00 0.00 0251 0.99 2570 0.00 0102 1.90 6500 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 0102 0.75 1590 0.00 00 0.00 00 0.00 0102 1.33 3890 0.00 00 0.00 00 0.00 0102 1.53 514102 0.72 1580 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 00 0.00 0102 1.08 324102 0.89 2350 0.00 00 0.00 0102 1.89 6460 0.00 00 0.00 00 0.00 0102 0.66 1750 0.00 00 0.00 00 0.00 00 0.00 0102 0.71 1750 0.00 00 0.00 0201 1.34 443251 1.12 284102 1.12 3650 0.00 0201 0.86 210212 30.0738 29.880 0.000 0.004327 86.56346 41.580 0.000 0.007000 39.110 0.00365 89.300 0.000 0.000 0.000 0.000 0.000 0.000 0.0019 12.750 0.000 0.000 0.00596 21.560 0.000 0.000 0.00731 24.7519 12.750 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0096 24.6419 18.270 0.000 0.0019 28.350 0.000 0.000 0.0038 15.630 0.000 0.000 0.000 0.006 12.750 0.000 0.00962 42.1677 51.5219 19.320 0.001348 23.58101112131415161718192021222324258910111213141516171819202122232425910111213141516171819202122232425101112131415161718666666666666666677777777777777777788888888888888888999999999123APPENDIX A:DATA FILE9 19 0 0.00 0 0.00 0 19 9 0 0.009 20 0 0.00 0 0.00 0 20 9 0 0.009 21 0 0.00 0 0.00 0 21 9 0 0.009 22 38 22.88 102 1.29 466 22 9 38 19.559 23 23 22.35 102 1.49 529 23 9 19 19.209 24 0 0.00 0 0.00 0 24 9 0 0.009 25 0 0.00 0 0.00 0 25 9 0 0.0010 11 0 0.00 0 0.00 0 11 10 0 0.0010 12 0 0.00 0 0.00 0 12 10 0 0.0010 13 0 0.00 0 0.00 0 13 10 0 0.0010 14 1712 22.80 102 1.19 336 14 10 1673 20.3210 15 0 0.00 0 0.00 0 15 10 0 0.0010 16 0 0.00 0 0.00 0 16 10 0 0.0010 17 0 0.00 0 0.00 0 17 10 0 0.0010 18 1750 25.21 102 1.45 565 18 10 1673 19.0110 19 77 17.28 102 0.89 150 19 10 58 12.8710 20 0 0.00 0 0.00 0 20 10 0 0.0010 21 0 0.00 0 0.00 0 21 10 0 0.0010 22 0 0.00 0 0.00 0 22 10 0 0.0010 23 0 0.00 0 0.00 0 23 10 0 0.0010 24 0 0.00 0 0.00 0 24 10 0 0.0010 25 0 0.00 0 0.00 0 25 10 0 0.0011 12 0 0.00 0 0.00 0 12 11 0 0.0011 13 0 0.00 0 0.00 0 13 11 0 0.0011 14 365 34.95 180 1.28 393 14 11 365 27.2411 15 19 29.82 180 0.85 231 15 11 19 22.6411 16 38 16.82 102 1.21 245 16 11 38 31.9711 17 38 12.92 102 0.73 192 17 11 38 19.0011 18 1442 33.65 180 1.16 386 18 11 1500 33.3411 19 0 0.00 0 0.00 0 19 11 0 0.0011 20 0 0.00 0 0.00 0 20 11 0 0.0011 21 5 16.95 102 1.13 291 21 11 7 21.3411 22 19 49.45 258 1.08 306 22 11 19 44.9511 23 0 0.00 0 0.00 0 23 11 0 0.0011 24 0 0.00 0 0.00 0 24 11 0 0.0011 25 0 0.00 0 0.00 0 25 11 0 0.0012 13 0 0.00 0 0.00 0 13 12 0 0.0012 14 0 0.00 0 0.00 0 14 12 0 0.0012 15 0 0.00 0 0.00 0 15 12 0 0.0012 16 0 0.00 0 0.00 0 16 12 0 0.0012 17 0 0.00 0 0.00 0 17 12 0 0.0012 18 154 13.92 102 0.91 245 18 12 173 15.0412 19 0 0.00 0 0.00 0 19 12 0 0.0012 20 0 0.00 0 0.00 0 20 12 0 0.0012 21 0 0.00 0 0.00 0 21 12 0 0.0012 22 0 0.00 0 0.00 0 22 12 0 0.0012 23 0 0.00 0 0.00 0 23 12 0 0.0012 24 0 0.00 0 0.00 0 24 12 0 0.0012 25 0 0.00 0 0.00 0 25 12 0 0.0013 14 77 32.64 102 2.04 717 14 13 58 32.6413 15 0 0.00 0 0.00 0 15 13 0 0.0013 16 0 0.00 0 0.00 0 16 13 0 0.0013 17 0 0.00 0 0.00 0 17 13 0 0.0013 18 269 15.93 102 0.82 191 18 13 269 16.0413 19 0 0.00 0 0.00 0 19 13 0 0.0013 20 0 0.00 0 0.00 0 20 13 0 0.0013 21 0 0.00 0 0.00 0 21 13 0 0.0013 22 0 0.00 0 0.00 0 22 13 0 0.0013 23 0 0.00 0 0.00 0 23 13 0 0.0013 24 0 0.00 0 0.00 0 24 13 0 0.00124APPENDIX A:DATA FILE13 25 0 0.00 0 0.00 0 25 13 0 0.0014 15 4288 40.45 253 0.86 213 15 14 4173 41.1214 16 115 35.68 102 2.23 805 16 14 115 42.3714 17 0 0.00 0 0.00 0 17 14 0 0.0014 18 15231 73.37 253 1.59 522 18 14 14962 76.7814 19 135 29.92 102 1.76 586 19 14 135 29.9214 20 77 26.39 201 0.64 95 20 14 38 29.5014 21 0 0.00 0 0.00 0 21 14 0 0.0014 22 1904 53.07 249 1.52 503 22 14 1750 52.6414 23 96 35.82 102 1.99 692 23 14 96 35.8214 24 58 25.08 102 1.32 377 24 14 58 22.4414 25 1327 13.86 102 0.77 197 25 14 1308 14.8815 16 19 19.04 102 1.27 448 16 15 19 25.9615 17 0 0.00 0 0.00 0 17 15 0 0.0015 18 2000 41.61 201 1.45 440 18 15 1942 53.7115 19 0 0.00 0 0.00 0 19 15 0 0.0015 20 77 48.02 102 0.92 218 20 15 58 31.2415 21 0 0.00 0 0.00 0 21 15 0 0.0015 22 269 36.02 201 1.03 315 22 15 308 34.7915 23 0 0.00 0 0.00 0 23 15 0 0.0015 24 0 0.00 0 0.00 0 24 15 0 0.0015 25 0 0.00 0 0.00 0 25 15 0 0.0016 17 0 0.00 0 0.00 0 17 16 0 0.0016 18 481 29.90 102 1.61 547 18 16 481 24.5316 19 0 0.00 0 0.00 0 19 16 0 0.0016 20 0 0.00 0 0.00 0 20 16 0 0.0016 21 0 0.00 0 0.00 0 21 16 0 0.0016 22 0 0.00 0 0.00 0 22 16 0 0.0016 23 19 18.66 102 0.86 230 23 16 19 10.6816 24 0 0.00 0 0.00 0 24 16 0 0.0016 25 0 0.00 0 0.00 0 25 16 0 0.0017 18 154 30.59 102 1.41 393 18 17 173 20.4517 19 0 0.00 0 0.00 0 19 17 0 0.0017 20 0 0.00 0 0.00 0 20 17 0 0.0017 21 7 25.83 102 1.23 321 21 17 7 23.3117 22 0 0.00 0 0.00 0 22 17 0 0.0017 23 0 0.00 0 0.00 0 23 17 0 0.0017 24 0 0.00 0 0.00 0 24 17 0 0.0017 25 0 0.00 0 0.00 0 25 17 0 0.0018 19 115 19.50 102 1.50 462 19 18 96 24.0018 20 1577 56.21 201 1.46 451 20 18 1615 53.6618 21 77 32.16 102 2.01 701 21 18 77 42.2118 22 1231 55.96 201 1.75 671 22 18 1154 47.8518 23 308 29.03 102 1.90 736 23 18 269 22.2818 24 231 18.30 102 1.13 293 24 18 212 17.6818 25 192 25.48 102 1.60 545 25 18 154 22.0819 20 0 0.00 0 0.00 0 20 19 0 0.0019 21 0 0.00 0 0.00 0 21 19 0 0.0019 22 0 0.00 0 0.00 0 22 19 0 0.0019 23 0 0.00 0 0.00 0 23 19 0 0.0019 24 0 0.00 0 0.00 0 24 19 0 0.0019 25 0 0.00 0 0.00 0 25 19 0 0.0020 21 0 0.00 0 0.00 0 21 20 0 0.0020 22 58 61.05 258 1.65 535 22 20 96 61.0520 23 0 0.00 0 0.00 0 23 20 0 0.0020 24 0 0.00 0 0.00 0 24 20 0 0.0020 25 0 0.00 0 0.00 0 25 20 0 0.0021 22 6 20.79 102 0.99 317 22 21 6 13.1621 23 0 0.00 0 0.00 0 23 21 0 0.0021 24 0 0.00 0 0.00 0 24 21 0 0.00125APPENDIX A:DATA FILE21 2522 2322 2422 2523 2423 2524 25o o.oo 0 25 21102 0.95 198 23 220 0.00 0 24 2225 2224 2325 230 0.00 0 25 240 0.0058 13.300 0.000 0.000 0.000 0.000 0.000 0.0058 14.250 0.000 0.000 0.000 0.000 0.000 0.00 00 0.00 00 0.00 0126APPENDIX B127+4165.OOY1T5+1212.28Y1T6T5+360.54Y1T14T5+449.82Y1TI8TSi-869.74Y1T6+589.OOY1T5T6÷508.17Y1T14T6+427.78Y1T18T6+183.81Y1T14+260.32Y1T5T14+1092.96Y1T6T14+533.33Y1T18T14+236.55Y1T18-i-303.5 1Y1TST18+820.67Y1T6T18+457.75Y1T14T18+475.84Y2T6+589.26Y2T14T6+8 17.54Y2T15T6+454.04Y2T18T6+1 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C:EFFICIENT PASSENGERS NETWORK SOLUTIONSOLUTION FILEEFFICIENT PASSENGERS NETWORKDECISION VARIABLE VALUE REDUCED COSTY1T18T5 1.000000 0.000000Y1T18T6 1.000000 0.000000Y1T18T14 1.000000 0.000000Y1T18 1.000000 0.000000Y2T18T6 1.000000 0.000000Y2T14 1.000000 0.000000Y2T14T15 1.000000 0.000000Y2T18 1.000000 0.000000Y2T14T19 1.000000 0.000000Y2T1BT2O 1.000000 0.000000Y2T14T22 1.000000 0.000000Y3T18T9 1.000000 0.000000Y3T18T11 1.000000 0.000000Y3T18T14 1.000000 0.000000Y3T18 1.000000 0.000000Y3T21 1.000000 0.000000Y3T18T23 1.000000 0.000000Y4T18T17 1.000000 0.000000Y4T18 1.000000 0.000000Y5T18T1 1.000000 0.000000Y5T18T6 1.000000 0.000000Y5T18T14 1.000000 0.000000Y5T18 1.000000 0.000000Y5T18T24 1.000000 0.000000Y6T1ST1 1.000000 0.000000Y6T18T2 1.000000 0.000000Y6T18T5 1.000000 0.000000Y6T1ST7 1.000000 0.000000Y6T1ST9 1.000000 0.000000Y6T1ST1O 1.000000 0.000000Y6T18T11 1.000000 0.000000Y6T14 1.000000 0.000000Y6T14T15 1.000000 0.000000Y6T18 1.000000 0.000000Y6T18T20 1.000000 0.000000Y7T18T6 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C:EFFICIENT COMBINED NETWORK SOLUTIONSOLUTION FILEEFFICIENT COMBINED NETWORKDECISION VARIABLE VALUE REDUCED COSTY1T18T5 1.000000 0.000000Y1T1ST6 1.000000 0.000000Y1T14 1.000000 0.000000Y1T18 1.000000 0.000000Y2T18T6 1.000000 0.000000Y2T14 1.000000 0.000000Y2T14T15 1.000000 0.000000Y2T18 1.000000 0.000000Y2T19 1.000000 0.000000Y2T20 1.000000 0.000000Y2T14T22 1.000000 0.000000Y3T18T9 1.000000 0.000000Y3T1ST11 1.000000 0.000000Y3T14 1.000000 0.000000Y3T18 1.000000 0.000000Y3T21 1.000000 0.000000Y3T18T23 1.000000 0.000000Y4T18T17 1.000000 0.000000Y4T18 1.000000 0.000000Y5T14T1 1.000000 0.000000Y5T18T6 1.000000 0.000000Y5T14 1.000000 0.000000Y5T18 1.000000 0.000000Y5T18T24 1.000000 0.000000Y6T18T1 1.000000 0.000000Y6T18T2 1.000000 0.000000Y6T18T5 1.000000 0.000000Y6T18T7 1.000000 0.000000Y6T18T9 1.000000 0.000000Y6T18T1O 1.000000 0.000000Y6T1ST11 1.000000 0.000000Y6T14 1.000000 0.000000Y6T1ST15 1.000000 0.000000Y6T1S 1.000000 0.000000Y6T18T20 1.000000 0.000000Y7T18T6 1.000000 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0.000000187881000000•0000000o00000000000000000000•o0000000000000•0000000•0000000•0000000•00000000000000•0000000’0000000•00000000000000000000000000000000000•0000000•00000000000000•0000000•0000000•0000000•0000000•0000000•0000000•0000000•000000000000000000000•00000000000000•0000000•0000000•0000000•0000000•0000000•00000000000000•0000000•00000000000000•0000000•0000000•0000000•00000000000000•0000000•0000000•0000000•0000000•0000000•0000000•0000000•0000000•00000000000000•00000001000000•1000000•1000000•10000001000000•10000000000001000000•10000001000000‘1000000•1000000I000000•1000000•T000000I000000•I0000001000000•I0000001000000•I000000100000010000001000000.1000000100000010000001000000•T000000-r000000•T0000001000000•I000000•1000000•1000000100000010000001000000•I00000010000001000000•I000000I0000001000000•1000000•I000000•1000000•1000000•10000001000000000000•I000000•I0000001000000•10000001000000•l000000•I000000•181t7119A‘vIIA8IIEA81IA918I1’vA81IA8lIE3A9181IEAF8IIE3261811E3AEI8TIEAE8IIA181IA081IA8I1AI‘vIA‘v11II811A618I1A81711It7118t11A8IITALI81I1A118111AEI81I1A8TI0A8II0A918110t7181L0A918110A10A810116IA!itl6IA0116IAL1t71161A16TA9iT191AT18TAE181A181AI18IA0181A6118IALII8IA91181A9I181AI181AEII8IAI18IA1118IA01181A6181A811I81ALI8IA9181A9181AI8IAEI8IANOIIWIOENOMINNINO31N2I3I..:XICNdVAPPENDIX D189APPENDIX D:EXISTING NETWORK ANALYSISANALYSIS FILELinkEXISTING NETWORKTotal Total ScheduleFr To Flow Flights Delay Cost Seat Mile PaxMile FactorTotal Cost per Cost per Load1 5 2 1 49.00 8330.00 0.65 33.320.021 14 404 2 24.50 74260.00 1.36 1.730.781 18 808 5 9.80 216150.00 0.59 0.740.802 14 3134 16 3.06 730720.00 0.79 0.82 0.972 18 3596 18 2.72 1057320.00 0.63 0.64 0.992 19 77 1 49.00 15680.00 0.52 0.68 0.752 20 212 2 24.50 60600.00 0.66 1.25 0.523 9 19 1 49.00 24000.00 0.71 3.79 0.193 11 58 1 49.00 18750.00 1.00 1.76 0.573 14 173 2 24.50 57120.00 0.51 0.60 0.853 18 577 6 8.17 195960.00 0.66 0.70 0.943 21 28 1 49.00 9380.00 0.62 2.25 0.273 23 19 1 49.00 18040.00 1.12 6.01 0.194 17 4 1 49.00 20160.00 0.31 7.88 0.044 18 385 4 12.25 88880.00 0.99 1.05 0.945 1 2 1 49.00 8330.00 0.65 33.32 0.025 6 58 1 49.00 32640.00 0.48 0.85 0.575 14 443 5 9.80 87900.00 0.76 0.87 0.875 18 615 7 7.00 143080.00 0.56 0.64 0.865 24 65 1 49.00 10980.00 0.72 1.13 0.646 5 77 1 49.00 28800.00 0.43 0.57 0.756 9 173 2 24.50 43500.00 0.55 0.64 0.856 10 192 2 24.50 65240.00 0.40 0.42 0.946 14 4231 17 2.88 1645600.00 0.50 0.51 0.986 15 346 2 24.50 111840.00 0.50 0.52 0.966 18 8499 34 1.44 1317840.00 0.60 0.60 1.007 10 19 1 49.00 12750.00 0.79 4.22 0.197 14 712 7 7.00 168840.00 0.61 0.61 1.007 18 808 8 6.12 191760.00 0.46 0.46 0.997 19 173 2 24.50 24480.00 0.76 0.90 0.858 14 134 2 24.50 49000.00 0.74 1.13 0.668 15 19 1 49.00 21160.00 0.88 4.74 0.198 22 38 1 49.00 16030.00 0.90 2.41 0.379 3 19 1 49.00 20130.00 0.59 3.18 0.199 6 173 2 24.50 60900.00 0.76 0.90 0.859 11 4 1 49.00 12780.00 0.72 18.26 0.049 14 1057 6 8.17 306720.00 0.57 0.66 0.889 15 77 1 49.00 49950.00 0.70 2.28 0.319 16 134 2 24.50 39600.00 0.53 0.81 0.669 18 1115 6 8.17 129540.00 0.51 0.55 0.929 22 38 1 49.00 22880.00 0.48 1.29 0.379 23 23 1 49.00 22350.00 0.41 1.84 0.2310 6 212 3 16.33 90210.00 0.36 0.53 0.6910 7 19 1 49.00 12750.00 0.79 4.22 0.1910 14 1712 17 2.88 387600.00 0.67 0.67 0.9910 18 1846 19 2.58 478989.97 0.44 0.46 0.9510 19 192 2 24.50 34560.00 1.13 1.20 0.9411 3 58 1 49.00 15120.00 0.81 1.42 0.5711 9 6 1 49.00 12750.00 0.71 12.14 0.0611 14 365 3 16.33 104850.00 0.49 0.73 0.68190APPENDIX D:EXISTING NETWORK ANALYSIS11 15 19 1 49.00 29820.000.72 6.79 0.1111 16 38 1 49.00 16820.00 0.671.81 0.3711 17 38 1 49.00 12920.00 0.661.77 0.3711 18 1480 9 5.44 302850.00 0.480.53 0.9111 21 5 1 49.00 16950.00 0.57 11.650.0511 22 19 1 49.00 49450.00 0.63 8.510.0712 18 154 2 24.50 27840.00 0.560.74 0.7513 18 346 4 12.25 63720.00 0.820.96 0.8514 1 442 2 24.50 74480.00 1.36 1.59 0.8614 2 3154 16 3.06 655360.00 0.71 0.73 0.9814 3 173 2 24.50 55080.00 0.49 0.58 0.8514 5 462 5 9.80 90150.00 0.78 0.86 0.9114 6 4327 18 2.72 1558080.00 0.45 0.47 0.9514 7 731 8 6.12 172480.00 0.54 0.61 0.9014 8 115 2 24.50 49280.00 0.75 1.32 0.5614 9 1077 6 8.17 252960.00 0.47 0.53 0.8914 10 1673 17 2.88 345440.00 0.59 0.61 0.9614 11 365 3 16.33 81720.00 0.39 0.57 0.6814 15 4307 18 2.72 728100.00 0.75 0.79 0.9514 18 15308 61 0.80 4475570.00 0.56 0.56 0.9914 20 173 1 49.00 26390.00 1.38 1.61 0.8614 22 2077 9 5.44 477630.00 0.42 0.46 0.9314 25 1327 14 3.50 194040.00 0.69 0.74 0.9315 6 346 2 24.50 83160.00 0.37 0.39 0.9615 8 19 1 49.00 18270.00 0.76 4.09 0.1915 9 77 1 49.00 51520.00 0.72 2.36 0.3115 11 19 1 49.00 22640.00 0.54 5.16 0.1115 14 4231 17 2.88 699040.00 0.76 0.78 0.9815 16 19 1 49.00 19040.00 0.42 2.24 0.1915 18 2000 10 4.90 416100.00 0.47 0.47 1.0015 20 77 1 49.00 48020.00 2.16 2.86 0.7515 22 269 2 24.50 72040.00 0.57 0.85 0.6716 9 134 2 24.50 38640.00 0.52 0.79 0.6616 11 38 1 49.00 31970.00 1.28 3.43 0.3716 15 19 1 49.00 25960.00 0.57 3.05 0.1916 18 481 5 9.80 149500.00 0.54 0.57 0.9416 23 19 1 49.00 18660.00 0.80 4.27 0.1917 4 2 1 49.00 22560.00 0.35 17.62 0.0217 11 38 1 49.00 19000.00 0.97 2.60 0.3717 18 154 2 24.50 61180.00 0.76 1.01 0.7517 21 7 1 49.00 25830.00 0.79 11.50 0.0718 1 846 5 9.80 261850.00 0.72 0.86 0.8418 2 3730 19 2.58 1292760.00 0.73 0.75 0.9718 3 577 6 8.17 153180.00 0.52 0.55 0.9418 4 462 5 9.80 83650.00 0.75 0.83 0.9118 5 596 6 8.17 127920.00 0.58 0.59 0.9718 6 8153 33 1.48 1290630.00 0.61 0.62 0.9818 7 827 9 5.44 222750.00 0.47 0.52 0.9018 9 1348 7 7.00 165060.00 0.56 0.58 0.9618 10 1788 18 2.72 342180.00 0.33 0.34 0.9718 11 1538 9 5.44 300060.00 0.48 0.51 0.9518 12 173 2 24.50 30080.00 0.60 0.71 0.8518 13 327 4 12.25 64160.00 0.82 1.03 0.8018 14 15058 60 0.82 4606800.00 0.58 0.59 0.9918 15 1942 10 4.90 537100.00 0.61 0.63 0.9718 16 481 5 9.80 122650.00 0.44 0.47 0.9418 17 173 2 24.50 40900.00 0.51 0.60 0.8518 20 1942 10 4.90 562100.00 0.62 0.64 0.9718 22 1308 7 7.00 391720.00 0.410.45 0.9318 23 308 4 12.25 116120.00 0.390.51 0.75191APPENDIX D:EXISTING NETWORK ANALYSISAverage Delay = 26.69 System Load Factor = 0.94Average Seat-Mi Cost = 0.66 Average Pax-Mi cost = 2.54Average Load Factor = 0.66Available Seat—Mile = 58683524 Passenger—Mile Flown = 5487589618 24 231 3 16.33 54900.00 0.610.81 0.7518 25 192 2 24.50 50960.00 0.460.49 0.9419 2 115 2 24.50 35360.00 0.58 1.03 0.5619 7 154 2 24.50 25500.00 0.79 1.05 0.7519 10 154 2 24.50 25740.00 0.84 1.11 0.7520 2 308 2 24.50 67880.00 0.73 0.96 0.7620 14 96 1 49.00 29500.00 1.543.23 0.4820 15 58 1 49.00 31240.00 1.402.47 0.5720 18 1980 10 4.90 536600.00 0.59 0.60 0.9921 3 17 1 49.00 14740.00 0.97 5.82 0.1721 11 7 1 49.00 21340.00 0.7210.48 0.0721 17 7 1 49.00 23310.00 0.7110.37 0.0721 22 83 1 49.00 20790.00 0.640.79 0.8122 8 38 1 49.00 15630.00 0.88 2.35 0.3722 9 38 1 49.00 19550.00 0.41 1.10 0.3722 11 19 1 49.00 44950.00 0.57 7.73 0.0722 14 1980 8 6.12 421120.00 0.42 0.42 0.9922 15 308 2 24.50 69580.00 0.55 0.72 0.7722 18 1231 7 7.00 334950.00 0.35 0.41 0.8722 21 83 1 49.00 13160.00 0.41 0.50 0.8122 23 154 2 24.50 28500.00 0.71 0.93 0.7523 3 19 1 49.00 11250.00 0.70 3.75 0.1923 9 19 1 49.00 19200.00 0.36 1.91 0.1923 16 19 1 49.00 10680.00 0.46 2.44 0.1923 18 269 3 16.33 66840.00 0.30 0.34 0.8823 22 154 2 24.50 26600.00 0.66 0.87 0.7524 5 65 1 49.00 10720.00 0.71 1.11 0.6424 18 212 3 16.33 53040.00 0.59 0.85 0.6925 14 1308 13 3.77 193440.00 0.74 0.75 0.9925 18 154 2 24.50 44160.00 0.40 0.53 0.75System Flights = 778 System Cost = 32989960.00 System Delay = 3736.87System Seat-Mi Cost = 0.56 System Pax-Mi Cost 0.60192APPENDIX D:EFFICIENT AIRLINE NETWORK PNALYSISANALYSIS FILEEFFICIENT AIRLiNE NETWORKLink Total Total Schedule Total Cost per Costper LoadFr To Flow Flights Delay Cost Seat Mile Pax Mile Factor1 14 406 2 24.50 74260.00 1.36 1.73 0.791 18 808 5 9.80 216150.00 0.59 0.74 0.802 14 3172 16 3.06 730720.00 0.79 0.81 0.982 18 3596 18 2.72 1057320.00 0.63 0.64 0.992 19 77 1 49.00 15680.00 0.52 0.68 0.752 20 212 2 24.50 60600.00 0.66 1.25 0.523 11 58 1 49.00 18750.00 1.00 1.76 0.573 14 173 2 24.50 57120.00 0.51 0.60 0.853 18 615 7 7.00 228620.00 0.66 0.77 0.863 21 33 1 49.00 9380.00 0.62 1.91 0.324 18 389 4 12.25 88880.00 0.99 1.04 0.955 14 387 4 12.25 70320.00 0.76 0.80 0.955 18 680 7 7.00 143080.00 0.56 0.58 0.956 2 538 3 16.33 262080.00 0.49 0.66 0.736 5 77 1 49.00 28800.00 0.43 0.57 0.756 7 96 1 49.00 28280.00 0.39 0.42 0.946 9 173 2 24.50 43500.00 0.55 0.64 0.856 10 192 2 24.50 65240.00 0.40 0.42 0.946 14 4231 17 2.88 1645600.00 0.50 0.51 0.986 15 346 2 24.50 111840.00 0.50 0.52 0.966 18 7865 32 1.53 1240320.00 0.60 0.61 0.987 14 577 6 8.17 144720.00 0.61 0.64 0.947 18 808 8 6.12 191760.00 0.46 0.46 0.997 19 192 2 24.50 24480.00 0.76 0.81 0.948 14 115 2 24.50 49000.00 0.74 1.32 0.568 22 76 1 49.00 16030.00 0.90 1.21 0.759 14 942 5 9.80 255600.00 0.57 0.61 0.949 18 1468 8 6.12 172720.00 0.51 0.56 0.9110 14 1866 19 2.58 433200.00 0.67 0.69 0.9610 18 1962 20 2.45 504199.97 0.44 0.45 0.9610 19 77 1 49.00 17280.00 1.13 1.50 0.7511 3 63 1 49.00 15120.00 0.81 1.30 0.6211 14 403 3 16.33 104850.00 0.49 0.66 0.7511 16 153 2 24.50 33640.00 0.67 0.90 0.7511 17 38 1 49.00 12920.00 0.66 1.77 0.3711 18 1486 9 5.44 302850.00 0.48 0.53 0.9212 18 154 2 24.50 27840.00 0.56 0.74 0.7513 14 77 1 49.00 32640.00 0.45 0.59 0.7513 18 269 3 16.33 47790.00 0.82 0.93 0.8814 1 444 2 24.50 74480.00 1.36 1.58 0.8614 2 3154 16 3.06 655360.00 0.71 0.73 0.9814 3 173 2 24.50 55080.00 0.49 0.58 0.8514 5 406 4 12.25 72120.00 0.78 0.78 1.0014 6 4327 18 2.72 1558080.00 0.45 0.47 0.95193APPENDIX D:EFFICIENT AIRLINE NETWORK ANALYSIS14 7 750 8 6.12 172480.000.54 0.59 0.9214 8 96 1 49.00 24640.000.75 0.79 0.9414 9 962 5 9.80 210800.000.47 0.49 0.9614 10 1673 17 2.88 345440.000.59 0.61 0.9614 11 499 3 16.33 81720.000.39 0.42 0.9214 15 4326 18 2.72 728100.00 0.750.79 0.9514 18 15289 61 0.80 4475570.00 0.560.56 0.9914 20 250 2 24.50 52780.00 1.382.22 0.6214 22 1942 8 6.12 424560.00 0.420.43 0.9714 23 96 1 49.00 35820.00 0.51 0.54 0.9414 24 58 1 49.00 25080.00 0.65 1.15 0.5714 25 1327 14 3.50 194040.00 0.69 0.74 0.9315 6 346 2 24.50 83160.00 0.370.39 0.9615 14 4327 18 2.72 740160.00 0.76 0.80 0.9515 18 2096 11 4.45 457710.00 0.47 0.50 0.9515 22 288 2 24.50 72040.00 0.57 0.79 0.7216 18 691 7 7.00 209300.00 0.54 0.55 0.9717 11 38 1 49.00 19000.00 0.97 2.60 0.3717 18 163 2 24.50 61180.00 0.76 0.96 0.8018 1 846 5 9.80 261850.00 0.72 0.86 0.8418 2 3192 16 3.06 1088640.00 0.73 0.74 0.9918 3 632 7 7.00 178710.00 0.52 0.59 0.8918 4 464 5 9.80 83650.00 0.75 0.82 0.9118 5 603 6 8.17 127920.00 0.58 0.59 0.9918 6 8596 35 1.40 1368850.00 0.61 0.62 0.9818 7 731 8 6.12 198000.00 0.47 0.53 0.9018 9 1526 8 6.12 188640.00 0.56 0.59 0.9518 10 1673 17 2.88 323170.00 0.33 0.34 0.9618 11 1606 9 5.44 300060.00 0.48 0.48 0.9918 12 173 2 24.50 30080.00 0.60 0.71 0.8518 13 327 4 12.25 64160.00 0.82 1.03 0.8018 14 15077 60 0.82 4606800.00 0.58 0.59 0.9918 15 2038 11 4.45 590810.00 0.61 0.66 0.9218 16 538 6 8.17 147180.00 0.44 0.50 0.8818 17 184 2 24.50 40900.00 0.51 0.57 0.9018 19 115 2 24.50 39000.00 0.41 0.73 0.5618 20 1942 10 4.90 562100.00 0.62 0.64 0.9718 21 90 1 49.00 32160.00 0.45 0.51 0.8818 22 1352 7 7.00 391720.00 0.41 0.43 0.9618 23 369 4 12.25 116120.00 0.39 0.43 0.9018 24 238 3 16.33 54900.00 0.61 0.79 0.7818 25 192 2 24.50 50960.00 0.46 0.49 0.9419 2 115 2 24.50 35360.00 0.58 1.03 0.5619 7 19 1 49.00 12750.00 0.79 4.25 0.1919 10 212 3 16.33 38610.00 0.84 1.21 0.6919 18 96 1 49.00 24000.00 0.51 0.54 0.9420 2 346 2 24.50 67880.00 0.73 0.86 0.8620 15 58 1 49.00 31240.00 1.40 2.47 0.5720 18 2038 11 4.45 590260.00 0.59 0.64 0.9221 18 114 2 24.50 84420.00 0.59 1.06 0.5622 8 76 1 49.00 15630.00 0.88 1.18 0.7522 14 1884 8 6.12 421120.00 0.42 0.44 0.9522 15 327 2 24.50 69580.00 0.55 0.68 0.8122 18 1236 7 7.00 334950.00 0.35 0.40 0.8822 23 58 1 49.00 14250.00 0.71 1.24 0.5723 14 96 1 49.00 35820.00 0.51 0.54 0.9423 18 326 4 12.25 89120.00 0.30 0.37 0.8023 22 58 1 49.00 13300.00 0.66 1.16 0.5724 14 58 1 49.00 22440.00 0.58 1.03 0.5724 18 219 3 16.33 53040.00 0.59 0.83 0.72194APPENDIX D:EFFICIENT AIRLINE NETWORK ANALYSIS25 14 1308 13 3.77 193440.000.74 0.75 0.9925 18 154 2 24.50 44160.000.40 0.53 0.75System Flights = 745 System Cost = 32449630.00System Delay = 2160.43System Seat—Mi Cost = 0.56 System Pax—Mi Cost = 0.59Average Delay 20.38 System Load Factor = 0.95Average Seat-Mi Cost 0.63 Average Pax—Mi cost= 0.84Average Load Factor = 0.83Available Seat—Mile 58069236 Passenger—Mile Flown = 55231064195APPENDIX D:EFFICIENT PASSENGERS NETWORK ANALYSISLinkANALYSIS FILEEFFICIENT PASSENGERS NETWORKTotal Total ScheduleFr To Flow Flights Delay Cost Seat MilePax Mile FactorTotal Cost per Cost per Load1 18 1214 7 7.00 302610.00 0.590.69 0.862 14 3211 16 3.06 730720.00 0.790.80 0.992 18 3808 19 2.58 1116060.00 0.630.64 0.993 18 846 9 5.44 293940.00 0.66 0.72 0.923 21 105 2 24.50 18760.00 0.621.20 0.514 18 389 4 12.25 88880.00 0.991.04 0.955 18 1067 11 4.45 224840.00 0.56 0.58 0.956 14 4577 19 2.58 1839200.00 0.50 0.53 0.956 18 8941 36 1.36 1395360.00 0.60 0.61 0.997 14 615 7 7.00 168840.00 0.61 0.71 0.867 18 827 9 5.44 215730.00 0.46 0.51 0.908 14 191 2 24.50 49000.00 0.74 0.79 0.949 18 2410 12 4.08 259080.00 0.51 0.51 1.0010 14 1789 18 2.72 410400.00 0.67 0.68 0.9710 18 1981 20 2.45 504199.97 0.44 0.45 0.9711 18 2023 12 4.08 403800.03 0.48 0.52 0.9411 21 5 1 49.00 16950.00 0.57 11.65 0.0512 18 154 2 24.50 27840.00 0.56 0.74 0.7513 18 346 4 12.25 63720.00 0.82 0.96 0.8514 2 3269 17 2.88 696320.00 0.71 0.74 0.9514 6 4673 19 2.58 1644640.00 0.45 0.46 0.9714 7 615 7 7.00 150920.00 0.54 0.63 0.8614 8 172 2 24.50 49280.00 0.75 0.88 0.8414 10 1731 17 2.88 345440.00 0.59 0.59 1.0014 15 4980 20 2.45 809000.00 0.75 0.76 0.9814 18 18250 73 0.67 5356010.00 0.56 0.56 0.9914 19 442 5 9.80 149600.00 0.50 0.58 0.8714 22 2230 9 5.44 477630.00 0.42 0.43 1.0014 25 1519 15 3.27 207900.00 0.69 0.69 0.9915 14 4865 20 2.45 822400.00 0.76 0.79 0.9615 18 2192 11 4.45 457710.00 0.47 0.47 0.9916 18 691 7 7.00 209300.00 0.54 0.55 0.9717 18 194 2 24.50 61180.00 0.76 0.80 0.9517 21 7 1 49.00 25830.00 0.79 11.50 0.0718 1 1290 7 7.00 366590.00 0.72 0.79 0.9218 2 4038 20 2.45 1360800.00 0.73 0.73 1.0018 3 923 10 4.90 255300.00 0.52 0.57 0.9018 4 464 5 9.80 83650.00 0.75 0.82 0.9118 5 1086 11 4.45 234520.00 0.58 0.60 0.9718 6 8596 35 1.40 1368850.00 0.61 0.62 0.9818 7 846 9 5.44 222750.00 0.47 0.51 0.9218 9 2661 14 3.50 330120.00 0.56 0.59 0.9518 10 1884 19 2.58 361190.00 0.33 0.34 0.9718 11 2079 12 4.08 400080.00 0.48 0.50 0.9618 12 173 2 24.50 30080.00 0.60 0.71 0.8518 13 327 4 12.25 64160.00 0.82 1.03 0.8018 14 17941 71 0.69 5451380.00 0.58 0.58 1.0018 15 2115 11 4.45 590810.00 0.61 0.63 0.9618 16 691 7 7.00 171710.00 0.44 0.45 0.9718 17 215 3 16.33 61350.00 0.51 0.73 0.70196APPENDIX D:EFFICIENT PASSENGERS NETWORK ANALYSISSystem Flights = 766 System Cost = 34420832.00 System Delay =System Seat—Mi Cost = 0.56 System Pax—Mi Cost = 0.58Average Delay = 12.60 System Load Factor = 0.97Average Seat—Mi Cost 0.60 Average Pax—Mi cost 1.58Average Load Factor 0.84Available Seat—Mile = 61540296 Passenger—Mile Flown = 5956262418 20 2404 12 4.08 674520.000.62 0.62 1.0018 22 1404 7 7.00 391720.000.41 0.42 1.0018 23 523 6 8.17 174180.000.39 0.45 0.8518 24 296 3 16.33 54900.000.61 0.63 0.9719 14 423 5 9.80 149600.000.50 0.60 0.8320 18 2442 13 3.77 697580.000.59 0.63 0.9321 3 17 1 49.00 14740.00 0.975.82 0.1721 11 7 1 49.00 21340.00 0.7210.48 0.0721 17 7 1 49.00 23310.000.71 10.37 0.0721 18 77 1 49.00 42210.00 0.59 0.78 0.7521 22 6 1 49.00 20790.00 0.64 10.93 0.0622 14 2134 9 5.44 473760.00 0.42 0.44 0.9522 18 1365 7 7.00 334950.00 0.35 0.37 0.9722 21 6 1 49.00 13160.00 0.41 6.92 0.0623 18 480 5 9.80 111400.00 0.30 0.32 0.9424 18 277 3 16.33 53040.00 0.59 0.65 0.9125 14 1462 15 3.27 223200.00 0.74 0.77 0.96843.98197APPENDIX D:EFFICIENT COMBINED NETWORK ANALYSISLinkANALYSIS FILEEFFICIENT COMBINED NETWORKTotal Total ScheduleFr To Flow Flights Delay Cost Seat MilePax Mile FactorTotal Cost per Cost per Load1 14 404 2 24.50 74260.00 1.361.73 0.781 18 810 5 9.80 216150.00 0.59 0.74 0.812 14 3134 16 3.06 730720.00 0.79 0.82 0.972 18 3596 18 2.72 1057320.00 0.63 0.64 0.992 19 212 3 16.33 47040.00 0.52 0.74 0.692 20 212 2 24.50 60600.00 0.66 1.25 0.523 14 173 2 24.50 57120.00 0.51 0.60 0.853 18 673 7 7.00 228620.00 0.66 0.70 0.943 21 28 1 49.00 9380.00 0.62 2.25 0.274 18 389 4 12.25 88880.00 0.99 1.04 0.955 14 387 4 12.25 70320.00 0.76 0.80 0.955 18 680 7 7.00 143080.00 0.56 0.58 0.956 14 4231 17 2.88 1645600.00 0.50 0.51 0.986 18 9287 37 1.32 1434120.00 0.60 0.60 1.007 14 577 6 8.17 144720.00 0.61 0.64 0.947 18 865 9 5.44 215730.00 0.46 0.49 0.948 14 191 2 24.50 49000.00 0.74 0.79 0.949 14 942 5 9.80 255600.00 0.57 0.61 0.949 18 1468 8 6.12 172720.00 0.51 0.56 0.9110 14 1731 17 2.88 387600.00 0.67 0.67 1.0010 18 2135 21 2.33 529410.00 0.44 0.44 1.0011 14 365 3 16.33 104850.00 0.49 0.73 0.6811 18 1663 10 4.90 336500.00 0.48 0.52 0.9212 18 154 2 24.50 27840.00 0.56 0.74 0.7513 18 346 4 12.25 63720.00 0.82 0.96 0.8514 1 444 2 24.50 74480.00 1.36 1.58 0.8614 2 3289 17 2.88 696320.00 0.71 0.74 0.9614 3 173 2 24.50 55080.00 0.49 0.58 0.8514 5 404 4 12.25 72120.00 0.78 0.79 0.9914 6 4327 18 2.72 1558080.00 0.45 0.47 0.9514 7 634 7 7.00 150920.00 0.54 0.61 0.8914 8 172 2 24.50 49280.00 0.75 0.88 0.8414 9 962 5 9.80 210800.00 0.47 0.49 0.9614 10 1673 17 2.88 345440.00 0.59 0.61 0.9614 11 365 3 16.33 81720.00 0.39 0.57 0.6814 15 4634 19 2.58 768550.00 0.75 0.78 0.9614 18 15808 63 0.78 4622310.00 0.56 0.56 0.9914 22 2230 9 5.44 477630.00 0.42 0.43 1.0014 25 1519 15 3.27 207900.00 0.69 0.69 0.9915 14 4519 18 2.72 740160.00 0.76 0.77 0.9915 18 2538 13 3.77 540930.00 0.47 0.48 0.9716 18 691 7 7.00 209300.00 0.54 0.55 0.9717 18 201 2 24.50 61180.00 0.76 0.77 0.9918 1 846 5 9.80 261850.00 0.72 0.86 0.8418 2 3730 19 2.58 1292760.00 0.73 0.75 0.9718 3 690 7 7.00 178710.00 0.52 0.54 0.9718 4 464 5 9.80 83650.00 0.75 0.82 0.9118 5 682 7 7.00 149240.00 0.58 0.61 0.9618 6 8942 36 1.36 1407960.00 0.61 0.61 0.9918 7 827 9 5.44 222750.00 0.47 0.52 0.90198APPENDIX D:EFFICIENT COMBINED NETWORK ANALYSISSystem Flights = 744 System Cost = 32808300.00 System Delay =System Seat—Mi Cost = 0.56 System Pax—Mi Cost = 0.58Average Delay = 11.60 System Load Factor = 0.96Average Seat—Mi Cost = 0.61 Average Pax—Mi cost = 0.71Average Load Factor = 0.89Available Seat—Mile = 58730592 Passenger—Mile Flown = 5654359218 9 1699 9 5.44 212220.000.56 0.59 0.9418 10 1884 19 2.58361190.00 0.33 0.34 0.9718 11 1721 10 4.90 333400.000.48 0.50 0.9618 12 173 2 24.50 30080.000.60 0.71 0.8518 13 327 4 12.25 64160.000.82 1.03 0.8018 14 15557 62 0.79 4760360.000.58 0.59 0.9918 15 2461 13 3.77 698230.000.61 0.64 0.9418 16 691 7 7.00 171710.000.44 0.45 0.9718 17 222 3 16.33 61350.000.51 0.70 0.7318 19 230 3 16.33 58500.00 0.410.55 0.7518 20 2192 11 4.45 618310.000.62 0.63 0.9918 21 95 1 49.00 32160.00 0.450.48 0.9318 22 1410 8 6.12 447680.00 0.410.47 0.8818 23 523 6 8.17 174180.00 0.39 0.450.8518 24 296 3 16.33 54900.00 0.61 0.630.9719 2 115 2 24.50 35360.00 0.581.03 0.5619 10 154 2 24.50 25740.00 0.841.11 0.7519 14 154 2 24.50 59840.00 0.50 0.66 0.7520 2 308 2 24.50 67880.00 0.73 0.96 0.7620 18 2134 11 4.45 590260.00 0.59 0.610.9721 18 114 2 24.50 84420.00 0.59 1.060.5622 14 2134 9 5.44 473760.00 0.42 0.44 0.9522 18 1371 7 7.00 334950.00 0.35 0.36 0.9723 18 480 5 9.80 111400.00 0.30 0.32 0.9424 18 277 3 16.33 53040.00 0.59 0.65 0.9125 14 1462 15 3.27 223200.00 0.74 0.77 0.96881.55199

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