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BUBLS : a mixed integer program for transit centre location in the Lower Mainland Willoughby, Keith Allan 1993

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BUBLS: A MIXED INTEGER PROGRAM FOR TRANSIT CENTRE LOCATIONIN THE LOWER MAINLANDbyKEITH ALLAN WILLOUGHBYB.Comm.(H.Hons.), The University of Saskatchewan, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCE (Business Administration)inTHE FACULTY OF GRADUATE STUDIESFACULTY OF COMMERCE AND BUSINESS ADMINISTRATIONWe accept this thesis as conformingto th re uired standardTHE UNIVERSITY OF BRITISH COLUMBIAJune 1993© Keith Allan Willoughby, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of Cerm k.cc 1 Bus / P4E 55 AD tO/ tuThe University of British ColumbiaVancouver, CanadaDate ^ /r13DE-6 (2/88)Page iiABSTRACTA mixed integer optimization model is developed to determineboth the optimal location of transit centres to serve BC Transit'sLower Mainland route network and the optimal allocation of buses tothose centres. The existing five transit centres are explored aswell as five candidate facilities. The model considers nonrevenuetransportation cost (deadhead), capital cost of constructingcandidate transit centres and the salvage values of existingcentres. A linear regression is generated to produce the traveltimes from the terminus of a route to potential transit centrelocations. The optimal solution is determined, resulting inpotential annual savings of over $560,000 compared to the currentlocation-allocation strategy. Various experiments are performed toexamine the sensitivity of model parameters and to determine theeffect of different planning scenarios. The effect of the optimalsolution on driver relief is considered. Conclusions as well asdirections for further research are offered.Page iiiTABLE OF CONTENTSAbstract^ iiTable of Contents^ iiiList of Tables viList of Figures^ viiAcknowledgements viii1.02.0IntroductionLiterature Review152.1 General Facility Location Literature 52.2 General Transit Literature 142.3 OR/MS Applications in Urban Transit 152.4 Transit Centre Location Studies 162.4.1 San Antonio 172.4.2 Calgary 172.4.3 Maze^(Detroit) 182.4.4 Ball^(Pennsylvania) 233.0 Urban Transit in British Columbia 254.0 The Location-Allocation MIP Model 304.1 Objective Function 344.1.1 Deadhead Times 344.1.2 Capital Costs 454.1.3 Salvage Values 474.2 Constraints 484.3 Variable Restrictions 525.0 MIP Optimal Solution 545.1 Comparison with LP Optimum 575.2 Comparison with Current Location-Allocation Scheme 586.0 Model Experiments 606.1 Eliminating the Maximum and Minimum Restrictionson Facility Size 606.2 Enforcing the "50 Trolley" Minimum Restriction 636.3 Increasing the Minimum Allowable Size of aCandidate Transit Centre 636.4 Elimination of OTC 656.5 Increase in Capacity of BTC 667.0 Effect on Driver Relief 68Page iv8.0 Conclusions^ 709.0 Directions for Further Research^ 72Bibliography^ 75Appendix 1^BC Transit-CPLEX Route Numbers^ 79Appendix 2^Weekly Deadheads per Location 80Appendix 3^BC Transit Routes & Termini^ 88Appendix 4^Linear Regression Deadhead Time Sample Data^92Appendix 5^Terminus-Transit Centre Deadhead Times(Diesels)^ 94Appendix 6^Diesel Bus Route Deadhead Times^ 97Appendix 7.1 Bus Route Requirements - NVT 100Appendix 7.2^Bus Route Requirements - PCT^ 101Appendix 7.3^Bus Route Requirements - STC 102Appendix 7.4^Bus Route Requirements - BTC^ 104Appendix 7.5 Bus Route Requirements - OTC 106Appendix 8.1 Optimal Solution Bus Assignments - NVT^108Appendix 8.2^Optimal Solution Bus Assignments - PCT^109Appendix 8.3^Optimal Solution Bus Assignments - STC^110Appendix 8.4 Optimal Solution Bus Assignments - BCRTC^112Appendix 8.5 Optimal Solution Bus Assignments - BTC^113Appendix 8.6^Optimal Solution Bus Assignments - OTC^115Appendix 8.7^Optimal Solution Bus Assignments - MN & TRM^117Appendix 9^Optimal Solution Route Assignments^118Appendix 10^Current vs. Optimal Bus Allocations 125Appendix 11^Total Bus Allocations and Cost Breakdowns^130Minimum Candidate Transit Centre Size of 100:Page vAppendix 12.1 Proposed Bus Assignments - NVT 131Appendix 12.2 Proposed Bus Assignments - PCT 132Appendix 12.3 Proposed Bus Assignments - STC 133Appendix 12.4 Proposed Bus Assignments - BCRTC 135Appendix 12.5 Proposed Bus Assignments - BTC 137Appendix 12.6 Proposed Bus Assignments - OTC 139Appendix 13 Elimination of OTC:Proposed Bus Assignments - RICH 141Appendix 14 Transit Centre Allocations for Driver Relief 142Appendix 15 Calculation of Weekly Driver Reliefs 144Appendix 16 Calculation of Driver Relief Savings 146Page viLIST OF TABLESTABLE A LINEAR REGRESSION RESULTS^ 38TABLE B EXISTING AND CANDIDATE TRANSIT CENTRELOCATIONS^ 39TABLE C TERMINUS-TRANSIT CENTRE DEADHEAD TIMES(TROLLEYS) 42TABLE D TROLLEY BUS ROUTE DEADHEAD TIMES^ 43TABLE E CAPITAL COSTS: CANDIDATE TRANSIT CENTRES^47TABLE F SALVAGE VALUES: EXISTING TRANSIT CENTRES^48Page viiLIST OF FIGURESFIGURE A OBJECTIVE FUNCTION VALUES^ 59Page viiiACKNOWLEDGEMENTSThis thesis was completed with the assistance of severalindividuals. Without implicating them, I wish to thank thefollowing three employees of BC Transit. Their contributions werevital. Robert N. Tribe, M.A.Sc., P.Eng., Vice President CapitalProjects, provided overall support and guidance and served as themotivator for this project. W.H. (Bill) Green, Schedule Supervisor& Technical Assistant, offered technical assistance on transitscheduling matters. Garry D. Andrews, P.Eng., Project Manager,furnished additional support in gathering data. Other employeeswho contributed their time and talents included: Gordon Chan,Dorothy Kerr, Greg McDonald, Ray Parker, Brenda Sleva, Glen Vernon,Andy Welsh and Tom Yang. I accept sole responsibility for the dataand its analysis. Any errors, omissions or miscalculations aremine. The conclusions and recommendations offered are completelymy own. They do not in any way imply either current or futuredirections regarding BC Transit facilities planning.I also wish to thank my thesis supervisor and friend, Dr. DeanUyeno. His insights, patience and enthusiasm were indeed a sourceof strength. In addition, I acknowledge the assistance of theother members of my thesis committee: Dr. Derek Atkins, who didmuch to help me overcome my initial scepticism of matrixgeneration; Dr. Trevor Heaver, who provided the initial impetus forthis thesis and Dr. Tom McCormick, who introduced me to the mixedinteger optimizer, CPLEX.Last, and certainly not least, I wish to thank my wife Leanne,to whom this thesis is dedicated. This present work would neverhave been finished without her constant encouragement, kind wordsof support and willingness to adjust.M.Sc. Thesis^ Page 11.0 INTRODUCTION"Our existence in time is determined for us, but we arelargely free to select our location".-August Losch, "The Economics of Location", p.3BC Transit, the provincial Crown Corporation charged withproviding effective and reliable public transit service to thecitizens of British Columbia, is seeking a more quantitativeapproach to the problem of transit centre location and theallocation of buses to those centres. Currently, the VancouverRegional Transit System, which administers transit needs in theLower Mainland, includes the following five transit centres:1) North Vancouver (NVT)2) Port Coquitlam (PCT)3) Surrey (STC)4) Burnaby (BTC)5) Oakridge (OTC), located at Oak & 41st in VancouverSeveral factors have created the need for a quantitativeapproach to this location-allocation problem. They include:1) severe overcrowding at the NVT and OTC facilities. Thishampers the movement of personnel and vehicles within thecentre. Any quantitative methods developed for this problemshould ensure that capacity restrictions are enforced.2) the value of the land at OTC. Located in the heart ofVancouver, its value has been increasing steadily.^TheKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 2 profits from its sale may more than pay for an alternativetransit centre.3) the planned expansion of the SkyTrain into the Richmond andLougheed Mall corridors. Should this occur, routes in thoseareas would be altered. The impact on facilities and theirlocation should be examined.4) the expansion of bus service into the suburban areas,particularly Maple Ridge and Pitt Meadows. As demand fortransit increases in these areas, a change in facilities maybe warranted.These transit centres act as bus barns or depots where thebuses are housed and various maintenance activities performed (theterms "bus barn", "depot" and "garage" are used interchangeablywith transit centre). All buses begin their service day from anassigned transit centre and return at the conclusion of the day tothat depot.Buses do not generally begin revenue service from the momentof their departure from the transit centre. A certain amount oftime is required to travel from the depot to a point along itsroute (hereafter referred to as the initiation point). Likewise,buses usually do not undertake revenue service to the bus barn atKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 3the end of the day. Rather, buses travel in nonrevenue servicefrom a point along its route (the termination point) to the transitcentre. The sum of these two travel times constitutes vehicledeadhead time, or the time taken in nonrevenue service.An additional component of nonrevenue transportation costsconsists of driver relief time. Essentially, this cost is incurredwhen a "run" (a vehicle service schedule) extends longer than themaximum driver time allowed by union contract. When this occurs,a driver is required to replace the one currently operating thevehicle. The former driver is then paid for the time required totravel back to the point where his/her shift began. Runs thatoperate specifically in the AM or PM peak do not extend longer thanthe maximum driver time. Therefore, driver relief is not aconsideration in those runs. However, the importance ofmaintaining adequate control over driver relief costs should notunderestimated. Various studies (see [35]) have shown that driverrelief costs can rise quickly with inefficient depot locationschemes.It is the aim of transit planning agencies to locate transitcentres and assign buses to those depots in such a way as tominimize vehicle deadhead time and driver relief costs. If newlocations are needed for transit centres, then these candidatedepots will incur capital costs. The aim of the present study isKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 4to develop a quantitative technique and methodology to find theleast cost solution. It is also hoped that this method can providetransit planning officials with a tool to measure the impact ofvarious scenarios in terms of deadhead and capital costs.The format of this thesis is as follows. Chapter 2 presentsa review of the literature pertaining to facility location problemsand the application of Operations Research/Management Science(OR/MS) techniques to the transit centre location problem. InChapter 3, a general overview and history of BC Transit isintroduced. The transit centre location-allocation model, BUBLS,is introduced in Chapter 4. The objective function, constraintsand variable restrictions are each explored. The optimal solutionto this mixed integer program is obtained in Chapter 5. Itsresults are compared with the current location-allocation strategy.Chapter 6 describes the results of several experiments run to testthe effect of different future scenarios or changes in modelparameters. The effect of the optimal solution on driver relief isconsidered in Chapter 7 while Chapter 8 reports on the conclusionsreached in this thesis. Finally, Chapter 9 offers a few directionsfor future research.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 52.0 LITERATURE REVIEWThis literature review will proceed as follows. The firstsection will be devoted to a review of many aspects of the generalfacility location problem. Single and multiple facilities,appropriate distance measures and heuristics are some areas to becovered. The next section will comment on some general transitliterature. Then, some OR/MS applications in urban transit will beintroduced. The literature review will finish with an analysis ofactual transit centre location case studies, from simpler ones tocomplex applications.2.1 GENERAL FACILITY LOCATION LITERATUREThe general capacitated fixed cost facility location-allocation problem may be formulated as follows:m nMINIMIZEE E c.x..+E^V I^Ii=1 j=1^j=1subject to:WE Xi?Dij=1(2)E XiiSSi^Vj=1,...,ni=1Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 6(3)E X iiSS rji =1W=1,-41Variable restrictions:Cii,Xii,Fi,Di,Sj >=-- 0= 0,1where:= per unit cost of servicing customer i's demand from a plant inlocation jnumber of units of customer i's demand serviced from locationF. = fixed cost of operating a plant in location jY 0 if a plant in location j is not opened1 if a plant in location j is openedDi = total demand of customer iSi = capacity of location jThis formulation seeks to find the minimum cost combination oflocations and the allocation of customers to those locations. Thefirst summation considers all the variable (per unit) costs of thelocation-allocation scheme. The second summation deals with thefixed costs of each location, those costs that will only beincurred should a location be utilized.The first set of constraints ensures that demand of eachcustomer is satisfied. The second set of constraints enforces thecapacity restrictions of each location. The third type ofconstraint acts as a "switch" or "on-off" constraint. If a plantin location j is not opened (Yi = 0), then this restriction forcesno units to be sent to any customer from this location. Else, ifKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 7Y = 1, then the allocation to all customers is bounded by thelocation's capacity.The facility location problem is one of the oldest problemstackled in Management Science (see [3],[12]). Warehouses,ambulance centres, audit offices and hotels are but a fewsituations in which facility location analysis has been used. Avariety of models, techniques and tools have been created toexamine the theory and applications of this area (see [15], [18],[19], [32], [40]).Facility locations models may be categorized into any one ofthese (non-mutually exclusive) areas: deterministic, stochastic anddynamic. Deterministic location models assume that all componentsof the problem (variable costs, fixed costs, supplies, demands,etc.) are known and constant. These models are the simplest toformulate. On the other hand, stochastic models assume that someparameter values are given by probability distributions.Mirchandani and Francis [32] give some examples of real-worldapplications using stochastic parameters:(1) Ambulance location analysis.^The demand for services(calls to the ambulance centre) may follow a probabilitydistribution according to time of day.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 8(2) Courier/parcel services.^Travel time may vary in aprobabilistic manner according to the time of day.(3) The fixed costs of opening a location may follow apessimistic/realistic/optimisticdistributionwithprobabilityvalues assigned to each scenario.Dynamic location models may contain deterministic orstochastic parts, or both. These models are used when the decisionto be currently made is affected by decisions made in an earliertime period.represented.importance.assignmentIn these models, the time element is explicitlyThe timing of establishing facilities is ofAn example of these models would be a police carvehicle would be designated toschedule where thecertain locations at various times of the day.Facility location models may be classified as single ormultiple facility problems. A widely-used technique to solve thesingle facility location problem is the center-of-gravity (CG)method. The optimal x coordinate, x*, of the location isdetermined by taking a weighted average of the x coordinates ofeach demand point. The weights are the total fraction of demandoccurring at each specific point. Similar analysis is repeated forthe optimal y coordinate. This method is relatively simple toconceptualize and implement.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 9 The multiple facility location problem is an extension of itssingle facility counterpart. Mixed integer programming, utilizinga branch-and-bound approach, is one method of solving this problem(see [8]). When solving multiple facility problems, one of twodecision-making rules may be utilized: the minisum or minimax rule.Under the minisum rule, one attempts to minimize the total distance(or time) between the facilities and demand points. Minimizing themaximum distance from a demand point to its allocated facilityoccurs under the minimax rule. The current study of transit centrelocation- bus allocation, as with most facility location problems,uses the minisum decision rule. The minimax rule would be employedin such applications as ambulance centre or police precinctlocation. In these cases, the maximum response time to a call isof prime importance.Minisum problems are frequently referred to as "median"problems while minimax types are mentioned as "center" problems.Therefore, an m-median problem seeks to establish m facilities inm potential locations such that total fixed and variable costs areminimized. Here, m is the sum of the 0-1 binary variables denotingclosure or opening of a facility.A multiple facility location problem borrowing heavily fromthe minimax rule was examined by Handler and Mirchandani [18]. Itis called the inverse centre problem. This formulation tries toKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 10find the minimum number of facilities required and their locationssuch that the distance from a demand point to its closest facilityis less than or equal to a specified value. It would findapplication, no doubt, if a community wished to locate severalemergency response facilities while ensuring that each residencewas no more than, say, five minutes from an ambulance.In both single and multiple facility problems, a variety ofmethods are used to calculate appropriate distances. One method isthat all travel occurs along Euclidean ("straight-line" or "as thecrow flies") distances. Another method postulates that all travelfollows rectilinear distances. In other words, travel is onlyallowed on right-angled routes on the grid. Other names for thismethod include rectangular, metropolitan or Manhattan distances.Finally, shortest path distance measures are used in many networkmodels. These allow significantly closer approximation to distanceand time costs than either Euclidean or rectangular distancemeasures.Love et al. [24] examine the 1 (X,a.) distance function, usedP^Jfor determining the distance between a new facility, X, and anyexisting facilities, aj. It is of the form:lp (X , aj) = ( X1 - a1 P +^- a2 P) iPKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 11The value of p will determine the method of measuringdistance. When p=1, this function gives the rectilinear distancemeasure. When p=2, the Euclidean or straight-line measure issupplied. A value of p between 1 and 2 (exclusive) provides theactual travel distance measure.Love et al. submit that a factor of between 18% and 30% needsto be allowed when computing approximate road distances fromstraight-line distances. Baxter [6] uses a hazard function in hisdepot location formulation. The straight-line distance of a routeis multiplied by a penalty factor to allow for obstructions.Facility location problems may further be classified aslocations on networks or locations on planes. The network problemsare discrete since only a feasible set of possible locations areconsidered. Locations on planes involve an infinite set oflocations and are therefore termed continuous. The current transitcentre study is a network location problem since a finite, feasibleset of potential sites can be used for depots.Various heuristics are also used to solve facility locationproblems, ranging from complex procedures to simple rules.Khumawala [20] discusses the delta and omega rules. Theircomplexity has not restricted their considerable usage in thetransit centre location problem. Essentially, his heuristic usesKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 12 three sets. The set A represents the set of open locations, B isthe set of closed locations, while the set of "free" locations (nodecision has yet been made) is in set C. At the beginning of theanalysis, sets A and B are empty while set C contains all feasiblelocations.A transportation problem for all locations fixed open issolved. Then, a certain location, say k, is removed and thetransportation problem is re-solved. The variable costs (whichwill increase when a facility is removed) are recalculated withoutlocation k. If the minimum increase in variable costs is greaterthan the fixed costs of keeping k open, then k is included in setA (locations fixed open).For fixing locations closed, one calculates the savings intotal variable costs that a location would generate if it wereopened, considered over the set of sites already opened. If themaximum savings do not exceed the fixed cost of that location, thenit should not be opened. It is then placed in set B.Sites that are still in set C after this procedure can bepositioned into sets B or C through a branch-and-bound procedure.Ballou [5] mentions the Kuehn-Hamburger heuristics. They are:Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 13 (1) Locations with the greatest promise are at or nearconcentrations of demand.(2) Optimality can be approached by adding, at each stage, thelocation with the greatest cost savings.(3) Only a small subset of feasible facility locations needsto be evaluated to determine which should be added.These intuitive heuristics may be applied to the currenttransit centre location problem. The first would stipulate that atransit centre should be located near a high concentration ofdeadheads. The next one presents a rule for adding garages to thenetwork. Those which provide greater cost savings should be addedbefore those with less value. The final heuristic means that,generally, there will only be a small number of locations to beevaluated at each step.Khumawala defines the term Y. It is:1^- slack capacity of location total capacity of location jThe closer this value is to 0(1), the greater likelihood ofthis facility being closed (open). If a facility is only allocateda small amount relative to its capacity, then it would not makeKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 14sense to keep that location opened.Love et al. [24] mention that an appropriate heuristic is tolocate the new facilities and allocate the existing demand areas tothe nearest new facility until neither locations nor allocationsare changed. This is similar to the location-interchange heuristicused in Ball's actual transit centre location case study [4].Cooper [12] postulated that the more "dense" the set ofdestinations, the more likely it is that some of the sources shouldbe located at destinations. This heuristic bears resemblance tothe first statement in the Kuehn-Hamburger model.2.2 GENERAL TRANSIT LITERATUREA few references exist in the area of urban transit theory.Anderson [1] describes a formula for the required size of a transitvehicle fleet. It is:N = No + No + No,where:N = required size of vehicle fleetNo= required number of occupied vehicles to meet peakdemandNo= number of empty vehicles in circulation during peakdemand as a result of nonuniform demandNm^extra vehicles required due to rush-hour breakdownsKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 15Anderson also classifies transit systems according to thegeometry of the routes. They consist of: loop, line-haul, networkand shuttle. BC Transit's Lower Mainland route layout is a networkand shuttle system.Giannopoulos [16] offers a practical guide in operating atransit centre. The average number of buses per depot is usuallybetween 200 and 300. This falls in line with comments from BCTransit representatives, who felt that 250 was the "right" size fora transit centre. Giannopoulos also describes the facilitiesrequired in any bus barn (hoists, machine shops, wash areas, etc.).2.3 OR/MS APPLICATIONS IN URBAN TRANSITOR/MS techniques have been utilized extensively in many majortransit applications, besides the transit centre location-busallocation problem. These techniques include, but are not limitedto, goal programming, simulation and quadratic programming.Categories of applications include analysis of bus ridership andestimation of ridership markets ([2],[9],[38],[43]), transit faresetting ([10],[13]) and transit scheduling [36]. Maintenanceissues ([29],[34]), capital allocation amongst competing ends [39]and transit planning ([21],[22]) are others.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 162.4 TRANSIT CENTRE LOCATION CASE STUDIESRand [33] describes some of the methodological choices thatmust be made in any depot location study. Many of these featureshave direct bearing on the present transit centre locationanalysis. Among those choices are:(1) potential locations. Is the location analysis to bedone on a plane (infinite set of possible locations) oron a network (a feasible set of sites is considered).(2) search procedures. Infinite set formulations may useheuristic methods while feasible set configurations mayuse mixed integer programming.(3) planning horizon.^For what time period is thefacility location to be planned?^Rand introducesstability analysis. This determines how the system wouldfare, in the long run, if no location decisions after thefirst were implemented.(4) capacity restrictions. Are these enforced or is themodel uncapacitated?An examination of the following actual transit centre locationKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 17studies will reveal that the above-mentioned decisions playedcrucial roles.2.4.1 SAN ANTONIOThe VIA Metropolitan Transit Authority [42] in San Antonio,Texas, used a rather simplistic model to analyze transit centrelocation. The city currently had one transit centre with acapacity of 600 buses. Bus fleet size totalled 473 vehicles. Amove to build an additional transit centre (when depot capacity wasattained) could only be done if the resulting savings in deadheadcosts compensated for the operating and capital costs of transitcentre construction. The San Antonio authorities considered fivepotential locations for this new transit centre. Weighing thedeadhead cost savings against the annualized construction costs(land included) of new transit centres, they found that anexpansion to an additional transit centre now (when the existingbus barn had spare capacity) could not be justified. However, theauthorities did gain insight into the optimal location for anadditional transit centre once fleet size reached 600 buses.2.4.2 CALGARYWaters et al. [44] used a discrete space location-allocationmodel to determine optimal bus garage location in Calgary. TheKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 18study, performed in 1984, used deadhead locations projected for theyear 1991 since transit centres must "cater to current as well asfuture demand". Driver relief costs were not estimated becausedetailed data regarding future operations was unavailable. Landcost and land availability were not considered. Consequently,vehicle deadhead and transit centre operating and constructioncosts were used.The Calgary transit system has three bus barns. Differentscenarios were constructed in which the existing transit centreswere forced to remain in their current location or were allowed tomove to their "optimal" location. Additional scenarios performedinvolved allowing four or six transit centres to be constructed.Their model considered environmental impact costs byproscribing a penalty cost to any bus deadheading through areaswith high residential population densities. If buses deadhead inthese areas, noise, air pollution and a higher risk of pedestrianaccidents may result. The probability of vehicle breakdown wasalso explicitly considered in the formulation.2.4.3 MAZE (DETROIT)The work of Thomas H. Maze and his collaborators has beenparticularly extensive in transit centre location area. Their 1981Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 19 paper offered a survey of the currently used methods in locatingbus garages. They described four techniques: center-of-gravity,rectilinear distance, scalar distance proxy and the actual time anddistance cost method. All of these methods attempt to locate busgarages by minimizing deadhead costs, although they find thedistance measure in different ways. For instance, the center-of-gravity method uses Euclidean distances while the rectilinearmethod assumes all travel occurs along a Manhattan grid system.Each of these techniques is deficient in that only deadhead costsare considered. Driver relief costs as well as the costs ofoperating and constructing transit centres are not considered. Inaddition, the size and number of the bus barns need to bedetermined independent of the deadhead minimization analysis.These disadvantages motivated Maze and his team to develop atheoretical, sophisticated mixed integer programming (MIP)formulation to the transit centre location-bus allocation problem.It was featured in their 1982 and 1983 papers. Essentially, it isof the form:m nmiNimizEE E E Tox+E Fojz; +E voiN; Fc,z;1=1 j=1 k^j=1^j=1^i=1^j=1subject to:Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 20WE X tik=1 Vi =1,...,m;VkJ =1yn„^mc^(2)E xifa+E^—NisO^Vj=1,...,ni=i^i=1bXiib+E x1,i.1 Ind(4)E +E x.. -N.s0 =1,...,nme^mf(5)E x,ie+E(6)E Xg +Ej=1^1=1mh^m,(7)E X1 + X 1.. -N.s01.1 ^Ii=1Vj=1,...,nVj=1,...,n(8)Ni -B(Zi) s 0^Vj=1,...,nVariable restrictions:-k.Xu = 0,1; = 0,1N. >= 0where:Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 21Maze's formulation considered vehicle "blocks", the routeassignment of buses. These are similar to the "runs" utilized byBC Transit. Only a small number of transit centre locations can behandled by this MIP, else the size of the problem grows immenselydue to the "curse of dimensionality".lem The objective function of this model minimizes all componentsof transit centre and vehicle cost. The term ;lc includes bothdeadhead and driver relief costs. Variable operating andconstruction costs are multiplied by the number of buses at eachgarage, while the fixed operating and construction costs are onlyincurred at a specific site should the transit centre be opened.After consulting with two transit agencies, the authors assumedthat operating and construction costs had a fixed charge and linearvariable cost portions.The first constraint insures that each block-service periodKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 22 combination is assigned to a garage.^Constraints 2 through 7determine the total number of buses assigned to each transitcentre. The different letters in the "k" subscript denote thefollowing:a= Monday-Friday AM blocksb= Monday-Friday PM blocksc= Monday-Friday all-day blocksd= Saturday AM blockse= Saturday PM blocksf= Saturday all-day blocksg= Sunday-Holiday AM blocksh= Sunday-Holiday PM blocks1= Sunday-Holiday all-day blocksThe total number of buses assigned to a bus barn is themaximum of either AM blocks plus all-day blocks or PM blocks plusall-day blocks. This occurs because buses used in the AM peak cansubsequently be used in the PM peak. Constraint 2 determines thetotal number of buses at a garage needed to satisfy Monday-FridayAM blocks (ma) and Monday-Friday all-day blocks (me). This is setless than or equal to the total number of buses assigned to thetransit centre. Constraints 3 through 7 perform similar functionsfor different day-service period combinations.Constraint 8 acts as an "on-off" constraint. If a transitcentre is opened (; = 1), then the total number of buses assignedto the transit centre, (Ni), will be less than some big number (busbarn capacities may be used). Should the transit centre not beused (; 0), then no buses will be assigned to it.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 23Attempts to solve a transit centre location problem using theMIP formulation proved futile given the computing resourcesavailable to them in the early 1980's. A model with 2,000 blockassignments and 12 candidate locations would have 24,000 integerassignment variables. To overcome this problem, the authorsdropped the fixed cost elements (FOJ and FC) in the objectivefunction. The problem was then solved as a transportation LPproblem, a type of problem which has a naturally-occurring integersolution. Khumawala's delta/omega decision rules were used whensolving the 4 site, 14 bus location-allocation problem.In 1983, Maze and his collaborators used the same methods tosolve the transit centre location problem, albeit this one was muchlarger than their 1982 version. They examined the merger of theSoutheastern Michigan Transportation Authority (SEMTA) and theDetroit Department of Transportation (D-DOT). The combined systemconsisted of 1064 active buses and 10 candidate transit centresites.2.4.4 BALL (PENNSYLVANIA)An alternative approach to locating transit centres has beenproposed by Ball et al. [4]. Their formulation appears to besomewhat more mathematical than that proposed by Maze et al. Theobjective of Ball's approach is to minimize the total cost of theKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 24location-allocation problem (vehicle deadhead costs, crew reliefcosts, fixed and variable site-related costs). Initially, theiralgorithm assumes that a set of locations for garages is specified.Their iterative procedure then uses a network flow-based algorithmto assign buses to sites. Once this is done, a locationinterchange heuristic is used to find a new group of sites thatcould handle the current allocation. This is done by solving anassignment problem. Optimality is reached when no improvement ismade in the objective function.Driver relief times are computed in a rather unique manner.They are obtained by calculating the shortest time path from thetransit centre to the relief point closest to the depot on theroute.The MIP formulation used by Maze can handle only a fewpossible transit centre locations. However, Ball's approach canhandle a huge number. Their model was implemented in southeasternPennsylvania on a problem that consisted of 11 current garages,1400 buses and 800 feasible new garage sites.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 253.0 URBAN TRANSIT IN BRITISH COLUMBIATransit service began in Vancouver on June 28, 1890 [41].Electrically-powered streetcars operated along 9.6 kilometres oftrack.In October 1891, North America's first interurban electricrailway opened. This carried passengers along a 45-minute tripbetween New Westminster and Vancouver. Gradually, this system grewto include the communities of Marpole, Richmond and Steveston. Thelast interurban trip ran on February 28, 1958, between Marpole andSteveston.On April 15, 1897, the British Columbia Electric RailwayCompany (BCER) was formed. This company was to run transit systemsin the Lower Mainland for the next 64 years.Streetcars were confined to certain routes (obviously, routeswhere there were rails). These cars could not pull over to oneside to pick up passengers. As a result, motor buses began regularservice in Vancouver in 1923. This supplemented the streetcarsystem by going places where it was too expensive to lay track.Motor buses completely replaced streetcars in New Westminster by1938 and in North Vancouver by 1947.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 26The first motor buses were not too powerful and could notcarry as many passengers as streetcars. Consequently, Vancouverswitched to the electric trolley bus system in 1948.In 1961, BC Hydro took over control of BCER. Between 1973 and1975, routes were added to Coquitlam, Surrey, Delta and White Rock.In 1977, SeaBus service began. The first marine transitservice of its kind in the world, it crosses Burrard Inlet betweenVancouver and North Vancouver carrying about 2 million passengersper year. With 126 sailings per day, the SeaBus achievedremarkable consistency by only missing four sailings in 1991/92.Control of transit operation went to a new Crown Corporationin 1978, the Urban Transit Authority (UTA). In 1982, UTA changedits name to BC Transit and adopted the current blue, red and whitescheme.HandyDart transit service for disabled individuals began in1980. Currently, BC Transit operates 188 HandyDart vans in theLower Mainland area. Additional steps have been taken to ensurethat effective public transit is available to individuals of allabilities. BC Transit was the first transit system in Canada tooffer accessible conventional transit service. On September 3,1990, lift-equipped buses began service in the Lower Mainland.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 27 Presently, about one-third of diesel buses are lift-equipped. By1995, half of the diesel bus fleet will be lift-equipped and by2006, all buses in the Vancouver Regional Transit System will bewheelchair accessible.Construction began on the SkyTrain system on March 1, 1982.The $854 million Vancouver - New Westminster link opened onDecember 11, 1985. This 130-car system, the longest completelyautomated, driverless rapid transit system in North America, nowlinks Vancouver, Burnaby, New Westminster and Surrey and willextend to Whalley in late 1993. Possible future extensions includethe cities of Richmond and Coquitlam. It has been a tremendouseconomic trigger for development and construction along its route.About 110,000 riders are carried per day, with 7,000 people usingit during a peak hour. The $32 million SkyBridge over the FraserRiver between New Westminster and Surrey is the longest rapid-transit-only bridge in the world.A 244-car electric trolley fleet represents the second largestfleet in North America, behind only the city of San Francisco.These trolleys are used exclusively on Vancouver city routes.Since these routes tend to carry more riders for shorter distancesthan their suburban counterparts, trolleys carry more passengersper year than the 650 diesels.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 28In 1991, the bus fleet was augmented by the addition of 60-foot articulated buses. These buses operate on suburban expressroutes. Plans are being made to include articulated trolley busesin future fleet configurations.BC Transit, the provincial Crown Corporation responsible forurban transit systems in British Columbia, has the followingmission:"to enhance the social and economic lifeof the communities it serves by providingsafe, reliable, environmentally sound,effective public transit".The corporation consists of three major transit systems:Vancouver Regional Transit System, Victoria Regional TransitSystem, and the Small Community Transit System (which oversees thetransit needs of non-metropolitan areas).The Vancouver Regional Transit System serves the largesttransit service area in Canada, covering an area roughly 1800 km2.Transit service is provided from Lions Bay in the northwest toLangley and Aldergrove in the southeast and from White Rock in thesouthwest to Maple Ridge in the northeast. This system, employingover 4000, serves a population base of 1.6 million people.The Vancouver system has experienced the highest growth rateKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 29 of any major transit system in Canada. Typical weekday ridershipis about 375,000. Over 128 million passengers use the systemannually. Studies have shown that 40% of people travelling todowntown Vancouver during the morning rush hour do so on publictransit.Expenditures during 1991/92 were $429.7 million. Operatingrevenues totalled $124 million, about 29% of expenditures.BC Transit is creating many methods to overcome the rush-hourcongestion faced by buses operating on suburban express routes.Bus lanes, transit priority signals and queue jumpers are but a fewof the ways the corporation is seeking to provide more reliablepublic transit service.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 304.0 THE LOCATION-ALLOCATION HIP MODELHaving discussed the nature of the problem BC Transit isfacing as well as providing a general review of facility locationliterature and its application to transit centre location, thecurrent location-allocation model is presented. This model hasbeen given the acronym of BUBLS (BUs Barn Location System). It isa 12,000 variable MIP which attempts to locate transit centres andallocate buses to those depots in such a way as to minimize vehicledeadhead costs and transit centre capital costs. The NIPformulation follows:r=210 d=3 p=4 s=20MINIMIZE EEE CrdpsXrdps + E vivs+EFsws— E RsZsr=101 d=1 p=1 s=11^s =candidate^s =18^s=existingSubject to:(1)E Xrdps =Drdp3=11r=210 d=1 p=312EXrdp.sr=101 d=1 p=1r=210 d=1 p=2 p=4(3)E EEE Xrdps -A s s0r=101 d=1 p=1 p=4Vr=101,...,210;d=1,2,3;p=1,2,...,4Vs=11,...,20Vs=11,...,20Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 31r=210 d=2 p=3(4) E EE Xnips -As s°r=101 d=2 p=1r=210 d=2 p=2 p=4(5) E EEE Xrdps -A s sOr=101 d=2 p=1 p=4r=210 d=3 p=3(6)E EE Xrdps -As sOr=101 d=3 p=1Vs =11,...,20Vs =11,...,20Vs =11,...,20r=210 d=3 p=2 p=4(7)E EEE X,s-AsSO^VS=11,...,20r=101 d=3 p=1 p=4(8)Ns- aAs 0^ Vs = 11,...,20(9)Ns- 6) sl's0^ Vs =candidate(10)N5Ys0^Vs-candidate(11)Ns—ps(1—z5)A^Vs-existing(12)Ns-ys(1 -Z) 0^Vs-existingr=112 d=3 p=4(13) E EE X rdps-8 sWss0^s=18r=101 d=1 p=1Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 32where:Xrdps= the number of buses assigned to route r on day d for serviceperiod p from transit centre s.r=101,...,210d=1,2,3 (M-F,Saturday,Sunday-holiday)p=1,2,3,4 (1-relief,2-relief,AM peak,PM peak)s=11,...,20C sips= the annual deadheading cost of operating one bus of route r onday d during service period p from transit centre s.Drdp= the number of buses required for route r on day d duringservice period p.As= the number of active buses assigned to transit centre s.Ns= the total number of buses assigned to transit centre s(including spares).Vs= annualized capital costs of constructing a candidate transitcentre at site s (in terms of number of buses at site s).Fs= annualized capital costs of electrifying Boundary Road betweenHastings Street and Broadway in order that trolleys may beallocated to the Burnaby Transit Centre.^Ws= 0^if Boundary Road is not electrified between Hastings andBroadway (trolleys are then not assigned to BTC).1^Boundary Road is electrified between Hastings andBroadway (trolleys are allocated to BTC).Ys= 0 if a transit centre in candidate location s is not opened.1 if a transit centre in candidate location s is opened.Zs= 0 if existing transit centre s remains open.1 if existing transit centre s is shut down.Rs= "salvage value" of eliminating existing transit centre s.as= spare factor (usually around 1.10) designed to augment thetotal number active buses assigned at transit centre s.cos= maximum allowed capacity of candidate transit centre s.Xs= minimum allowed capacity of candidate transit centre s.Os= maximum allowed capacity of existing transit centre s.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 33minimum allowed capacity of existing transit centre S.19s= maximum allowed allocation of trolleys to BTC.Variable restrictions:Xrdp >=0A„Ns >=0 and integerws, Xs, Os, Ts, Os >=0as >=1147„ Y„ Z, = 0 , 1The objective function sums the total deadheading costs aswell as capital costs for constructing candidate transit centres.Furthermore, the benefits in terms of salvage value for closing anexisting transit centre are considered.The first constraint forces the total number of assigned busesfor a given route on a certain day for a specific service period toequal the "demand" of that route-day-service period combination.Constraints 2 -7 sum the number of active bus assignments foreach transit centre. The summation is done for all-day + AM peakor all-day + PM peak, for each of the three different days. Sincethe heaviest service demands occur during the Monday-Friday serviceperiod, constraints 2 and 3 will undoubtedly determine A.Constraint 8 augments the active buses assigned to transitcentre s by a certain spare factor, thus giving us Ns, the totalnumber of buses assigned to transit centre s.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 34 Constraints 9 and 10 are used for the candidate transit centrelocations. Operating in much the same way as a "big-M" constraint,they seek to place bounds on the minimum and maximum sizes acandidate transit centre can take.Constraints 11 and 12 repeat a similar analysis to thepreceding two constraints, except that existing transit centrelocations are used.Constraint 13 considers the cost of electrifying Boundary Roadbetween Hastings and Broadway. If trolleys are assigned to BTC,then this electrification will need to take place and the resultingcapital costs will be incurred.4.1 OBJECTIVE FUNCTIONBUBLS minimizes the sum of the following components of transitsystem costs: vehicle deadhead, capital cost (candidate transitcentres) and salvage value (a benefit of eliminating or sellingexisting transit centres).4.1.1 DEADHEAD TIMESThe current route structure of BC Transit's Lower Mainlandsystem was used in developing the location-allocation MIP.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 35Presently, BC Transit operates over 160 routes in this area.However, the process of interlining reduced the number of routesthat were required to be considered in the model. Interlininginvolves one bus operating a multiple number of routes during theday. Therefore, routes that had the same termini (end points)could be grouped together. A total of 110 routes are used inBUBLS. Routes are numbered from 101 to 210 (rather than 1 to 110)to ensure that each variable name has an identical number ofcharacters. For a listing of the BC Transit routes analyzed andthe corresponding route number in CPLEX (the optimization package),see Appendix 1.Initially, considerable work was undertaken in deriving theactual deadhead points used by each route in the system. The "runschedules" for each route were analyzed. These listed the times atwhich a specific run for an individual route would leave thetransit centre and the corresponding time at which it would returnto the depot. The actual point at which the bus would consequentlyenter and leave revenue service was indicated. Over 200 locationswere found to be used as initiation/termination points. SeeAppendix 2 for a record of the number of weekly deadheads occurringat each separate location. These deadheads correspond to thenumber of buses using that location as a deadhead point.A definite pattern existed regarding the deadhead points.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 36Many of the points with large numbers of deadheads were close totransit centres. This phenomenon was quite evident along 41stAvenue close to OTC (Oak & 41st). This would seem to suggest that,in many cases, the closest point to the transit centre along thatroute was used as a deadhead location. Consequently, any MIPanalysis using these points would most certainly show that thecurrent transit centre location-bus allocation is appropriate. Theprevailing scheme would be preordained to be optimal!It was felt that a more realistic indicator for deadheadpoints would be the termini of each route. Routes generally areformed for at least two reasons: to serve a (known) customer demandpattern (students travel from downtown Vancouver to UBC) or tocover major urban arteries (routes cover Main, Fraser, Oak, etc. inVancouver). Therefore, the termini of routes should be independentof transit centre location. Appendix 3 reviews the termini for the110 routes analyzed in BUBLS. The current depot from which eachroute is dispatched is also listed.The next step was a critical one: deriving an estimate for thetravel time from a transit centre to the termini of each route.Currently, BC Transit uses visual estimations and prior experienceto develop predictions for vehicle deadhead time. For this study,a more quantitative tool was used to create deadhead timeestimates. Griffiths [17] reports on the applicability ofKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 37regression analysis in developing travel time estimates in depotlocation exercises. For the current bus barn location problem,travel times are not simply linear functions of distance. Buseswhich deadhead via divided highways will obviously be able totravel faster than buses deadheading through downtown Vancouver.A linear regression was thus created to generate appropriatedeadhead travel times. Deadheading occurs in either non-peak timeperiods or in the opposite direction of travel during peak times.Non-peak deadhead travel times are consequently employed. Fiveindependent variables, all indicative of different road types, wereused. They included:XI: downtown Vancouver streetsX2: roads in Burnaby, New Westminster and North VancouverX3: roads in any other Lower Mainland cityX4: non-divided highwayX5: divided highwayA distinction was made between X2 and X3 since it was perceivedthat, a priori, lower average speeds would be encountered on roadsin Burnaby, New Westminster and North Vancouver than on streets inother Lower Mainland locales. (This perception proved to beincorrect. The resulting coefficients for X, and X3 were almostidentical).A sample of 40 deadhead times was taken from the BC Transitrun schedules. The distance in kilometres covered under each tripKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 38was measured with a ruler and scaled. Appendix 4 lists the 40sample trips, complete with total deadhead time (dependentvariable) and kilometres under each road type.The results of the linear regression are presented below:TABLE ALINEAR REGRESSION RESULTSint. X1 X2 X3 1 X4 x5Coefficient 2.24531 4.6767 2.1557 2.2177 1.4313 0.6845t-value 8.7536 8.0832 9.2958 10.0107 7.5979R2 0.93109The fli (i=1,...,5) coefficients are the inverses of speed. 0means that a bus will take 4.6767 minutes to travel one kilometrein downtown Vancouver.Armed with the linear regression results, deadhead times canconceivably be generated for every termini-transit centre pair inthe Lower Mainland. One simply needs to determine the number ofkilometres by road type between any pair of points and multiply bythe regression coefficients.Ten transit centre locations are analyzed in the MIP. Five ofthese are the current depots and five represent candidatelocations. The five candidates include sites near the followingKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 39landmarks:1) The British Columbia Rapid Transit Corporation (BCRTC)facility between the Edmonds and 22nd Street SkyTrainstations.2) Cloverdale3) Lougheed Park & Ride4) Sexsmith & Cambie (Richmond)5)^Main & Terminal (Vancouver)A list of all the existing and candidate transit centrelocations is displayed below.TABLE BEXISTING AND CANDIDATE TRANSIT CENTRE LOCATIONSCPLEXSITE#LOCATION STATUS TROLLEY-ACCESSIBLE(*)S11 North Vancouver ExistingS12 Port Coquitlam ExistingS13 Surrey ExistingS14 near BCRTC facility CandidateS15 Cloverdale CandidateS16 Lougheed Park & Ride CandidateS17 Richmond (Sexsmith & Cambie) CandidateS18 Burnaby Existing *S19 Oakridge Existing *S20 Main & Terminal Candidate *Since trolley buses use overhead electrical wires, only thoselocations currently serviced by overhead wires can house them. TheBurnaby (BTC) location has been considered as a possible depot forKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 40trolley buses. Should this occur, trolley wires will need to beplaced on Boundary Road between Hastings and Broadway. Officialswith BC Transit have estimated this cost at $3.5 million. Theannual amortized payment is included in the objective function,coming into effect if and only if trolleys are allocated to BTC.Sites are numbered from 11 to 20 (instead of 1 to 10) so that, asin the case of the routes, all variable names are the same length.Deadhead travel times (for diesel buses) between transitcentre and termini are shown in Appendix 5. It is not necessary toconstruct deadhead times between every depot-terminus pair. Forinstance, it would be ludicrous to assign a bus to North Vancouverfrom a transit centre in Cloverdale. Therefore, this travel timein Appendix 5 is given by "**". In the NIP, that time is replacedby a large number. The deadhead times determined by linearregression were used in every other case but one, the travel timebetween PCT and the Port Coquitlam Centre. Since these points arelocated side by side, the distance between them does not fall inthe relevant range for the linear regression. A deadhead time of1 minute was subsequently used.Using Appendices 3 and 5 results in the deadhead times foreach route-transit centre combination. The process to calculatethe deadhead time is relatively straightforward. Every route has2 termini (call them A and B).^To produce the deadhead timeKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 41between a transit centre and this route, add the travel timebetween the transit centre and A and the transit centre and B. Thesum is the total deadhead time for that route-depot combination.For a realistic example, notice that Route 41 has as its terminithe UBC Loop and Joyce Station. From Appendix 5, the deadhead timebetween the UBC Loop and BTC is 34 minutes. For Joyce Station, itis 12 minutes. This gives a deadhead time of 46 minutes if route41 is operated from BTC. Appendix 6 offers a complete list ofroute-transit centre deadhead times.However, this procedure works for diesel buses, not thetrolleys. Since trolley buses cannot pass one another, they canonly go as fast as the trolley ahead of them. If the front trolleyis on revenue service, trailing trolleys cannot "express" travel toa specific deadhead point. For this reason, trolleys are inservice from the moment they leave the garage. For the purposes ofthe present analysis, they will deadhead to their termini at theirsystem-wide average speed (18 km/h). A regression is not needed.The distance between any terminus-transit centre pair is determinedand divided by the average speed. Table C provides a list of thedeadhead times used for each terminus-transit centre combinationwhile Table D gives the deadhead times for each trolley bus route.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 42TABLE CTERMINUS-TRANSIT CENTRE DEADHEAD TIMES (TROLLEYS)LOCATION BTC OTC MN/TRMCambie & 64th 45 10 26Dunbar Loop 54 14 34Fraser & Marine 39 17 24Granville & 63rd 50 10 30Harrison Loop 36 23 27Main & Marine 42 14 22Marpole Loop 55 12 3629th Avenue Station 16 25 20Boundary Loop 2 36 24Eton & Renfrew 11 39 19Kootenay Loop 3 41 22Metrotown Station 33 34 35Nanaimo Station 15 24 19UBC Loop 59 40 39Davie & Denman 35 25 17Davie & Richards 30 20 11Granville & Robson 27 22 9Stanley Park Loop 33 30 15Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 43TABLE DTROLLEY BUS ROUTE DEADHEAD TIMESROUTE CPLEX BTC OTC MN/TRM3 101 77 39 394 102 70 79 587 103 69 38 538 104 74 42 419 105 61 76 6310 106 62 81 6114 107 53 51 5215 108 72 32 3516 109 46 45 3117 110 82 34 4519 111 66 64 5020 112 91 35 63Route 3 uses Main & Marine and Davie & Denman as its termini.From the Main & Terminal location, travel time to Main & Marine(for a trolley) is 22 minutes while it is 17 minutes to Davie &Denman. This yields a deadhead time of 39 minutes if route 3 isoperated from the Main & Terminal candidate location.The coefficient Cidps is thus the annual deadhead cost foroperating route r on day d during service period p from transitcentre s. Days are broken down in the following manner:Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 441 = Monday - Friday (260 per year)2 = Saturday (53 per year)3 = Sunday/Holiday (52 per year)Service periods are composed of peak runs and all-day runs:1 = all-day (one relief)2 = all-day (two relief)3 = AM peak4 = PM peakRuns that operated less than the maximum allowable driver time(7.5 hours) were designated peak runs. Those that occurred before12:00 noon were AM peak runs while those that occurred after 12:00noon were PM peak runs. Runs that covered a time period between7.5 and 15 hours in duration were called "1-relief" runs. Finally,those which lasted longer than 15 hours were "2-relief" runs. SeeAppendices 7.1 - 7.5 for a display of the total number of runs ineach service period category on each day for a specific route.They are broken down into one relief and two relief runsbecause the latter will involve larger driver relief costs (morereliefs per day). However, BUBLS does not explicitly considerdriver relief cost in the objective function. There was no way ofsetting, a priori, the distinct driver relief points to be used bythe routes operated from the different transit centres. The effectof the optimal solution on driver relief will be examined in alater section.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 45Through discussions with operating department staff, thedeadhead costs were found to be $60 per hour.4.1.2 CAPITAL COSTSThe MIP formulation proposed by Maze indicated two sets oftransit centre costs: capital (construction) and operating costs.Discussions with various representatives of the Capital ProjectsDepartment at BC Transit revealed that operating costs are a linearfunction of the number of buses stored at a depot. In addition, asone would expect, there is no significant difference between themarginal operating costs at alternative transit centre locations.Therefore, operating costs were not considered in the optimization.Maze also uses a fixed and variable component in the capitalcost configuration. This was done to indicate that certain itemswould need to be built, regardless of bus barn size. Some costsare incurred no matter how small the transit centre. BC Transitofficials mentioned that their capital cost analysis showed that afixed charge is incurred for the first 30 to 40 buses at a garage,but then after that, the capital costs are linear. Furthermore, itwas difficult to ascertain how much this fixed cost may be. ThisMIP model thus treats capital costs as a linear function of thenumber of buses housed at a centre. Depot size is restricted to beat least a certain minimum size (if it is built) to avoidKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 46situations in which the model would construct a transit centre andassign, say, 10 buses to it.Capital cost calculations for candidate transit centres aredisplayed in Table E. The cost for constructing the most recentlybuilt transit centre, STC, is used as a starting point. It cost$15 million to build the 250-bus facility. That translates into a$60,000 per bus cost, exclusive of land.BUBLS considers the land cost of alternative candidate transitcentre locations, something not considered in Maze's model. It wasfelt that these costs needed to be considered in the Vancouverregion, given the high variability of land costs from area to area.Square footage land costs were estimated, in consultation with BCTransit, for each of the five candidate transit centre locations.Assuming that one acre can house 25 buses, a land cost per bus wascalculated. Adding this to the previously-mentioned $60,000 chargeand amortizing over 25 years at 8% gives the annualized capitalcost (per bus) for each candidate garage location.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 47TABLE ECAPITAL COSTS: CANDIDATE TRANSIT CENTRESCPLEXSITE #LOCATION LAND COST(persq.ft)LAND COST PERACRELAND COSTPER BUSCOST PERBUS (excl.LAND)TOTALCOST PERBUSANNUALIZEDCOSTS14 BCRTC 21 $914,760 $36,590 $60,000 $96,590 $9,048S15 CLVDL 20 $871,200 $34,848 $60,000 $94,848 $8,885S16 LHEED 22 $958,320 $39,413 $60,000 $99,413 $9,313S17 RICH 24 $1,045,440 $41,818 $60,000 $101,818 $9,538S20 MN/TRM 37 $1,611,720 $64,469 $60,000 $124,469 $11,660A further component of capital cost is the fixed charge thatwould be incurred if trolleys are assigned to BTC. As examinedpreviously, overhead trolley wires would be required on BoundaryRoad between Hastings and Broadway to facilitate trolley allocationto BTC. Capital Projects representatives have estimated the totalcost at $3.5 million. The annualized cost ($327,875) is multipliedby a binary integer variable which only assumes a non-zero valueshould trolleys be assigned to this depot.4.1.3 SALVAGE VALUESThe capital costs of existing transit centres are sunk costs.However, if a current transit centre were closed (no busesallocated to it), a salvage value would be incurred. Since the MIPhas an objective function based on cost minimization, these valuesare displayed with a negative sign to show that they would beKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 48benefits accruing to BC Transit. Square foot land costs wereestimated for the five current depots. Multiplying this cost bythe number of acres at a location and amortizing over 25 years at8% results in an annualized salvage value. Table F shows thesesalvage value calculations.TABLE PSALVAGE VALUES: EXISTING TRANSIT CENTRESCPLEXSITE #LOCATION LAND COST(per sq.ft)CAPACITY NUMBEROFACRESNUMBER OFSQUAREFEETTOTAL SALVAGEVALUEANNUALIZEDSALVAGE VALUES11 NVT 25 60 2.4 104,544 $2,613,600 $244,839S12 PCT 20 250 10 435,600 $8,712,000 $816,130S13 SIC 20 250 10 435,600 $8,712,000 $816,130518 BTC 30 160 6.4 278,784 $8,363,520 $783,484S19 OTC 47 350 14 609,840 $28,662,480 $2,685,0664.2 CONSTRAINTSThe first constraint in this model is significantly differentfrom the corresponding constraint in Maze's formulation. Theassignment variables (blocks to garages) were forced in Maze'smodel to be binary integer. The summation of the assignmentvariables over all feasible depot locations was constrained toequal 1 (i.e. a block was assigned to one and only one garage).The practical impact of this assumption is that a large number ofinteger variables are created, perhaps hindering the process ofKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 49finding the optimal solution. BC Transit's system has over 1800blocks. Combining this with the 10 transit centres would give over18,000 integer variables.The current model proposes a different approach.^Theassignment variables ( Acips) allocate buses to transit centres.These variables are not restricted to be integral. Their sum overall transit centre locations is forced to equate the number ofbuses required for that route on a specific day during a givenservice period. In other words, the first constraint ensures thatthe total number of buses allocated for a certain period issufficient to cover the demand of that route-day-service periodcombination.The effect of this technique is two-fold.^First, notrestricting the Xwps variables to be integer dramatically reducesthe number of integer variables in the model. The problem has 12trolley routes which can be assigned to any of 3 transit centresand 98 diesel routes which can be allocated to any of the 10garages. This would give a total of 12*3*(d=3)*(p=4) = 432 trolleyand 98*10*3*4 = 11,760 diesel assignment variables. Consequently,eliminating the integrality restriction on the Xrcips variables doesaway with 12,192 integer variables.Secondly,^this formulation allows the modeller toKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 50systematically alter the demand for buses on a route-day-serviceperiod combination. If one believes that future populationexpansion will double the demand for transit on a route, the right-hand side figures for this constraint can be easily changed.Constraints 2 through 7 add up the number of active busesassigned to each transit centre location. Active buses are thosewhich are assigned a journey. Basically, the number of busesallocated to a depot is the maximum of the all-day plus AM peakassignments and the all-day plus PM peak runs. This is done sincea bus performing an AM peak journey may subsequently be used on aPM peak run. Constraint 2 determines the Monday-Friday all-dayplus AM peak allocations at each transit centre while constraint 3sums the all-day and PM peak assignments. These totals are setless than or equal to the number of active buses assigned to agarage. Constraints 4 and 5 (6 and 7) repeat similar analysis forSaturday (Sunday-Holiday) runs.The active number of buses at a depot is augmented by a 10%"spare" factor to allow for such considerations as vehiclebreakdown, accidents or extended maintenance activities. This isperformed by constraint 8.This model did not consider fixed costs in the objectivefunction. Rather, the capital costs of construction were assumedKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 51to be a linear function of the total number of buses at a bus barn.Discussions with BC Transit personnel revealed that this was thebest approximation. Their analysis had shown that a certain fixedcapital charge was incurred for the first 30-40 buses at a transitcentre. However, after that initial allocation, costs increasedlinearly. The major concern with this procedure is that theoptimization may assign a small number of buses, say 5, to a depot.This result is purely illogical since BC Transit would neveroperate a bus facility with such a small allocation. To alleviatethis, maximum (constraint 9) and minimum (constraint 10) sizes areenforced for candidate transit centres. The present analysis useda maximum size of 250 and a minimum of 50 at each depot. Thevariable Y, is a binary integer variable. If it is equal to 1(candidate transit centre s is built), then the maximum and minimumsizes will fall between the limits permitted. Should this variableequal 0 (the depot is not constructed), then no buses will beassigned to this garage.Existing transit centres are treated next. The maximum sizes(constraint 11) are the capacities of the individual transitcentres. It is assumed that the minimum size (constraint 12) is50. It was felt that assigning fewer than 50 buses to an existinggarage would be somewhat nonsensical. If this did occur, it wouldmost likely be better to simply close the facility and collect thesalvage value. The variable Z8, as with Ys, is binary integer. IfKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 52Z, is equal to 0 (the existing depot remains open), then theallocation of buses will fall between the minimum size allowed andthe garage's capacity. If Z, is equal to 1 (the existing bus barnis closed), then no buses can be allocated to that garage.The fixed cost for electrifying Boundary Road between Hastingsand Broadway is treated in constraint 13. Should the binaryvariable equal 1 (electrification takes place), allocation oftrolleys to BTC is limited by the transit centre's capacity. Ifthis variable is 0, then no trolleys can be assigned to BTC. Theresulting capital cost is not incurred.4.3 VARIABLE RESTRICTIONSAs mentioned previously, the X,(11), variables are not restrictedto be integer. The model forces only 31 variables to be integer(11 binary integer and 20 general integer). The variables Y„ Z,and Ws are binary while A, and N, are general integer. In everymodel run, all Xrdp, variables turned out to be integer.Maze (1982) was able to solve the transit centre locationproblem as a transportation LP by eliminating the fixed costs. Theright-hand side vector was integral and the matrix of constraintcoefficients contained entries of 0, 1 or -1. This unimodularformulation ensured integer results.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 53BUBLS adopts a similar formulation. The fixed costs of depotconstruction are dropped and replaced with a linear function. Theright-hand side vectors are integral and the matrix of constraintcoefficients contains entries of 0 or 1. The only exception occursin the spare factor constraint (#8). The active number of busesare multiplied by 1.10 to determine the total number of buses at adepot. However, the variables A, and N, are forced to be generalinteger.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 545.0 MIP OPTIMAL SOLUTIONThe final model had over 12,000 variables (31 integer). Amatrix generator was written in Turbo Pascal to produce therequired input to the mixed integer optimizer, CPLEX. The problemwas solved on a UNIXG workstation at the University of BritishColumbia.CPLEX uses a branch-and-bound procedure to solve this problem.In the process of optimizing a NIP, it determines the bestobjective function value of all the unexplored nodes in the branch-and-bound tree. When the best integer solution found thus far iswithin a pre-specified percentage of the best "unexplored" value,the optimization stops and the current integer solution is declaredoptimal. Except as noted otherwise in this thesis, this percentageis 0.05%.The optimal solution to BC Transit's depot location-busallocation problem was found in just over 5.5 minutes. Theobjective function value was $14,324,090 (an improvement of$561,497 over the current configuration).None of the existing transit centres was closed. Maximumallocations were observed at three depots (NVT, BTC and OTC).Trolleys are only assigned to OTC and Main & Terminal (i.e. theKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 55fixed cost of electrifying Boundary Road is not incurred).Candidate transit centres were opened at the BCRTC facility and theMain & Terminal location. Both of these garages were assigned theminimum allowable number of buses, 50. These two locations receivea "benefit" (the savings in deadhead costs more than compensatesfor the resulting capital costs of transit centre construction) forthe first, say, 35 or 40 buses. Adding the remaining busesrequired to attain the minimum allowable size is done at a cost toBC Transit. However, the benefit for the first set of busesoutweighs the cost of the remainder. Therefore, a transit centreis constructed at the minimum allowable size. Appendices 8.1 - 8.7lists the vehicle assignments for each transit centre. The routesthat are dispatched from each garage as well as the total number ofvehicles required on each day during individual service periods isoutlined.Appendix 9 lists the garage from which each route isdispatched under the current configuration, optimal strategy andeach experiment. Blank cells in the table indicate that theallocation scenario for that route is identical to the currentscheme. Three patterns of bus allocation are readily seen whencomparing the optimal strategy with the current one. They are asfollows:1) Routes operating in the South Burnaby/ New WestminsterKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 56 area (i.e. #101, #106, #108, #112, #115) are completelyor partially reallocated from BTC to the BCRTC facility.The savings in deadhead costs are quite substantial whenthese buses are moved from a facility in North Burnaby toone near New Westminster. For instance, #112 and #115incur daily deadhead times of 51 and 37 minutesrespectively from BTC. However, these deadhead costs are15 and 16 minutes from BCRTC.2) Trolleys which generally follow an "east-west" route(#4, #9 and #10) are moved, either completely orpartially, from OTC to the Main & Terminal location.Buses from these routes travel from the eastern edge ofVancouver to the UBC area through downtown or alongBroadway. As such, their routes are closer to the Main& Terminal location than to OTC.3) Some North Vancouver routes (#210, #247 and #292) aretransferred fully or partially from NVT to BTC. NVT iscurrently overcapacitated (78 buses allocated vs. 60 buscapacity), so it needs to eliminate a few of its buses.The #210 and #292 routes are viable candidates since theytravel down Hastings Street, crossing the Second NarrowsBridge into North Vancouver.^BTC is close to thissector.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 57A total of 36 routes are either completely or partiallyassigned to a different transit centre than the one currently used.About 97 buses (under 11% of the total bus fleet) are relocated.Appendix 10 shows the routes and their assigned transit centreunder the current and optimal plan. In the case of a partialreallocation, the indicated amounts represent the proportion ofbuses for that route allocated to each transit centre.5.1 COMPARISON WITH LP OPTIMUMRemoving the integrality restriction on the Y„ Z„ N, and A,variables results in the LP (continuous) solution. The objectivefunction value for this less-constrained problem will be at leastas good as the MIP solution. It turns out to be $13,051,354. Thisrepresents a percentage difference between the optimal IP and LPsolutions of 9.75%. A brief review of the optimal LP solutionshowed that the improvement was partially realized by setting theY, and Z, variables to fractional values between 0 and 1. Insightmay be gained by examining the Y, values for each candidate transitcentre in the optimal LP solution. A larger Y, value would supportthe notion that a candidate centre is "better" to construct thanits counterparts. The following Y, values were obtained:Y14 (BCRTC) = 0.28Y15 (CLVDL) = 0.02Y16 (LHEED) = 0.011/7 (RICH) = 0.13(MNTRM) = 0.20Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 58 This shows that the BCRTC and Main & Terminal locations arethe best sites for candidate transit centres. Richmond is nextwhile the Cloverdale and Lougheed Park & Ride facilities appear tobe marginal at best.5.2 COMPARISON WITH CURRENT LOCATION -ALLOCATION SCHEMEAn important part of this analysis is to determine thepotential savings that may result if the optimal location-allocation strategy is pursued. To calculate these savings, thecosts of deadhead travel under the current scheme must bedetermined. It was assumed that the deadhead points for each routewere the termini of that route, a similar assumption to that usedin the preceding analysis. The annual cost of deadhead travelunder the current plan is $14,885,587. The optimal solution thusrepresents an annual savings of $561,497 (3.77%). The net presentvalue (NPV) for the optimal solution is $5,993,855. The cost ofthe optimal solution, however, includes the annualized capitalcosts of constructing the BCRTC and Main & Terminal locations($1,035,400). The deadhead cost of the optimal solution is$13,288,690. Therefore, the annual savings in deadhead costs is$1,596,897 (10.73%). The total number of buses allocated to eachtransit centre under all scenarios as well as the various costbreakdowns are provided in Appendix 11. A bar graph illustratingthe objective function values of all scenarios is presented below.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 59FIGURE Awhere:1 = Elimination of OTC2 = Current location-allocation scheme3 = Increase minimum size of candidate facilities to 1004 = Increase minimum size of candidate facilities to 755 = Enforcing the "50 trolley" minimum size rule6 = Optimal location-allocation strategy7 = Increase capacity of BTC (no capital costs)8 = No minimum/maximum facility size restrictions9 = Continuous (LP) modelKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 60 6.0 MODEL EXPERIMENTSThe true value of any real-world optimization exercise is notgenerating the optimal solution to the problem, but rather in beingable to analyze different scenarios and their impact on the currentoperating system. The optimal solution did, in this case, offersignificant insight into BC Transit's facility location process.However, additional intuition may be gained by running a variety ofexperiments. Certain parameters can be added, deleted or alteredand the resulting effect on the solution quickly observed.6.1 ELIMINATING THE MAXIMUM AND MINIMUM RESTRICTIONS ONFACILITY SIZEThe first experiment involved eliminating the bounds that wereset on transit centre size. Currently, all existing transitcentres are forced, if they remain open, to fall between a minimumsize of 50 and their individual capacities. If candidate transitcentres are constructed, their size is restricted to fall between50 and 250.Results from this model run were quite interesting. The BTCreceived a total allocation of 378 buses, more than twice itscurrent capacity. This is partly due to the fact that both the NVTand PCT facilities were shut down. The buses that formerly wereKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 61allocated to these centres were fully or partially reallocated toBTC. The rather large allocation of buses to this centre may alsobe explained by its location in the centre of BC Transit's LowerMainland system. By not being located on the periphery, it avoidedmany of the extreme deadhead costs associated with an exteriordepot.The closure of the NVT and PCT facilities caused concern. Ifthey receive an allocation in the optimal solution, should they notreceive some buses when bounds are removed? However, it wasnoticed that each of these facilities shared an importantcharacteristic. They both had a small number of routes assigned tothem. Furthermore, most of these routes did not operate completelywithin the districts of North Vancouver and Port Coquitlamrespectively. Of the 14 routes dispatched from NVT, only 6operated within North Vancouver. Four of the 11 routes handledfrom Port Coquitlam operated completely within that district.Therefore, it was advantageous to reassign these routes, shut downthe two centres and collect the salvage values.Additional runs were performed by setting the respectivesalvage values for these two facilities to zero. Then, there wouldno longer be a monetary "benefit" to eliminating these centres. Asexpected, the total allocation to NVT increased to 43 when thisoccurred. The number of buses assigned to BTC consequently fell toKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 62335 (378-43 = 335). For PCT, it received 99 buses and BTC'sallotment fell to 300. This total did not equal 378-99, since theredistribution of buses when PCT was closed went to other centresbesides BTC.With the exception of NVT, PCT and the Main & Terminallocation, all facilities received an allocation of buses. Theabsence of buses at Main & Terminal is explained by its closeproximity to BTC and OTC, which between them garnered 728 buses(over 80% of the total bus fleet).The runs in this first scenario all used an integer optimumsolution bound of 0.07%, rather than 0.05%. When the latter boundwas first utilized, the solution times were quite long (in excessof 15 minutes). CPLEX had found an integer solution and wassearching the branch-and-bound tree for the best remaining node.As the optimization progressed, the objective function value forthe best remaining node did not show significant improvement. Itwould remain at the same value for several hundred nodes. Ratherthan spending considerable time waiting for CPLEX to find aninteger solution within the 0.05% bound, the bound was consequentlyincreased to 0.07%.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 636.2 ENFORCING THE "50 TROLLEY" MINIMUM RESTRICTIONBC Transit capital projects personnel wanted to know theimpact of a certain operational consideration. In the optimalsolution, the Main & Terminal facility was allocated 50 buses.This total included both trolleys and diesel buses. It was feltthat a transit centre would never be built with less than 50trolleys, due to the special maintenance and electrical overheadrequirements necessary to operate those buses.A model run was performed to enforce this restriction. It didnot have much impact on the objective function value for theoptimal solution (an increase of only $1,928) since out of the 50buses at Main & Terminal, the vast majority were trolleys. Thus,allowing this restriction did not result in a massive movement ofbuses. The total number of buses assigned to Main & Terminalincreased from 50 to 51.6.3 INCREASING THE MINIMUM ALLOWABLE SIZE OF A CANDIDATETRANSIT CENTREThe optimal solution resulted in candidate transit centres ofthe minimum allowable size (50) being constructed at Main &Terminal and BCRTC. The minimum limit of 50 was chosen ratherarbitrarily. It was desired to know the impact on the solution ifdifferent minimum sizes were enforced.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 64An initial run was made by setting this minimum size to 75.The objective function value increased to $14,437,007 (a jump of$112,917 or 0.79%). The Main & Terminal facility was notconstructed. Trolleys were therefore assigned to both OTC and BTC,as the capital costs of Boundary Road electrification were thusincurred. The BCRTC facility proved to be a rather beneficialfacility as it was allocated 75 buses. Both PCT and STC receivedincreases in their allotments (15 and 8 respectively). All othercentres remained at their optimal solution levels.The increase for BCRTC came from routes which had previouslybeen allocated to BTC (i.e. #26, #29, #131/32, #134, #144) butwhich were now split between BCRTC and BTC. Furthermore, routeswhich had previously been split between BTC and BCRTC (#114 and#116) were now completely assigned to BCRTC.The minimum allowable size was then increased to 100 buses.The objective function value increased to $14,501,487 (an increaseof only $64,480 over the "minimum 75" model). The BCRTC facilitycontinued to show great advantages. Its size increased to 100buses. This verifies some of the results from the LP (continuous)run, which showed that the BCRTC facility had the highest Y, value(0.28). The Main & Terminal location is again not opened (it hada lower Y, value in the continuous solution) and trolleys areassigned to BTC. PCT loses 9 buses from the optimal solution whileKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 65STC picks up 8.Comparing the allocations for the 75 and 100 minimum sizescenarios reveals the additional routes that BCRTC is assigned.When the minimum size of candidate facilities was set at 75 buses,the #120 and #154 routes were both split between PCT and BCRTC.When the minimum size was increased to 100, both of these routeswere completely allocated to BCRTC.Furthermore, route #130 was assigned completely from BTC whena minimum of 75 buses was used. Now, under the higher minimum, itis split between BTC and BCRTC.Appendices 12.1 - 12.6 gives a vehicle assignment schedule foreach of the six transit centres opened when the minimum size is setat 100.6.4 ELIMINATION OF OTCA scenario of vital interest to capital projects personnel atBC Transit involved the elimination of OTC. The largest transitcentre in the Lower Mainland, it occupies prime real estate.Eliminating this transit centre and selling the land would resultin a large salvage value.This model was run by setting Z 19 (OTC) to 1. This forced noKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 66buses to be assigned to the transit centre and also allowed itssalvage value to be obtained. The objective function value anddeadhead costs for this scenario were $15,545,526 and $14,163,252respectively, the highest of any of the model runs. This shows thegeneral importance of OTC in terms of deadhead costs. Without it,deadhead costs increase substantially.Closing OTC forced the reallocation of its 350 buses. Main &Terminal received 250 buses (the maximum allowed) while a facilityis constructed at Richmond for 130 buses. The BCRTC location isagain utilized for 50 buses. No trolleys are allocated to BTC, sothe Main & Terminal centre is the only depot for these buses.Appendix 13 contains a vehicle assignment schedule for theproposed Richmond facility. Generally, it is assigned Richmond andSouth Delta buses. It also receives a Vancouver diesel route(#22A) and a downtown Vancouver - Surrey route (#310/11).6.5 INCREASE IN CAPACITY OF BTCThe optimal solution gave maximum allocations to three transitcentres (NVT, BTC and OTC). BC Transit personnel indicated that anoption was available to purchase land adjacent to BTC.Consequently, a model was constructed which increased the maximumsize of BTC to 250 buses. Capital costs were assigned only on theKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 67extra 90 buses added to the current capacity of 160.Using a land cost of $30 per square foot and a per bus cost of$60,000 (exclusive of land), the annualized capital costs for theBTC addition amounted to $10,518 per bus. Individuals from BCTransit indicated that since this project would be an expansionrather than a new construction, the capital costs seemed ratherhigh, so suggested a price in the "low 9's". Consequently, a perbus capital cost of $9,300 was used (this represents a combinationof the $30 per square foot land cost and a $47,000 per bus cost).The different capital costs had no effect on the resultingoptimal solutions. In both cases, the adjacent land was notpurchased and the capacity remained at 160. The objective functionvalue was identical to the one for the optimal solution.It was then decided to use a capital cost of zero for extraBTC capacity. This was done to see which routes would bereassigned to BTC if the extra capacity were available free ofcharge. The objective function value for this scenario was$13,872,106. This represented an improvement of $5,022 per bus forthe 90-bus expansion. BTC was assigned 250 buses, the increasecoming mainly from an allocation of trolleys to this facility. Italso received buses from Port Coquitlam routes (PCT was closed).Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 687.0 EFFECT ON DRIVER RELIEFThe optimal solution resulted in an annual overall deadheadand capital costs savings of $561,497. However, nothing wasmentioned about the aspect of driver relief. The only part ofnonrevenue transportation costs which the optimization sought tominimize was vehicle deadhead costs. Driver relief can be animportant part of any location-allocation strategy. For instance,a transit centre located at the termini of a route may offerpotential deadhead cost savings. The opportunities for efficientdriver relief may be somewhat limited, however. A transit centrelocated in the vicinity of the middle of a route has the advantageof catching vehicles going both directions along a route.In order to obtain a rough idea of the impact of the optimalsolution on driver relief, the following analysis was performed.Only the 36 routes which changed transit centres between thecurrent and optimal configurations were considered. The middle ofeach of these routes was determined and a straight-line distancecalculated between this point and the competing transit centres.In the case where a route was reassigned to multiple transitcentres, the total driver relief distance was a linear combinationof the distances from the middle point to the transit centres. Theweights reflected the proportions of all-day vehicles assigned tothe centres.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 69 Appendix 14 lists all routes which were reassigned between thecurrent and optimal strategies. The individual weights in the caseof multiple transit centres are also given. The calculation of theweekly number of driver reliefs is shown in Appendix 15. Thecomputation of potential driver relief savings is offered inAppendix 16. The straight-line distance (in centimetres) wasscaled to its kilometre equivalent and an average driver reliefspeed of 25 km/h was assumed. This generated a driver relief timeper route (in hours). Assuming a driver relief cost of $20 perhour (the approximate driver hourly wage), the cost of each driverrelief was then determined. Multiplying this by the number ofweekly driver reliefs gave the weekly driver relief cost under thecurrent and optimal plan. This was then translated into an annualdriver relief cost. The optimal configuration offers a 15.74%improvement in driver relief costs, $270,800 versus the current$321,373. Much of this benefit was derived from routes which werereallocated to BCRTC from BTC. The #101, #106 and #112 routesoffered annual driver relief savings of $9,360, $17,901 and $11,050respectively. Other substantial costs savers included #49(transferred from BTC to OTC) and #100 (reassigned from PCT to OTC)which generated savings of $14,014 and $16,744. This was by nomeans an all-inclusive treatment of the impact of driver reliefcosts. Nonetheless, it showed that the optimal solution does nothamper driver relief performance.Keith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 708.0 CONCLUSIONSA mixed integer program has been developed to systematicallyshow the quantitative effects of transit centre location for BCTransit in the Lower Mainland. The model considered the presentnetwork of routes and buses and the current five transit centres.It also examined five candidate transit centres located throughoutBC Transit's system. An optimal solution was found to thislocation-allocation problem and various model runs were performedto gain additional insight into the techniques of transit centrelocation. The following conclusions and recommendations are made:1) A facility located near the BCRTC area offerssubstantial deadhead cost savings. The optimal solutionsuggested that a 50 bus facility be constructed.However, when the minimum allowable size was increased to75 and 100, the BCRTC facility continued to be used (atthose minima). It housed buses operating many of theroutes in the South Burnaby and New Westminster areawhich had previously been dispatched from BTC.2) No existing transit centres should be closed. Theymay be downsized, but a total elimination of them wouldnot be worthwhile. Generally, the existing network oftransit centres are not badly located with respect to theKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 71Lower Mainland transit system.3) A transit centre at Main & Terminal should beconstructed. The optimal solution indicated that a 50-bus facility be built there. When minimum allowablesizes were subsequently increased, no facility wasallowed at this location. In terms of candidate centres,the BCRTC facility would be best followed by Main &Terminal.4) Should OTC be eliminated, a 130-bus facility should beconstructed in Richmond. It would mainly service busesoperating Richmond and South Delta routes. Under thisscenario, the Main & Terminal location becomes quiteimportant as it is assigned 250 buses.5) The allocation of trolleys to BTC is dependent on theminimum allowable size of candidate transit centres.When this size is 50 buses, the Main & Terminal locationis opened. Some trolleys are assigned to it. However,when the minimum size is increased to 75 or 100 buses,trolleys are allocated between OTC and BTC. The Main &Terminal facility is not constructed.6) The option of purchasing land adjacent to BTC shouldKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 72 not be exercised. The potential savings in deadheadcosts for assigning more buses to this centre would notcompensate the capital costs of expansion.9.0 DIRECTIONS FOR FURTHER RESEARCHThis project has provided a variety of quantitative answers toBC Transit's facility location analysis. The process of obtainingthese answers has, nevertheless, opened the door on other areaswhich need to be explored. They are as follows:1) The present analysis assumed that a route's busescould be split between multiple transit centres. Thecurrent strategy of BC Transit is to operate all busesfor a specific route from a single depot. The mixedinteger program could be altered by "bundling" allroutes. A binary integer variable would be introducedthat would take a value of 0 (1) if no (all) buses for aroute were assigned to a transit centre. The objectivefunction value for this scenario would not be as good asthe optimal solution. For instance, during theoptimization, a transit centre may only have room leftfor 10 buses. Suppose that the next best route for thiscentre included 15 buses. Under the optimizationstrategy followed in this thesis, 10 buses for this routeKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis^ Page 73 would be assigned to the transit centre and the remaining5 to another centre. If the "bundling" strategy werefollowed, none of this route's buses could be allocatedto this transit centre. A less-optimal route would beused to fill up the extra space (or the space may be leftempty).2) Driver relief could be incorporated directly into theobjective function.^This analysis assumed thatnonrevenue transportation costs consisted of vehicledeadhead costs only. A simple heuristic was used inChapter 7 to show that the optimal solution's impact ondriver relief was anything but negative. Nevertheless,if the nonrevenue transportation cost (Crdps) consideredthe effect of a route-transit centre combination ondriver relief, planning officials would immediately knowthe effect of this important variable.3) The model should be enhanced to show the effects ofSkyTrain extension to Richmond or along the Lougheed Mallcorridor. The changes to the mixed integer program wouldinvolve more than altering constraints or parametervalues. Rather, actual routes would change.^In theRichmond example, all #400 (Vancouver-Richmond) routeswould cease.^New routes would be introduced in theKeith A. Willoughby - The University of British ColumbiaM.Sc. Thesis Page 74 Richmond and South Delta area feeding into this SkyTrainsystem. Routes in Vancouver would also begin to feedinto this SkyTrain network. A change of routes wouldnecessitate a change in termini and service patterns.Once these changes were determined, analysis with thecurrent mixed integer program could begin.This mixed integer program has the capability to effectivelyanalyze facilities planning for a number of urban transitauthorities. The same ingredients used in the analysis for BCTransit could be applied elsewhere. Most transit systems wouldfollow the basic procedures outlined in this thesis: deadheadoccurs when buses are sent to their routes at the beginning of ajourney and also when they return home at its conclusion, a highernumber of buses are allocated to routes to cover peak demands andthe minimization of deadhead and capital costs is of great concern.This quantitative technique provides an practical tool fordecision-making.Keith A. Willoughby - The University of British ColumbiaPage 75BIBLIOGRAPHY[1] Anderson, J. Edward.^Transit Systems Theory.^Lexington,Mass.: Lexington Books, 1978.[2] Bachman, Wallace and Richard Katzev.^"The Effect of Non-Contingent Free Bus Tickets and Personal Commitment on UrbanBus Ridership", Transportation Research - A, vol.16A, no.2,103-108, (1982).[3] Balinski, Michael L. 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"Application of a Bus Garage Locationand Sizing Optimization", Transportation Research - A,vol.17A, no.1, 65-72, (1983).[29] Maze, Thomas H. et a/.^"Estimating Bus Component FailureDistributions from Censored Samples", Transportation ResearchPage 77- B, vol. 18B, no.3, 201-208, (1984).[30] Maze, Thomas H. et a/.^"Optimization Methodology for BusGarage Locations",^Transportation Engineering Journal ofASCE, vol.108, no.TE6, 550-569, (1982).[31] Maze, Thomas H. et a/.^"Proposed Approach to DetermineOptimal Number, Size and Location of Bus Garage Additions",Transportation Research Record 798, 11 -18, (1981).[32] Mirchandani, Pitu B. and Richard L. Francis (eds.). DiscreteLocation Theory. New York: John Wiley & Sons, 1990.[33] Rand, Graham K. "Methodological Choices in Depot LocationStudies", Operational Research Quarterly, vol.27, no.1, 241 -249, (1976).[34] Small, Kenneth A. and Stephanie J. Frederick.^"Cost-Effectiveness of Emissions Control Strategies for TransitBuses: The Role of Photochemical Pollutants", TransportationResearch - A, vol.23A, no.3, 217-227, (1989).[35] Spielberg, Frank and Marvin Golenberg. "Systematic Procedurefor Analysis of Bus Garage Locations", Transportation ResearchRecord 746, 39-42, (1980).[36] Stephanedes, Yorgos J. et a/.^"Dynamic Transit SchedulingUnder Efficiency Constraints", Transportation Research - B,vol.19B, no.2, 95-111, (1985).[37] Stevens, Benjamin H. and Carolyn A. Brackett.^IndustrialLocation: A Review and Annotated Bibliography of Theoretical,Empirical and Case Studies. U.S.A.: Regional Science ResearchInstitute, 1967.[38] Sumi, Tomonori et a/. "Departure Time and Route Choice ofCommuters on Mass Transit Systems", Transportation Research -B, vol.24B, no.4, 247-262, (1990).[39] Taylor, Bernard W. III and Arthur J. Keown. "An Integer GoalProgramming Model for Solving the Capital Allocation Problemfor Metropolitan Mass Transportation Agencies, TransportationResearch - A, vol.17A, no.5, 375-383, (1983).[40] Tompkins, James A. and John A. White. Facilities Planning.New York: John Wiley & Sons, 1984.[41] Transitions: One Hundred Years of Transit in British Columbia,1890-1990.[42] Via Metropolitan Planning Department. Satellite FacilitiesStudy. Unified Work Program Element 85-8, September, 1986.Page 78[43] Wang, George H.K. and David Skinnner. "The Impact of Fare andGasoline Price Changes on Monthly Transit Ridership: EmpiricalEvidence from Seven U.S. Authorities", Transportation Research- B, vol.18B, no.1, 29-41, (1984).[44] Waters, N.M. et a/. "Location of Bus Garages", Journal ofAdvanced Transportation, vol.20, 135 - 150, (1986).[45] Wilson, Trevor. Industrial Location: Concepts and Techniques.Oxford: Basil Blackwell, 1977.Page 79APPENDIX 1BC TRANS IT-CPLEX ROUTE NUMBERSBC TRANSITROUTE NUMBERSCPLEX ROUTENUMBERSI^BC TRANSITROUTE NUMBERSCPLEX ROUTENUMBERSI^BC TRANSITROUTE NUMBERSCPLEX ROUTENUMBERS3 101 114 138 241/42 1754 102 115 139 246 1767 103 116 140 247 1778 104 112 141 286 1789 105 120 142 292 17910 106 130 143 740 18014 107 131/32 144 310/11 18115 108 134 145 312 18216 109 137 146 314 18317 110 139 147 315 18419 111 140 148 316 18520 112 141 149 317 18622A 113 135 150 320 18722B 114 142 151 321 18832 115 144 152 390 18941 116 136 153 322 19042 117 109 154 323 19151 118 410 155 329 192400 119 100 156 325 193404 120 158 157 328 194413 121 143 158 332 195601 122 147 159 326 1961 123 151 160 335 1972 124 154 161 330 19825 125 160 162 501 19926 126 161 163 509 20027 127 166 164 340 20128 128 701A 165 353 20229 129 701B 166 354 20331 130 210 167 393 20449 131 214 168 395 20550 132 228 169 502 206101 133 229 170 506 207102 134 232 171 507 208106 135 236 172 511 209108 136 239 173 640 210110 137 240 174Page 80APPENDIX 2WEEKLY DEADHEADS PER LOCATIONLOCATION WEEKLYDEADHEADSBurrard Station 675Richmond Exchange 527Port Coquitlam Center 522Broadway & Granville 405Dunbar Loop (Dunbar & 41st) 335Kootenay Loop (Hastings & Kootenay) 333Marpole Loop 329Fraser & 41st 328Newton Exchange 323Victoria & 41st 297Granville & 41st 293Main & 41st 274Helmcken & Hornby 263Scottsdale Mall 235New Westminster Station 219Phibbs Exchange 215Scott Road Station 210Coquitlam Center 208Lougheed Mall 195White Rock Center 192Brentwood Exchange 180Broadway & Oak 180South Delta Recreation Center 171Metrotown Station 166Lonsdale Quay 159Whalley Exchange 157Page 81LOCATION WEEKLYDEADHEADSKnight & Marine 151Cambie & 64th 148Langley Center 140Guildford Exchange 139Alma & 10th 138Earles & Kingsway 137Joyce & Kingsway 135Vancouver Bus Depot 135SFU 118Granville & 63rd 116Lonsdale & 15th 115Broadway & Main 10922nd Street Station 105Grand & 15th 103Joyce Station 91UBC 90Knight & 41st 88Lynn Valley Road & Mountain Highway 84Carnarvon & 41st 81Coquitlam Recreation Center 81Blanca Loop (Blanca & 10th) 76Blenheim & 16th 75Curtis & Duthie 71Capilano & Marine 68128th Street & 16th Avenue 67Nanaimo Station 61Ladner Exchange 59Prospect & Rockland 59Municipal Hall (New Westminster) 57Page 82LOCATION WEEKLYDEADHEADSMackenzie & 41st 54Fraser Highway & 152nd Street 51Cariboo Hill School 50Davie & Howe 50Granville & 49th 50116th Avenue & 227th Street 4929th Avenue Station 46Broadway & Willow 45Scott Road & 96th Avenue 44Oak & 41st 43Beecher & Sullivan 42Granville & King Edward 42Carrall & Pender 41128th Street & Crescent Road 40Davie & Denman 40Fleetwood Way & Fraser Highway 40Pender & Rupert 40BC Rail Station 39Granville & Robson 39Oak Street Bridge (last stop south of) 39Columbia & Powell 37Main & Mountain Highway 37loco & 1st 34208th Street & 40th Avenue 30Bainbridge & Lougheed 30Brunette & Woolridge 30Steveston & No. 5 Road 30Willoughby Way & 200th Street 30Crown & 41st 29Page 83LOCATION WEEKLYDEADHEADSEdmonds Station 298th Avenue & 8th Street 28Coronoda & Phillips 28Dewdney Trunk & 248th Street 28Boundary & Kingsway 26Boundary & 22nd 25Broadway & Renfrew 25Capilano & Montroyal 25Moncton & No. 2 Road 25Stanley Park Loop 25Brunette & Lougheed 23Buswell & Park 23Canada Way & Edmonds 23Burrard & Davie 22Capilano College 22King & No. 5 Road 22Dempsey & Lynn Valley Road 20Garden & Marine 20Hastings & Homer 20Airport Departure Level 19Bidwell & Davie 18177B Street & 58th Avenue 17212th Street & 88th Avenue 15Broadway Station 15Burrard & Melville 15Cape Horn & Mundy 15Hamilton & Pender 15King George Highway & 96th Avenue 15Main & 49th 15Page 84LOCATION WEEKLYDEADHEADSMcKinnon & 54th 15Walnut Grove Park & Ride 15Braid & Columbia 13Cambie & 41st 13Delbrook & Queens 13Dunbar & King Edward 12Broadway & Clark 1110th Avenue & 8th Street 10140th Street & 77th Avenue 10177B Street & 57th Avenue 10198th Street & 24th Avenue 10Bedwell Bay Road Loop 10Bewicke & Marine 10Broadway & Kingsway 10Broadway & Rupert 10Burrard & Helmcken 10Burrard & Robson 10Cambie & Sexsmith 10Canada Way & 10th Avenue 10Canada Way & Ledger 10Carlisle & Hastings 10Curtis & Holdom 10Dempsey & Underwood 10Duthie & Halifax 10Gilley & Westminster Highway 10Grand & 19th 10Shaughnessy Loop 10Park Royal South 9Broadway & Cambie 8Page 85LOCATION WEEKLYDEADHEADSSouthgate & Steveston 8Boundary Loop (Boundary & Eton) 7Georgia & Granville 7Naughton & Panorama 7Phillips & 22nd 7128th Street & 25th Avenue 652A Street & 2nd Avenue 66th Avenue & 6th Street 6Colborne & Ovens 6Imperial & Kingsway 6120th Street & 56th Avenue 5132nd Street & 76th Avenue 5148th Street & 20th Avenue 56th Avenue & 8th Street 5Broadway & Fir 5Burrard & Pender 5Carnation & Emerson 5Chas. Best School^(Como Lk. Rd.) 5Cowley Crescent (Richmond) 5Deer Lake Park 5Electronic & St. Johns 5Emerson & Mt. Seymour Parkway 5Gilley & Kingsway 5Hammarskojld & Hastings 5Harr. Road & Ford Road 5Harvie & 88th Avenue 5Hastings & Willingdon 5Inlet Crescent 5Killarney & 49th 5Page 86LOCATION WEEKLYDEADHEADSKing Edward & Main 5King Edward & Oak 5King George Highway & 152nd Street 5King George Highway & 76th Avenue 5Kingsway & 12th (New Westminster) 5Kingsway & Walker 5Lougheed & Underhill 5McRoberts School^(nr. Williams & #3 Rd.) 5Old Yale Road & 134A Street 5Steveston High School^(nr. Stev.^& #2 Rd.) 5Steveston & No. 3 Road 5Steveston & No. 4 Road 5St. Johns & Williams Street 5Surrey Civic Center 5Vancouver Technical School 5Waterfront Station 5West Boulevard & 49th Avenue 5Granville & Pender 3Alma & 4th 2Chatham & 2nd 2Clearview & St. Johns 2Dunbar & 16th 2Edmonds & Kingsway 2King Edward & Knight 2177B Street & 56th Avenue 1Broadway & Macdonald 1Cambridge & Howard 1Davie & Richards 1Grand & Keith 1Page 87LOCATION WEEKLYDEADHEADSHall & Kingsway 1Kingsway & Slocan 1Page 88APPENDIX 3BC TRANSIT ROUTES & TERMINIRoute Garage Terminus 1 Terminus 23 OTC Main & Marine Davie & Denman4 OTC UBC Loop Eton & Renfrew7 OTC Dunbar Loop Nanaimo Station8 OTC Fraser & Marine Davie & Denman9 OTC UBC Loop Boundary Loop10 OTC UBC Loop Kootenay Loop14 OTC Granville & 63rd Kootenay Loop15 OTC Cambie & 64th Granville & Robson16 OTC Davie & Richards 29th Avenue Station17 OTC Marpole Loop Granville & Robson19 OTC Stanley Park Loop Metrotown Station20 OTC Marpole Loop Harrison Loop22A OTC Carnarvon & 41st Knight & Marine22B OTC Blenheim & 16th Carrall & Pender32 OTC Dunbar Loop Burrard Station41 OTC UBC Loop Joyce Station42 OTC UBC Botanical Garden Spanish Banks51 OTC Broadway & Granville Granville Island400 OTC Richmond Exchange Burrard Station404 OTC Airport Dept. Level Ladner Exchange413 OTC Buswell & Park 22nd Street Station601 OTC Burrard Station 2nd Avenue & 52A Street1 BTC Waterfront Station Bidwell & Davie2 BTC Burrard & Davie Pender & Rupert25 BTC Blanca Loop Brentwood Exchange26 BTC 29th Avenue Station Joyce Station27 BTC Kootenay Loop Joyce StationPage 89Route Garage Terminus 1 Terminus 228 BTC Phibbs Exchange Joyce Station29 BTC Fraserview & Nanaimo 29th Avenue Station31 BTC UBC Loop Broadway Station49 BTC Dunbar Loop Metrotown Station50 BTC Waterfront Station Broadway & Willow101 BTC Gilley & Westminster Lougheed Mall102 BTC New Westminster Station Cumberland & 6th Avenue106 BTC Metrotown Station New Westminster Station108 BTC New Westminster Station Colborne & Ovens110 BTC Metrotown Station Lougheed Mall114 BTC Metrotown Station Gilley & Marine115 BTC Metrotown Station Edmonds Station116 BTC Metrotown Station Greenall & Marine112 BTC Edmonds Station New Westminster Station120 BTC Burrard Station New Westminster Station130 BTC Kootenay Loop Metrotown Station131/32 BTC Kootenay Loop Edmonds Station134 BTC Kootenay Loop Lougheed Mall137 BTC Kootenay Loop Cambridge & Howard139 BTC Kootenay Loop Pender & Willingdon140 BTC Kootenay Loop Eton & Gilmore141 BTC Kootenay Loop Eton & Gilmore135 BTC Kootenay Loop SFU142 BTC 22nd Street Station SFU144 BTC Metrotown Station SFU136 BTC Brentwood Exchange Phillips & Coronoda109 BTC Boundary Loop Brentwood Exchange410 BTC Richmond Exchange 22nd Street Station100 PCT Airport Dept. Level New Westminster StationPage 90Route Garage Terminus 1 Terminus 2158 PCT New Westminster Station Port Coquitlam Centre143 PCT SFU Coquitlam Centre147 PCT New Westminster Station Coquitlam Centre151 PCT Hornby & Nelson Port Coquitlam Centre154 PCT Lougheed Mall 22nd Street Station160 PCT Helmcken & Hornby Port Coquitlam Centre161 PCT Eastern & Western Port Coquitlam Centre166 PCT Noon's Ck & Honeysckl. Coquitlam Centre701A PCT Coquitlam Centre Dewdney T.R.^& 248 St.701B PCT Helcmken & Hornby 116th Ave.^& 227th St.210 NVT Burrard Station Dempsey & Underwood214 NVT Phibbs Exchange Hyannis & Sechelt228 NVT Lonsdale Quay Dempsey & L.V. Road229 NVT Lonsdale Quay Phibbs Exchange232 NVT Phibbs Exchange Grouse Mountain236 NVT Lonsdale Quay Grouse Mountain239 NVT Park Royal Capilano College240 NVT Vancouver Bus Depot Grand Blvd. & 15th241/42 NVT Vancouver Bus Depot Prospect & Rockland246 NVT Vancouver Bus Depot Lonsdale Quay247 NVT Vancouver Bus Depot Capilano & Montroyal286 NVT UBC Loop Bewicke & Marine292 NVT Burrard Station Dempsey & Underwood740 NVT Vancouver Bus Depot Lonsdale Quay310/11 STC Burrard Station Scottsdale Mall312 STC Scott Road Station Scottsdale Mall314 STC 22nd Street Station Scottsdale Mall315 STC Scott Road Station Ladner Exchange316 STC Whalley Exchange Scottsdale MallPage 91Route Garage Terminus 1 Terminus 2317 STC Guildford Exchange Scottsdale Mall320 STC Langley Centre Scott Road Station321 STC White Rock Centre Scott Road Station390 STC White Rock Centre Scott Road Station322 STC Newton Exchange Scottsdale Mall323 STC Newton Exchange Whalley Exchange329 STC Whalley Exchange Scott Road & 96th Ave.325 STC Newton Exchange Whalley Exchange328 STC Whalley Exchange Grosvenor & Gladstone332 STC Guildford Exchange Whalley Exchange326 STC Guildford Exchange Whalley Exchange335 STC Guildford Exchange Fraser Hwy.^& 152nd St.330 STC Guildford Exchange Scott Road Station501 STC Langley Centre Scott Road Station509 STC 88th Ave.^& 212th St. Scott Road Station340 STC 22nd Street Station 177B Street & 58th Ave.353 STC 22nd Street Station 128th Street & 16thAve.354 STC White Rock Centre 160th St.^& 20th Avenue393 STC Newton Exchange Scott Road Station395 STC Will. Way & 200th St. Scott Road Station502 STC Langley Centre Scott Road Station506 STC Fraser Hwy.^& 272nd St. Langley Centre507 STC Glover & 96th Ave. Langley Centre511 STC Fraser Hwy.^& 272nd St. Langley Centre640 STC Tsawwassen Ferry Term. Scottsdale MallPage 92APPENDIX 4LINEAR REGRESSION DEADHEAD TIME SAMPLE DATATRIP TIME(mins)X1(km)X2(km)X3(km)X4(km)X5(km)FROM OTC TO:Richmond Exchange 16 4.95 5.17522nd Street Station 30 0.45 9.225 6.75Burrard Station 20 1.575 0.9 4.5Carrall & Pender 22 2.25 0.9 4.5Ladner Exchange 21 1.575 6.975 10.8Airport Dept.^Level 21 5.4 3.6South Delta Rec. Centre 25 1.575 13.225 10.8Beecher & Sullivan 40 1.575 10.175 32.8FROM ETC TO:Broadway & Willow 23 0.9 7.2Bidwell & Davie 28 3.825 0.9 5.4Metrotown Station 17 4.95 1.35UBC Loop 40 0.9 8.1 8.55Lougheed Mall 20 1.575 9.9Canada Way & Edmonds 20 7.2 1.35Burrard Station 25 2.475 0.9 5.4SFU 18 7.65FROM PCT TO:Helmcken & Hornby 53 2.925 2.925 9.45 18.225Coquitlam Centre 8 1.125 1.8New Westminster Station 25 5.175 2.25 6.075Lougheed Mall 21 2.925 8.122nd Street Station 39 7.425 2.7 6.075loco & 1st 16 5.4 4.5Brunette & Lougheed 15 2.925 5.85Braid & Columbia 18 2.025 2.925 5.85FROM NVT TO:Burrard Station 27 2.475 2.475 7.65Lonsdale Quay 6 2.025Vancouver Bus Depot 27 2.025 2.475 7.65Lonsdale & 15th 6 2.475Page 9 3TRIP TIME(mins)X1(km)X,(km)X3(km)X4(km)X5(km)UBC Loop 50 3.15 5.4 7.875 5.175Bewicke & Marine 4 2.475Park Royal Shopping Centre 15 5.625 0.45Lynn Valley Road & Mountain Highway 8 4.05FROM STC TO:Scottsdale Mall 11 3.375Burrard Station 61 1.575 0.45 20.25 26.1Guildford Exchange 19 3.825 5.625Newton Exchange 6 0.9 0.9Scott Road Station 22 0.45 8.775Fraser Highway & 152nd 15 4.05 2.7Ladner Exchange 28 0.45 20.25Whalley Exchange 15 0.9 5.4 4Page 94APPENDIX 5TERMINUS-TRANSIT CENTRE DEADHEAD TIMES (DIESELS)LOCATION NVT PCT SIC BCRTC CLVDL LHEED RICH BTC OTC MN/TRMBrentwood Exchange 19 25 ** 22 ** 15 42 6 23 18Cambridge & Howard (BBY) 19 33 ** 27 ** 22 49 10 30 18Eton & Gilmore 14 31 ** 29 ** 20 46 7 27 15Gilley & Marine 35 38 ** 7 ** 27 33 22 29 24Greenall & Marine 31 44 ** 14 ** 34 27 18 27 21Lougheed Mall 31 22 ** 18 ** 8 54 18 34 23Metrotown Station 26 35 ** 13 ** 24 32 15 23 18Pender & Willingdon 15 29 ** 26 ** 19 45 6 26 14Phill. & Coronoda (BBY) 27 30 ** 24 ** 16 49 14 32 26SFU 33 32 ** 27 ** 19 55 20 36 322nd Avenue & 52A Street ** ** 54 ** 58 ** 35 ** 42 50Ladner Exchange ** ** 36 ** 40 ** 17 ** 24 32Tsawwassen Ferry Term. ** ** 50 ** 54 ** 31 ** 38 46198th Street & 24th Ave. ** 49 44 60 27 43 ** ** ** **88th Ave. & 212th St. ** 25 35 34 19 19 ** ** ** **Fraser Hwy. & 272nd St. ** 57 51 67 35 51 ** ** ** **Glover & 96th Ave. ** 30 40 39 24 24 ** ** ** **Langley Centre ** 39 34 50 17 33 ** ** ** **Will. Way & 200th St. ** 36 30 46 14 30 ** ** ** **116th Ave. & 227th St. ** 22 44 41 38 26 ** ** ** **Dewdney T.R. & 248 St. ** 27 49 47 43 31 ** ** ** **Bewicke & Marine 8 ** ** ** ** ** ** 21 37 30Capilano & Montroyal 22 ** ** ** ** ** ** 21 40 33Capilano College 11 ** ** ** ** ** ** 12 31 18Dempsey & L.V. Road 15 ** ** ** ** ** ** 18 37 24Dempsey & Underwood 15 ** ** ** ** ** ** 18 37 24Grand Blvd. & 15th 6 ** ** ** ** ** ** 13 31 19Grouse Mountain 28 ** ** ** ** ** ** 27 44 40Hyannis & Sechelt (NV) 16 ** ** ** ** ** ** 16 35 22Lonsdale Quay 6 ** ** ** ** ** ** 18 36 24Park Royal 15 ** ** ** ** ** ** 17 32 23Phibbs Exchange 7 ** ** ** ** ** ** 10 29 16Prospect & Rockland 13 ** ** ** ** ** ** 16 44 22Page 95LOCATION NVT PCT STC BCRTC CLVDL LHEED RICH BTC OTC MN/TRMBidwell & Davie 39 53 61 40 64 42 29 32 20 18Burrard & Davie 32 46 57 34 60 36 25 25 16 13Burrard & Helmcken 32 46 57 34 61 35 26 24 16 12Burrard Station 29 43 59 30 63 32 28 22 18 8Carrall & Pender 21 35 63 27 67 24 32 14 22 5Davie & Denman 38 52 61 40 65 42 30 31 20 19Davie & Richards 31 45 55 32 58 34 23 24 14 11Granville & Robson 28 42 58 31 62 31 27 20 17 9Helmcken & Hornby 31 45 57 33 60 34 25 24 16 12Hornby & Nelson 30 44 57 32 61 34 26 23 16 11Stanley Park Loop 36 50 68 40 72 39 37 28 27 18Vancouver Bus Depot 26 40 61 27 64 29 29 18 20 5Waterfront Station 27 41 60 31 64 30 29 20 19 929th Avenue Station 26 ** ** 19 ** ** 30 13 17 12Boundary Loop 16 ** ** 22 ** ** 31 4 21 13Broadway Station 20 ** ** 23 ** ** 25 9 15 7Eton & Renfrew 13 ** ** 28 ** ** 35 8 24 11Joyce Station 24 ** ** 16 ** ** 30 12 19 14Kootenay Loop 13 ** ** 24 ** ** 35 5 25 12Nanaimo Station 27 ** ** 19 ** ** 29 13 17 12Pender & Rupert 13 ** ** 25 ** ** 36 6 24 11Airport Dept. Level ** 65 ** 41 ** 54 11 32 15 24Cambie & 64th ** 57 ** 32 ** 47 12 26 9 20Fraser & Marine ** 51 ** 26 ** 41 16 23 14 17Fraserview & Nanaimo ** 46 ** 22 ** 36 23 20 19 18Granville & 63rd ** 60 ** 36 ** 50 11 24 8 15Harrison Loop ** 46 ** 22 ** 36 21 21 18 18Knight & Marine ** 49 ** 24 ** 38 19 22 16 17Main & Marine ** 53 ** 28 ** 43 14 25 12 17Marpole Loop ** 60 ** 35 ** 49 8 27 10 17Blanca Loop 42 ** ** ** ** ** 30 29 21 20Blenheim & 16th 37 ** ** ** ** ** 24 24 17 15Carnarvon & 41st 40 ** ** ** ** ** 20 27 10 18Crown & 41st 43 ** ** ** ** ** 23 30 13 21Dunbar Loop 42 ** ** ** ** ** 21 29 12 20Spanish Banks 45 ** ** ** ** ** 34 32 24 23Page 9 6LOCATION NVT PCT SIC BCRTC ,^CLVDL LHEED RICH BTC OTC MN/TRMUBC Botanical Garden 50 ** ** ** ** ** 39 37 29 28UBC Loop 48 ** ** ** ** ** 36 34 26 26128th Street & 16th Ave. ** ** 35 40 39 ** 44 ** 51 59160th St. & 20th Avenue ** ** 27 32 31 ** 36 ** 43 51White Rock Centre ** ** 26 31 29 ** 34 ** 41 5022nd Street Station ** 32 27 6 37 21 18 26 33 27Colborne & Ovens (NW) ** 23 24 12 33 13 27 22 33 24Cumberland & 6th Avenue ** 24 23 14 32 13 27 26 34 25Edmonds Station ** 30 30 3 40 19 22 22 29 23New Westminster Station ** 26 22 12 32 14 25 29 35 29Coquitlam Centre ** 8 33 30 27 13 ** 24 40 34Eastern & Western (POCO) ** 9 37 34 31 16 ** 28 43 37Noons Ck & Honey. (POCO) ** 15 40 37 34 19 ** 32 49 40Port Coquitlam Centre ** 1 36 33 30 15 ** 27 42 36Buswell & Park ** ** 38 20 44 ** 9 ** 21 29Gilley & Westminster ** ** 25 8 32 ** 15 ** 22 30Richmond Exchange ** ** 38 20 44 ** 9 ** 21 29177B Street & 58th Ave. ** 31 22 42 4 25 40 ** ** **Fraser Hwy. & 152nd St. ** 24 15 28 15 18 44 ** ** **Grosv. & Gladstone (SRY) ** 26 16 23 26 20 43 ** ** **Guildford Exchange ** 18 19 29 21 12 47 ** ** **Newton Exchange ** 36 6 32 21 30 32 ** ** **Scott Road & 96th Ave. ** 35 16 30 28 29 34 ** ** **Scott Road Station ** 28 17 16 26 22 44 ** ** **Scottsdale Mall ** 42 12 38 27 36 24 ** ** **Whalley Exchange ** 27 13 23 23 21 41 ** ** **Broadway & Granville ** ** ** ** ** ** 17 17 9 8Broadway & Willow ** ** ** ** ** ** 19 15 10 6Granville Island ** ** ** ** ** ** 20 19 11 10-"*" denotes an "illogical" transit centre-deadhead point combination. For purposes of computation,their distances are assumed to be twice the maximum (ie. 2 * 72 = 144).Page 97APPENDIX 6DIESEL BUS ROUTE DEADHEAD TINESBC TransitroutenumberCPLEXroutenumberNVT PCTrSIC BCRTC CLVDL LHEED RICH BTC OTC MN/TRM22A 113 184 193 288 168 288 182 39 49 26 3522B 114 58 179 207 171 211 168 56 38 39 2032 115 71 187 203 174 207 176 49 51 30 2841 116 72 288 288 160 288 288 66 46 45 4042 117 95 288 288 288 288 288 73 69 53 5151 118 288 288 288 288 288 288 37 36 20 18400 119 173 187 97 50 107 176 37 166 39 37404 120 288 209 180 185 184 198 28 176 39 56413 121 288 176 65 26 81 165 27 170 54 56601 122 173 187 113 174 121 176 63 166 60 581 123 66 94 121 71 128 72 58 52 39 272 124 45 190 201 59 204 180 61 31 40 2425 125 61 169 288 166 288 159 72 35 44 3826 126 50 288 288 35 288 288 60 25 36 2627 127 37 288 288 40 288 288 65 17 44 2628 128 31 288 288 160 288 288 174 22 48 3029 129 168 190 288 38 288 180 53 32 38 3231 130 68 288 288 167 288 288 61 43 41 3349 131 68 179 288 157 288 168 53 44 35 3850 132 171 185 204 175 208 174 48 35 29 15101 133 175 166 169 26 176 152 69 162 56 53102 134 288 50 45 26 64 27 52 55 69 54106 135 170 61 166 25 176 38 57 44 58 47108 136 288 49 46 24 65 27 52 51 68 53110 137 57 57 288 31 288 32 86 33 57 41114 138 61 73 288 20 288 51 65 37 52 42115 139 170 65 174 16 184 43 54 37 52 41116 140 57 79 288 27 288 58 59 33 50 39112 141 288 56 52 15 72 33 47 51 64 52120 142 173 69 81 42 95 46 53 51 53 37130 143 39 179 288 37 288 168 67 20 48 30131/32 144 157 174 174 27 184 163 57 27 54 35Page 9 8BC TransitroutenumberCPLEXroutenumberNVT PCT SIC BCRTC CLVDL LHEED RICH BIC OTC,MN/TRM134 145 44 166 288 42 288 152 89 23 59 ,^35137 146 32 177 288 51 288 166 84 15 55 30139 147 28 173 288 50 288 163 80 11 51 26140 148 27 175 288 53 288 164 81 12 52 27141 149 27 175 288 53 288 164 81 12 52 27135 150 46 176 288 51 288 163 90 25 61 44142 151 177 64 171 33 181 40 73 46 69 59144 152 59 67 288 40 288 43 87 35 59 50136 153 46 55 288 46 288 31 91 20 55 44109 154 35 169 288 44 288 159 73 10 44 31410 155 288 176 65 26 81 165 27 170 54 56100 156 288 91 166 53 176 68 36 61 50 53158 157 288 27 58 45 62 29 169 56 77 65143 158 177 40 177 57 171 32 199 44 76 66147 159 288 34 55 42 59 27 169 53 75 63151 160 174 45 93 65 91 49 170 50 58 47154 161 175 54 171 24 181 29 72 44 67 50160 162 175 46 93 66 90 49 169 51 58 48161 163 288 10 73 67 61 31 288 55 85 73166 164 288 23 73 67 61 32 288 56 89 74701A 165 288 35 82 77 70 44 288 168 184 1787018 166 175 67 101 74 98 60 169 168 160 156210 167 44 187 203 174 207 176 172 40 55 32214 168 ,^23 288 288 288 288 288 288 26 64 38228 169 21 288 288 288 288 288 288 36 73 48229 170 13 288 288 288 288 288 288 28 65 40232 171 35 288 288 288 288 288 288 37 73 56236 172 34 288 288 288 288 288 288 45 80 64239 173 37 288 288 288 288 288 288 38 72 56240 174 32 184 205 171 208 173 173 31 51 24241/42 175 39 184 205 171 208 173 173 34 64 27246 176 32 184 205 171 208 173 173 36 56 29247 177 48 184 205 171 208 173 173 39 60 38286 178 56 192 192 192 192 192 192 69 85 78292 179 44 187 203 174 207 176 172 40 55 32Page 9 9BC TransitroutenumberCPLEXroutenumberNVT PCT SIC BCRTC CLVDL LHEED RICH BTC OTCFMN/TRM740 180 32 184 205 171 208 173 173 36 56 29310/11 181 173 85 71 68 90 68 52 166 162 152312 182 288 70 29 54 53 58 68 288 288 288314 183 288 74 39 44 64 57 42 170 177 171315 184 288 172 53 160 66 166 61 288 168 176316 185 288 69 25 61 50 57 65 288 288 288317 186 288 60 31 67 48 48 71 288 288 288320 187 288 67 51 66 43 55 188 288 288 288321 188 288 172 43 47 55 166 78 288 185 194390 189 288 172 43 47 55 166 78 288 185 194322 190 288 78 18 70 48 66 56 288 288 288323 191 288 63 19 55 44 51 73 288 288 288329 192 288 62 29 53 51 50 75 288 288 288325 193 288 63 19 55 44 51 73 288 288 288328 194 288 53 29 46 49 41 84 288 288 288332 195 288 45 32 52 44 33 88 288 288 288326 196 288 45 32 52 44 33 88 288 288 288335 197 288 42 34 57 36 30 91 288 288 288330 198 288 46 36 45 47 34 91 288 288 288501 199 288 67 51 66 43 55 188 288 288 288509 200 288 53 52 50 45 41 188 288 288 288340 201 288 63 49 48 41 46 58 170 177 171353 202 288 176 62 46 76 165 62 170 84 86354 203 288 288 53 63 60 288 70 288 84 101393 204 288 64 23 48 47 52 76 288 288 288395 205 288 64 47 62 40 52 188 288 288 288502 206 288 67 51 66 43 55 188 288 288 288506 207 288 96 85 117 52 84 288 288 288 288507 208 288 69 74 89 41 57 288 288 288 288511 209 288 96 85 117 52 84 288 288 288 288640^_ 210 288 186 62 182 81 180 55 288 182 190Page 100APPENDIX 7.1BUS ROUTE REQUIREMENTS - NVTCPLEXROUTENUMBERSBCTRANSITMONDAY - FRIDAY^I SATURDAY^I SUNDAY - HOLIDAYROUTENUMBERS AM PM 1 2 TOT. AM PM 1 2 TOT. AM PM 1 2 TOT.167 210 12 11 4 5 21 0 0 0 4 4 0 0 0 4 4168 214 0 0 0 0 0 0 0 1 3 4 0 1 2 1 4169 228 2 0 3 1 6 0 1 1 1 3 0 0 1 1 2170 229 1 3 3 2 8 0 0 3 2 5 0 0 0 2 2171 232 1 1 0 3 4 0 0 0 3 3 0 0 0 3 3172 236 0 0 2 0 2 0 0 2 0 2 0 0 1 0 1173 239 1 2 3 3 8 0 0 3 3 6 0 0 2 2 4174 240 6 3 6 0 12 0 1 1 2 4 0 0 0 3 3175 241/42 6 3 0 0 6 0 0 0 0 0 0 0 0 0 0176 246 5 4 5 1 11 0 1 2 2 5 0 0 1 2 3177 247 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0178 286 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0179 292 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0180 740 0 1 0 0 1 _^3 3 0 0 3 3 3 0 0 3 Page 101APPENDIX 7.2BUS ROUTE REQUIREMENTS - PCTCPLEXROUTENUMBERSBCTRANSITMONDAY - FRIDAY^I SATURDAY^I SUNDAY - HOLIDAYROUTENUMBERS AM PM 1 2 TOT. AM PM 1 2 TOT. AM PM 1 2 TOT.156 100 2 2 2 1 5 0 0 2 1 3 0 1 0 2 3157 158 4 3 6 2 12 0 0 5 1 6 0 1 0 2 3158 143 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0159 147 1 2 4 5 11 0 1 6 3 10 0 1 0 5 6160 151 12 8 10 8 30 0 0 4 10 14 0 0 3 9 12161 154 7 6 7 4 18 0 0 4 5 9 0 0 0 5 5162 160 13 12 6 0 19 0 1 5 0 6 0 0 0 0 0163 161 2 1 3 0 5 0 0 1 1 2 0 0 0 1 1164 166 1 2 1 0 3 0 0 1 0 1 0 0 0 0 0165 701A 2 3 2 0 5 0 0 0 1 1 0 0 0 2 2166 7018 4 1 3 0 7 _^0 0 0 2 2^_ 0 0 0 1 1 Page 102APPENDIX 7.3BUS ROUTE REQUIREMENTS - STCCPLEXROUTENUMBERSBCTRANSIT MONDAY - FRIDAY I^SUNDAY - HOLIDAYI^SATURDAYROUTENUMBERS AM PM 12 TOT. AM PM 1 2 TOT. AM PM 1 2 TOT.181 310/11 8 6 0A0 8i^a0 0I0 0 0 0 0 0 0 0182 312 6 5 4 3 13 0 0 3 3 6 0 0 1 3 4183 314 2 2 0 0 2 0, 0 0 0 0 0 0 0 0 0184 315 1 2 0 0 2 0 0 0 0 0 0 0 0 0 0185 316 2 1 2 2 6 0 0 2 2 4 0 0 0 2 2186 317 2 1 3 0 5 0 0 3 0 3 0 0 0 0 0187 320 0 1 3 4 8 0 0 3 4 7 0 0 1 3 4188 321 2 1 3 2 7 0 0 3 4 7 0 0 2 2 4189 390 0 1 2 1 4 0 0 0 0 0 0 0 0 0 0190 322 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1191 323 0 0 1 1 2 0 0 1 1 2 0 0 0 1 1192 329 0 0 0 2 2 0 0 1 1 2 0 0 0 1 1193 325 3 3 1 0 4 0 0 0 1 1 0 0 1 0 1194 328 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1195 332 1 1 1 0 2 0 0 0 0 0 0 0 0 1 1196 326 0 0 2 0 2 0 0 1 0 1 0 0 1 1 2197 335 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0198 330 3 5 2 2 9 0 0 1 2 3 0 0 0 3 3199 501 1 2 1 2 5 0 0 1 2 3 _^0 0 0 1 1Page 103CPLEXROUTENUMBERSBCTRANSITMONDAY - FRIDAYI^SUNDAY - HOLIDAY1^SATURDAYROUTENUMBERS AM PM 1 2 TOT. AM PM 1 2 TOT. AM PM 1 2 TOT.200 509 2 1 0 0 2 0 0 0 0 0 0 0 0 0 0201 340 4 4 2 2 8 0 0 2 2 4 0 0 0 2 2202 353 14 13 2 1 17 0 0 2 1 3 0 0 2 0 2203 354 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0204 393 3 3 0 0 3 0 0 0 0 0 0 0 0 0 0205 395 3 3 0 0 3 0 0 0 0 0 0 0 0 0 0206 502 2 2 0 0 2 0 0 1 0 1 0 0 0 0 0207 506 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0208 507 2 1 0 0 2 0 0 1 0 1 0 0 1 0 1209 511 0 1 2 0 3 0 0 1 0 1 0 0 0 0 0210 640 0 0 0 2 2 _^0 0 0 2 2 0 0 0 2 2 Page 104APPENDIX 7.4BUS ROUTE REQUIREMENTS - BTCCPLEXROUTENUMBERSBCTRANSIT MONDAY - FRIDAY 1 SATURDAY I SUNDAY - HOLIDAYROUTENUMBERS AM PM 12 TOT. AM PM 12 TOT. AM PM 1 2 TOT.123 1 0 0 6A2 81^A0 0•6A2 8 0 0 0 0 0124 2 4 4 0 0 4 0 0 0 0 0 0 0 0 0 0125 25 4 2 6 3 13 0 0 4 4 8 0 2 0 4 6126 26 0 0 5 1 6 0 0 4 2 6 0 1 1 1 3127 27 0 0 5 1 6 0 0 3 2 5 0 0 1 1 2128 28 1 0 1 2 4 0 0 2 2 4 0 0 1 1 2129 29 0 0 1 1 2 0 0 0 1 1 0 0 0 2 2130 31 2 1 0 0 2 0 0 0 0 0 0 0 0 0 0131 49 3 4 3 4 11 0 0 4 3 7 0 1 2 2 5132 50 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2133 101 3 2 2 2 7 0 ... 0 2 2 4 0 0 0 2 2134 102 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1135 106 1 0 6 3 10 0 0 4 4 8 0 0 1 4 5136 108 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0137 110 2 2 1 1 4 0 0 0 1 1 0 0 0 1 1138 114 0 0 1 1 2 0 0 0 1 1 0 0 0 1 1139 115 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1140 116 2 0 2 0 4 0 0 0 1 1 0 0 1 0 1141 112 2 1 3 1 6 0 0 1 2 3 0 0 0 2 2Page 105CPLEXROUTENUMBERSBCTRANSITMONDAY - FRIDAY^I^SATURDAY^I^SUNDAY - HOLIDAYROUTENUMBERS AM PM 1 2 TOT. AM PM 1 2 TOT. AM PM 1 2 TOT.142 120 1 1 3 4 8 0 0 5 3 8 0 0 0 3 3143 130 0 0 3 4 7 0 0 0 5 5 0 0 3 4 7144 131/32 3 3 2 0 5 0 0 3 0 3 0 0 0 0 0145 134 2 1 2 1 5 0 0 1 2 3 0 0 0 1 1146 137 0 1 0 1 2 0 0 0 1 1 0 0 0 2 2147 139 0 1 2 0 3 0 0 0 0 0 0 0 0 0 0148 140 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0149 141 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0150 135 5 3 1 2 8 0 0 2 3 5 0 0 0 3 3151 142 1 1 1 0 2 0 0 0 0 0 0 0 0 0 0152 144 2 0 2 2 6 0 0 0 2 2 0 0 1 1 2153 136 0 0 1 1 2 0 0 0 2 2 0 0 0 1 1154 109 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1155 410 3 3 0 0 3 0 0 0 0 0 -^0 0 0 0 0 Page 106APPENDIX 7.5BUS ROUTE REQUIREMENTS - OTCCPLEXROUTENUMBERSBCTRANSIT MONDAY - FRIDAY^I SATURDAY^I SUNDAY - HOLIDAYROUTENUMBERS AM PM 1 2 TOT. AM PM 1 2 ■TOT. AM PM 1 2 TOT.101 3 6 5 13■5 24 0 2 11 5 18 0 0 10 4 14102 4 1 0 6 5 12 0 0 3 5 8 0 0 2 5 7103 7 2 1 6 5 13 0 0 4 7 11 0 1 4 5 10104 8 2 4 8 8 20 0 3 7 8 18 0 2 7 5 14105 9 13 9 20 3 36 0 2 4 8 14 0 0 6 6 12106 10 5 6 10 4 20 0 2 6 5 13 0 0 4 5 9107 14 4 6 7 4 17 0 3 3 5 11 0 0 3 6 9108 15 3 4 5 3 12 0 2 4 3 9 0 1 3 2 6109 16 4 1 7 2 13 0 0 4 5 9 0 1 1 4 6110 17 2 4 5 2 11 0 2 3 2 7 0 0 2 2 4111 19 4 2 6 4 14 0 1 5 4 10 0 0 2 5 7112 20 10 8 15 7 32 0 4 15 7 26 0 3 4 9 16113 22A 7 7 4 8 19 0 1 6 3 10 0 0 0 9 9114 22B 7 6 4 0 11 0 1 5 3 9 0 0 0 0 0115 32 4 4 0 0 4 0 0 0 0 0 0 0 0 0 0116 41 7 4 4 6 17 0 0 4 6 10 0 0 2 5 7117 42 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1118 51 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1119 400 _^34 30 17 9 60 1 0 9 14 ,^24 0 3 7 8 18Page 107CPLEXROUTENUMBERSBCTRANSITMONDAY - FRIDAY I^SATURDAY^1^SUNDAY - HOLIDAYROUTENUMBERS AM PM 1 2 TOT. AM PM 1 2 TOT. AM PM 1 2 TOT.120 404 4 4 7 1 12 0 1 3 3 7 0 1 2 3 6121 413 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0122 601 12 12 12 2 26 4 3 7 2 13 0 0 3 5 8 Page 108APPENDIX 8.1OPTIMAL SOLUTION BUS ASSIGNMENTS - NVTDIESEL BUSESCplex RouteNumberBC Transit Route Monday - Friday Saturday Sunday - HolidaysNumberAM PM 1 2 AM PM 1 2 AM PM 1 2167 210A4168 214 1 3 1 2 1169 228 2 3 1 1 1 1 1 1170 229 1 3 3 2 3 2 2171 232 1 1 3 3 3172 236 2 2 1173 239 1 2 3 3 3 3 2 2174 240 6 6176 246 5 4 5 1 1 2 2 1 2178 286 2 2180 740 1 3 2 3PERIOD TOTAL 18 13 26 10 0 5 12 14^2 4 7 11ACTIVE BUSES 54 31 22SPARES 6 29 38ITOTAL BUSES ALLOCATED 60 60 60Page 109APPENDIX 8.2OPTIMAL SOLUTION BUS ASSIGNMENTS - PCTDIESEL BUSESCplex RouteNumber BC Transit Monday - Friday Saturday Sunday - HolidayRoute Number AM PM 1, 2 AM PM 1 2 AM PM 1 2157 158 4 3 6 2 5 1 1 2158 143 1 1159 147 1 2 4 5 1 6 3 1 5160 151 12 8 10 8 4 10 3 9161 154 7 4162 160 13 12 6 1 5163 161 2 1 3 1 1 1164 166 1 2 1 1165 701A 2 3 2 1 2166 701B 4 1 3 2 1208 507 2 1 1 1PERIOD TOTAL^42 34 42 2 23 18^0 2 4 20ACTIVE BUSES 103 43 26SPARES^11I19°711188ITOTAL BUSES ALLOCATED^114 114 114Page 110APPENDIX 8.3OPTIMAL SOLUTION BUS ASSIGNMENTS - STCDIESEL BUSESCplex RouteNumberBC Transit Route Monday - Friday Saturday Sunday - HolidayNumberAM PM 1 2 AM PM 1 2 AMr PM^y 1 2134 102•1136 108 1181 310/11 8 6182 312 6 5 4 3 3 3 1 3183 314 2 2184 315 1 2185 316 2 1 2 2 2 2 2186 317 2 1 3 3187 320 1 3 4 3 4 1 3188 321 2 1 3 2 3 4 2 2189 390 1 2 1190 322 1 1 1191 323 1 1 1 1 1192 329 2 1 1 1193 325 3 3 1 1 1194 328 1 1 1 1195 332 1 1 1 1196 326 2 1 1 1197 335 1 1Page 111Cplex RouteNumber BC Transit Route Monday - Friday SaturdaySunday - HolidayNumberAM PM 1 2 AM PM 1, 2 AM PM 1 2198 330 3 5 2 2 1 2i3199 501 1 2 1 2 1 2 1200 509 2 1201 340 4 4 2 2202 353 6 1 2 1203 354 1 1204 393 3 3205 395 3 3206 502 2 2 1207 506 1 1209 511 1 2 1210 640 2 2 2PERIOD TOTAL 52 49 33 26^0 0 25 23^0 0 8 20ACTIVE BUSES 111 48 28SPARES 12 75I95ITOTAL BUSES ALLOCATED 123 123 123Page 112APPENDIX 8.4OPTIMAL SOLUTION VEHICLE ASSIGNMENTS - BCRTCDIESEL BUSESCplex RouteNumber BC Transit Monday - Friday Saturday Sunday - HolidayRoute Number AM PM 1 2 AM PM 1 2 AM PM 1 2121 413 3133 101 3 2 2 2 2 2 2134 102 1 1135 106 1 6 3 4 4 1 4136 108 1137 110 1 1138 114 1 1139 115 1 1 1140 116 2 1 1141 112 2 1 3 1 1 2 2142 120 1 5 3 3151 142 1155 410 3 3161 154 7 6 4 5 5201 340 2 2 2202 353 8 12 2 1 2PERIOD TOTAL 28 28 11 6 0 0 21 24 0 0 4 22ACTIVE BUSES 45 45 26SPARES 5I5I24ITOTAL BUSES ALLOCATED 50 50 50Page 113APPENDIX 8.5OPTIMAL SOLUTION BUS ASSIGNMENTS - BICDIESEL BUSESCplex RouteNumbersBC Transit Monday - Friday Saturday Sunday - HolidaysRoute NumbersAM PM 1 2 AM PM 1 2 AM 7^PM 1 2114 22B 6 4116 41 7 2 4 6124 2 4 4125 25 4 2 6 3 4 4 2 4126 26 5 1 4 2 1 1 1127 27 5 1 3 2 1 1128 28 1 1 2 2 2 1 1129 29 1 1 1 2130 31 2137 110 2 2 1 1138 114 1 1140 116 2142 120 3 4143 130 3 4 5 3 4144 131/32 3 3 2 3145 134 2 1 2 1 1 2 1146 137 1 1 1 2147 139 1 2148 140 1149 141 _^1Page 114Cplex RouteNumbers BC Transit Monday - Friday SaturdaySunday - HolidaysRoute NumbersAM PM 1 2 AM PM 1 2 AM PM 1 2150 135 5 3 1 2 2 3 3151 142 1 1152 144 2 2 2 2 1 1153 136 1 1 2 1154 109 1 1 .._ 1167 210 12 11 5 4 2174 240 3 1 1 2 3175 241/42 6 3177 247 2 2179 292 1PERIOD TOTAL^60 39 48 37 0 1 21 32^0 3 7 27ACTIVE BUSES 145 54 37ISPARES^15I106 123TOTAL BUSES ALLOCATED^160 -^160 160Page 115APPENDIX 8.6OPTIMAL SOLUTION BUS ASSIGNMENTS - OTCTROLLEYS AND DIESEL BUSESCplex RouteNumbersBC Transit Monday - Friday Saturday Sunday - HolidayRoute Numbers AM PM 1 2 AM PM 1 2 AM ,^PM 1 2Trolleys:A101 3 6 5 13 5 2 11 5 10 4103 7 2 1 6 5 4 7 1 4 5104 8 2 4 8 8 3 7 8 2 7 5105 9 2 20 3 4 8106 10 2 4107 14 4 6 7 4 3 3 5 3 6108 15 3 4 5 3 2 4 3 1 3 2109 16 7 2 4 2110 17 2 4 5 2 2 3 2 2 2111 19 6 4112 20 10 8 15 7 4 15 7 3 4 9PERIOD TOTAL^31 32 94 47 0 16 55 47 0 7 33 33ACTIVE BUSES 173SPARES^I^17118 7372 117ITOTAL TROLLEYS ALLOCATED^190 190 190DIESELS:113 22AI^77 4 8^I 1 6 3^I 9115 32^4 4Page 116Cplex RouteNumbers_BC Transit Monday - Friday Saturday Sunday - HolidayRoute NumbersAM PM 1 2 AM PM 1 2 AM PM 1 2116 41 2 4 6 2 5117 42 1 1 1118 51 1 1 1119 400 34 30 17 9 1 9 14 3 7 8120 404 4 4 7 1 1 3 3 1 2 3122 601 12 12 12 2 1 3 7 2 3 5123 1 6 2 6 2131 49 3 4 3 4 4 3 1 2 2156 100 2 2 2 1 2 1_ _ 1 2PERIOD TOTAL 66 65 53 27 2 5 43 34 0 6 18 34ACTIVE BUSES 146 82 58SPARES 14 78 102TOTAL DIESELS ALLOCATED 160 160 160TOTAL TROLLEYS ALLOCATED 190 190 190TOTAL BUSES ALLOCATED 350 -^350 350Page 117APPENDIX 8.7OPTIMAL SOLUTION BUS ASSIGNMENTS - MAIN & TERMINALTROLLEYS AND DIESEL BUSESCplex RouteNumbers BC TransitMonday - Friday Saturday Sunday - HolidayRoute NumbersAM PM 1 2 AM PM 1 2 AM PM 1 2Trot eys:A 1102 4 1 6 5 3 5 2 5105 9 11 9 2 6 6106 10 5 6 8 2 6 5 4 5109 16 4 1 3 1 1 4111 19 4 2 1 5 4 _ 2 5Diesels:114 22B 1 6 1 5 3122 601 3130 31 1132 50 2142 120 1167 210 2180 740 3 1PERIOD TOTAL 26 26 14 5 3 6 19 20 1 1 15 29ACTIVE BUSES 45 45 45SPARES 5 5 5TOTAL BUSES ALLOCATED -^50 -^50 -^50Page 118APPENDIX 9OPTIMAL SOLUTION ROUTE ASSIGNMENTSCPLEX ROUTENUMBERS,BC TRANSIT SCENARIOSROUTENUMBERS CURRENT OPTIMAL NO MINIMUMor MAXIMUM"50 TROLLEY"MINIMUMINCREASEMIN. SIZETO 75INCREASEMIN. SIZETO 100ELIMINATEOTCINCREASECAPACITY OFBTC (no cap.costs)101 3 OTC MN/TRM102 4 OTC MN/TRM BTC MN/TRM BTC BTC MN/TRM BTC103 7 OTC MN/TRM104 8 OTC MN/TRM105 9 OTC OTCMN/TRMBTC OTCMN/TRMBTC BTC MN/TRM BTC106 10 OTC OTCMN/TRMBTC OTCMN/TRMBTC BTC MN/TRM BTC107 14 OTC MN/TRM108 15 OTC MN/TRM109 16 OTC OTCMN/TRMOTCMN/TRMMN/TRM110 17 OTC MN/TRM111 19 OTC OTCMN/TRMOTCMN/TRMMN/TRM112 20 OTC MN/TRM113 22A OTC RICHBTCMN/TRM114 22B OTC BTCMN/TRMBTC BTCMN/TRMBTCOTCBTCOTCBTCMN/TRMBTCOTC115 32 OTC MN/TRMPage 119CPLEX ROUTENUMBERSBC TRANSIT SCENARIOS^ IROUTENUMBERS CURRENT OPTIMAL NO MINIMUMor MAXIMUM"50 TROLLEY"MINIMUMINCREASEMIN. SIZETO 75INCREASEMIN. SIZETO 100ELIMINATEOTCINCREASECAPACITY OFBTC (no cap.costs)116 41 OTC BTCOTCBIGOTCBTCMN/TRM117 42 OTC BTCMN/TRM118 51 OTC BTCMN/TRM119 400 OTC RICHOTCBCRTCOTCBCRTCOTCRICHMN/TRM120 404 OTC RICHOTCRICH121 413 OTC BCRTC BCRTCRICHBCRTC BCRTC BCRTC BCRTCRICHBCRTC122 601 OTC OTCMN/TRMOTCMN/TRMRICHMN/TRM123 1 BTC OTC OTC OTC OTC OTC BIGMN/TRMOTC124 2 BTC125 25 BTC126 26 BIG BCRTCBTCBCRTCBIG127 27 BIG128 28 BIG129 29 BIG BCRTCBIGBCRTCBIGBIGMN/TRM130 31 BIG BIGMN/TRMOTC BIGOTCOTC OTC OTCPage 120CPLEX ROUTENUMBERS BC TRANSITSCENARIOSROUTENUMBERS CURRENT OPTIMAL NO MINIMUMor MAXIMUM"50 TROLLEY"MINIMUMINCREASEMIN. SIZETO 75INCREASEMIN. SIZETO 100ELIMINATEOTCINCREASECAPACITY OFBTC (no cap.costs)131 49 BTC OTC OTC OTC OTC OTC BTCMN/TRMOTC132 50 BTC MN/TRM OTC MN/TRM OTC OTC MN/TRM OTC133 101 SIC BCRTC BCRTC BCRTC BCRTC BCRTC BCRTC BCRTC134 102 BTC SICBCRTCSICLHEEDSICBCRTCSICBCRTCSICBCRTCSICBCRTCSICBCRTC135 106 BTC BCRTC BCRTCBTCBCRTCSICBCRTC BCRTC BCRTC BCRTC136 108 SIC SICBCRTCSICBCRTCSICBCRTCSICBCRTCSICBCRTCSICBCRTCSICBCRTC137 110 BTC BCRTCBTCBCRTCBTCPCTBCRTCBTCPCTBCRTCBTCPCTBCRTCBTCBCRTCSIC138 114 BTC BCRTCSICBCRTCSICBCRTCBTCBCRTC BCRTC BCRTC BCRTC139 115 SIC BCRTC BCRTC BCRTC BCRTC BCRTC BCRTC BCRTC140 116 BTC BCRTCSICBCRTCBTCBCRTCBTCBCRTC BCRTC BCRTCBTCBCRTCSIC141 112 SIC BCRTC BCRTC BCRTC BCRTC BCRTC BCRTC BCRTC142 120 SIC BCRTCSICMN/TRMBCRTCLHEEDBTCBCRTCSICMN/TRMPCTBCRTCBCRTC PCTBCRTCBTCMN/TRMBCRTCBTC143 130 SIC BCRTCBTC144 131/32 BTC BCRTCSICBCRTCBTCBCRTCBTCBCRTCBTCPage 121CPLEX ROUTENUMBERSBC TRANSIT SCENARIOS^ IROUTENUMBERS CURRENT OPTIMAL NO MINIMUMor MAXIMUM"50 TROLLEY"MINIMUMINCREASEMIN. SIZETO 75INCREASEMIN. SIZETO 100ELIMINATEOTCINCREASECAPACITY OFBTC (no cap.costs)145 134 SIC BCRTCBTC146 137 BTC147 139 BTC148 140 BTC149 141 BTC150 135 SIC151 142 SIC BCRTCBTCBCRTCBTCBCRTC BCRTC PCTBCRTCBCRTCBTC152 144 SIC PCTBCRTCBTCBCRTCBTC153 136 BTC PCTBTCPCTBTC154 109 BTC155 410 BTC BCRTC BCRTC BCRTC BCRTC BCRTC BCRTCRICHBCRTC156 100 PCT OTC RICHOTCOTC BCRTCOTCBCRTCOTCRICH OTC157 158 PCT LHEEDBTCLHEED158 143 PCT LHEEDBTCLHEED159 147 PCT LHEEDBTCSICLHEED160 151 PCT BTC LHEEDSICPage 12 2CPLEX ROUTENUMBERSBC TRANSIT SCENARIOSROUTENUMBERS CURRENT OPTIMAL NO MINIMUMor MAXIMUM"50 TROLLEY"MINIMUMINCREASEMIN. SIZETO 75INCREASEMIN. SIZETO 100ELIMINATEOTCINCREASECAPACITY OFBTC (no cap.costs)161 154 PCT PCTBCRTCBCRTCBTCPCTBCRTCPCTBCRTCBCRTC PCTBCRTCBCRTCLHEED162 160 PCT SIC LHEEDBTC163 161 PCT LHEEDBTCLHEED164 166 PCT LHEEDSICLHEED165 701A PCT LHEED LHEED166 7018 PCT LHEED LHEED167 210 NVT NVTBTCMN/TRMBIG NVTBTCMN/TRMNVTBTCNVTBIGNVTSICMN/TRMNVTBTC168 214 NVT SIC169 228 NVT SIC170 229 NVT BTC171 232 NUT BTC172 236 NUT BTC173 239 NVT BTC174 240 NVT NVTSICSIC NVTBTCNVTSICNVTSICNVTBTCMN/TRMNUTSIC175 241/42 NVT SIC BTC BTC BTC BTC SIC SIC176 246 NVT BIG NVTMN/TRM177 247 NVT BIG BIG SIC BTC SIC BIG SICPage 123CPLEX ROUTENUMBERS BC TRANSIT SCENARIOSROUTENUMBERS CURRENT OPTIMAL NO MINIMUMor MAXIMUM"50 TROLLEY"MINIMUM INCREASEMIN. SIZETO 75INCREASEMIN. SIZETO 100ELIMINATEOTCINCREASECAPACITY OFBTC (no cap.costs)178 286 NVT BTC179 292 NVT BTC BTC BTC BTC BTC BTC180 740 NVT NVTMN/TRMBTC NVTMN/TRMNVTMN/TRM181 310/11 SIC RICH SICRICH182 312 SIC183 314 STC184 315 SIC185 316 SIC186 317 SIC187 320 SIC SICCLVDL188 321 SIC189 390 STC190 322 STC191 323 SIC192 329 SIC193 325 SIC194 328 SIC195 332 SIC196 326 SICPage 12 4CPLEX ROUTENUMBERS BC TRANSIT SCENARIOSROUTENUMBERS CURRENT OPTIMAL NO MINIMUMor MAXIMUM "50 TROLLEY"MINIMUMINCREASEMIN. SIZETO 75INCREASEMIN. SIZETO 100ELIMINATEOTCINCREASECAPACITY OFBTC (no cap.costs)197 335 SIC SICLHEED198 330 STC SICLHEEDSICLHEED199 501 SIC200 509 SIC SICLHEEDSICLHEED201 340 SIC SICBCRTCSICLHEEDSICBCRTCSICBCRTCSICBCRTCSTCBCRTCSICLHEED202 353 SIC SICBCRTCSICBCRTCSICBCRTCSICBCRTCSICBCRTCSTCBCRTCSICBCRTC203 354 SIC204 393 SIC205 395 SIC206 502 SIC SICCLVDL207 506 SIC CLVDL208 507 SIC PCT CLVDL PCT PCT PCT PCT SICLHEED209 511 SIC SICCLVDL210 640 SIC SICRICHPage 125APPENDIX 10CURRENT vs. OPTIMAL BUS ALLOCATIONSReallocation Route CurrentGarageOptimal Garage,3 OTC OTCFULL 4 OTC MN/TRM7 OTC OTC8 OTC OTCPARTIAL 9 OTC OTC^(0.55)MN/TRM^(0.45)PARTIAL 10 OTC OTC^(0.20)MN/TRM^(0.80)14 OTC OTC15 OTC OTCPARTIAL 16 OTC OTC^(0.60)MN/TRM^(0.40)17 OTC OTCPARTIAL 19 OTC OTC^(0.52)MN/TRM (0.48)20 OTC OTC22A OTC OTCFULL 22B OTC BTC^(0.53)MN/TRM^(0.47)32 OTC OTCPARTIAL 41 OTC BTC^(0.78)OTC^(0.22)42 OTC OTC51 OTC OTC400 OTC OTC404 OTC OTCFULL 413 OTC BCRTCPage 126Reallocation Route CurrentGarageOptimal GaragePARTIAL 601 OTC OTC^(0.99)MN/TRM^(0.01)FULL 1 BTC OTC2 BTC BTC25 BTC BTC26 BTC BTC27 BTC BTC28 BTC BTC29 BTC BTCPARTIAL 31 BTC BTC^(0.67)MN/TRM^(0.33)FULL 49 BTC OTCFULL 50 BTC MN/TRMFULL 101 BTC BCRTCFULL 102 BTC STC^(0.71)BCRTC^(0.29)FULL 106 BTC BCRTCFULL 108 BTC STC^(0.83)BCRTC^(0.17)PARTIAL 110 BTC BCRTC^(0.06)BTC^(0.94)PARTIAL 114 BTC BCRTC^(0.17)BTC^(0.83)FULL 115 BTC BCRTCPARTIAL 116 BTC BCRTC^(0.55)BTC^(0.45)FULL 112 BTC BCRTCPARTIAL 120 BTC BCRTC^(0.29)BTC^(0.62)MN/TRM^(0.09)130 BTC BTCPage 127Reallocation Route CurrentGarageOptimal Garage131/32 BTC BTC134 BTC BTC137 BTC BTC139 BTC BTC140 BTC BTC141 BTC BTC135 BTC BTCPARTIAL 142 BTC BCRTC^(0.33)BTC^(0.67)144 BTC BTC136 BTC BTC109 BTC BTCFULL 410 BTC BCRTCFULL 100 PCT OTC158 PCT PCT143 PCT PCT147 PCT PCT151 PCT PCTPARTIAL 154 PCT PCT^(0.41)BCRTC^(0.59)160 PCT PCT161 PCT PCT166 PCT PCT701A PCT PCT701B PCT PCTPARTIAL 210 NVT NVT^(0.12)BTC^(0.87)MN/TRM^(0.01)214 NVT NVTPage 128Reallocation Route CurrentGarageOptimal Garage228 NVT NVT229 NVT NVT232 NVT NVT236 NVT NVT239 NVT NVTPARTIAL 240 NVT NVT^(0.73)BTC^(0.27)FULL 241/42 NVT BTC246 NVT NVTFULL 247 NVT BTC286 NVT NVTFULL 292 NVT BTCPARTIAL 740 NVT NVT^(0.76)MN/TRM^(0.24)310/11 STC STC312 STC STC314 STC STC315 STC STC316 STC STC317 STC STC320 STC STC321 STC STC390 STC STC322 STC STC323 STC STC329 STC STC325 STC STC328 STC STCPage 129Reallocation Route CurrentGarageOptimal Garage332 STC STC326 STC STC335 STC STC330 STC STC501 STC STC509 STC STCPARTIAL 340 STC STC^(0.91)BCRTC^(0.09)PARTIAL 353 STC STC^(0.32)BCRTC^(0.68)354 STC STC393 STC STC395 STC STC502 STC STC506 STC STCFULL 507 STC PCT511 STC STC640 STC STC"FULL" refers to those routes that are completely reallocatedto another transit centre (18 such routes). "PARTIAL" signifiesthose routes which are partially allocated between another centreand the current depot (18 such routes).Occasionally, the buses of a route are split betweenalternative transit centres. For these cases, the numbers givenafter each location represent the proportion of buses allocated tothat transit centre.Page 130APPENDIX 11TOTAL BUS ALLOCATIONS AND COST BREAKDOWNSCPLEXSITE # LOCATION TOTAL NUMBER OF BUSESCURRENT OPTIMAL NO MIN. ORMAX. MIN. 50TROLLEYS INCREASEMIN. SIZETO 75INCREASEMIN. SIZETO 100ELIMINATEOTC INCREASEBTCCAPACITY(no. cap.costs)S11 NorthVancouver78 60 0 60 60 60 60 60S12 PortCoquit lam114 114 0 113 129 105 125 0S13 Surrey 132 123 122 123 131 131 131 143S14 BCRTCfacility0 50 22 50 75 100 50 52S15 Cloverdale 0 0 4 0 0 0 0 0S16 LougheedPark & Ride0 0 21 0 0 0 0 51S17 Richmond 0 0 9 0 0 0 130 0S18 Burnaby 166 160 378 160 160 160 160 250S19 Oakridge 410 350 350 350 350 350 0 350S20 Main &Terminal0 50 0 51 0 0 250 0COST BREAKDOWNSDEADHEAD COSTS $14,885,587 $13,288,690 $13,693,827 $13,278,958 $13,430,532 $13,268,812 $14,163,252 $13,414,902CAPITAL COSTS 0 $1,035,400 $843,886 $1,047,060 $1,006,475 $1,232,675 $4,067,340 $1,273,334SALVAGE VALUES 0 0 ($1,060,969) 0 0 0 ($2,685,066) ($816,130)TOTAL COSTS I^$14,885,587 I^$14,324,090 $13,476,744 $14,326,018 $14,437,007 $14,501,487 $15,545,526 $13,872,106Page 131APPENDIX 12.1MINIMUM CANDIDATE TRANSIT CENTRE SIZE OF 100PROPOSED BUS ASSIGNMENTS - NVTDIESEL BUSESCplex RouteNumberBC Transit Route Monday - Friday Saturday Sunday - HolidaysNumber AM PM 1 21AM PM 1 2 AM PM 1 2167 210I , A41 i168 214 1 3 1 2 1169 228 2 3 1 1 1 1 1 1170 229 1 3 3 2 3 2 2171 232 1 1 3 3 3172 236 2 2 1173 239 1 2 3 3 3 3 2 2174 240 6 6176 246 5 4 5 1 1 2 2 1 2178 286 2 2180 740 1 3 3 3 3PERIOD TOTAL 18 13 22 14 3 5 12 14 3 4 7 11ACTIVE BUSES 54 31 22SPARES 6 29 3811TOTAL BUSES ALLOCATED -^60 60 60Page 132APPENDIX 12.2MINIMUM CANDIDATE TRANSIT CENTRE SIZE OF 100PROPOSED BUS ASSIGNMENTS - PCTDIESEL BUSESCplex RouteNumber BC TransitRoute Number Monday - Friday Saturday Sunday - Holiday/ AM PM 1 2 AM PM 1 2 AM PM 1I 2137 110 1i153 136 1 1157 158 4 3 6 2 5 1 1 2158 143 1 1159 147 1 2 4 5 1 6 3 1 5160 151 12 8 10 8 4 10 3 9162 160 13 12 6 1 5163 161 2 1 3 1 1 1164 166 1 2 1 1165 701A 2 3 2 1 2166 701B 4 1 3 2 1208 507 _^2 1 1 1PERIOD TOTAL 42 34 37 16 0 2 23 18 0 2 4 20ACTIVE BUSES 95 43 26SPARES 10I621179ITOTAL BUSES ALLOCATED 105 105 105Page 133APPENDIX 12.3MINIMUM CANDIDATE TRANSIT CENTRE SIZE OF 100PROPOSED BUS ASSIGNMENTS - SICDIESEL BUSESCplex RouteNumberBC Transit Route Monday - Friday Saturday Sunday - HolidayNumberAM^, PM 1 2 AM PM 1 r 2 AM i PM 1 2134 102A1136 108 1181 310/11 8 6182 312 6 5 4 3 3 3 1 3183 314 2 2184 315 1 2185 316 2 1 2 2 2 2 2186 317 2 1 3 3187 320 1 3 4 3 4 1 3188 321 2 1 3 2 3 4 2 2189 390 1 2 1190 322 1 1 1191 323 1 1 1 1 1192 329 2 1 1 1193 325 3 3 1 1 1194 328 1 1 1 1195 332 1 1 1 1196 326 2 1 1 1Page 13 4Cplex RouteNumber BC Transit Route Monday - Friday SaturdaySunday - HolidayNumberAM PM 1 2 AM ,^PM 1 2 AM PM 1 2197 335 1 1198 330 3 5 2 2 1 2 3199 501 1 2 1 2 1 2 1200 509 2 1201 340 4 4 2 2202 353 14 2 1203 354 1 1204 393 3 3205 395 3 3206 502 2 2 1207 506 1 1209 511 1 2 1210 640 2_ 2 2PERIOD TOTAL^60 48 33 26 0 0 25 23^0 0 8 20ACTIVE BUSES 119 48 28ISPARES^12I83 103TOTAL BUSES ALLOCATED^131 131 131Page 135APPENDIX 12.4MINIMUM CANDIDATE TRANSIT CENTRE SIZE OF 100PROPOSED BUS ASSIGMENTS - BCRTCDIESEL BUSESCplex RouteNumberBC Transit Monday - Friday Saturday Sunday - HolidayRoute NumberAM PM 1 2 AM PM 1 2 AM PM 1 2119 400 2121 413 3126 26 5 1129 29 1 1133 101 3 2 2 2 2 2 2134 102 1 1135 106 1 6 3 4 4 1 4136 108 1137 110 2 1 1 1138 114 1 1 1 1139 115 1 1 1140 116 2 2 1 1141 112 2 1 3 1 1 2 2142 120 1 1 3 4 5 3 3143 130 1144 131/32 3 2 3151 142 1 1 1152 144 2 2 2Page 136Cplex RouteNumber BC Transit Monday - Friday Saturday Sunday - HolidayRoute Number AM PM 1 2 AM PM , 1 2 AM PM 1 2155 410 3 3156 100 2 2 1161 154 7 6 7 4 4 5 5201 340 2 2 2202 353 13 2 1 _ 2PERIOD TOTAL^31 31 38 21^0 0 24 24^0 0 4 22ACTIVE BUSES 90 48 26SPARES^ 10I52I7411TOTAL BUSES ALLOCATED^100 100 100Page 137APPENDIX 12.5MINIMUM CANDIDATE TRANSIT CENTRE SIZE OF 100PROPOSED BUS ASSIGNMENTS - BTCTROLLEYS AND DIESEL BUSESCplex RouteNumbersBC Transit Monday - Friday Saturday Sunday - HolidaysRoute NumbersAM PM 1 2 AM PM 1 , 2 AM PM 1 2TROLLEYS:■ I102 4 1 6 5 3 5 2 5105 9 13 9 20 3 2 4 8 6 6106 10 5 6 10 4 2 6 5 4 5PERIOD TOTAL 19 15 36 12 0 4 13 18 0 0 12 16ACTIVE BUSES 67 35 28SPARES 5 37 44TOTAL TROLLEY BUSES 72 72 72DIESELS:A ■ 1114 22B 6 1 5 3124 2 4 4125 25 4 2 6 3 4 4 2 4126 26 4 2 1 1 1127 27 5 1 3 2 1 1128 28 1 1 2 2 2 1 1129 29 1 2137 110 2143 130 2 4 5 3 4Page 138Cplex RouteNumbersBC Transit Monday - Friday Saturday Sunday - HolidaysRoute NumbersAM PM 1 2 AM PM 1 2 AM PM 1 2144 131/32 3145 134 2 1 2 1 1 2 1146 137 1 1 1 2147 139 1 2148 140 1149 141 1150 135 5 3 1 2 2 3 3152 144 2 1 1153 136 2 1154 109 1 1 1167 210 12 11 4 1 4 4174 240 3 1 1 2 3175 241/42 6 3177 247 2 2179 292 1PERIOD TOTAL 38 42 24 16 0 2 23 35 0 3 7 29ACTIVE BUSES 82 60 39SPARES 6 28 49TOTAL DIESEL BUSES 88 88 88TOTAL TROLLEY BUSES _^72 72 72TOTAL BUSES ALLOCATED^1^160 I^160 I^160Page 139APPENDIX 12.6MINIMUM CANDIDATE TRANSIT CENTRE SIZE OF 100PROPOSED BUS ASSIGNMENTS - OTCTROLLEYS AND DIESEL BUSESCplex RouteNumbersBC Transit Monday - Friday Saturday Sunday - HolidayRoute Numbers AM PM 1 2 AM PM 1 2 AM PM 1 2TROLLEYS:101 3 6 5 13 5 2 11 5 10 4103 7 2 1 6 5 4 7 1 4 5104 8 2 4 8 8 3 7 8 2 7 5107 14 4 6 7 4 3 3 5 3 6108 15 3 4 5 3 2 4 3 1 3 2109 16 4 1 7 2 4 5 1 1 4110 17 2 4 5 2 2 3 2 2 2111 19 4 2 6 4 1 5 4 2 5112 20 10 8 15 7 4 15 7 3 4 9PERIOD TOTAL 37 35 72 40 0 14 56 46 0 8 36 42ACTIVE BUSES 149 116 86SPARES 15 48I78ITOTAL TROLLEYS ALLOCATED 164 164 164DIESELS:113 22A 7 7 4 8 1 6 3 9114 22B 7 4I115 32 4 4Page 14 0Cplex RouteNumbersBC Transit Monday - Friday Saturday Sunday - HolidayRoute Numbers AM PM 1 2 AM PM 1 2 AM PM 1 2116 41 7 4 4 6 4 6 2 5117 42 1 1 1118 51 1 1 1119 400 34 30 17 9 1 9 14 3 7 8120 404 4 4 7 1 1 3 3 1 2 3122 601 12 12 12 2 4 3 7 2 3 5123 1 6 2 6 2130 31 2 1131 49 3 4 3 4 4 3 1 2 2132 50 2156 100 2 2 1 1 2PERIOD TOTAL 78 68 59 32^5 8 43 34 0 6 18 36ACTIVE BUSES 169 85 60SPARES 17 101I126TOTAL DIESELS ALLOCATED 186 186 186TOTAL TROLLEYS ALLOCATED  164 164 164TOTAL BUSES ALLOCATED^1^350 I^350 1^350Page 141APPENDIX 13ELIMINATION OF OTCPROPOSED BUS ASSIGMENTS - RICHDIESEL BUSESCplex RouteNumber BC Transit Monday - Friday Saturday Sunday - HolidayRoute Number AM PM 1 2 AM PM 1 2 AM PM 1 2113 22AA7 7■4 4 1119 400 34 30 17 9 1 9 14 3120 404 4 4 7 1 1 3 3 1 2 3121 413 2122 601 12 5 12 2155 410 3156 100 2 2 2 1 2 1 1 2181 310/11 6210 640 2 2PERIOD TOTAL 59 59 42 17^1 1 15 20 0 5 2 7ACTIVE BUSES 118 36 14SPARES 12I94I116ITOTAL BUSES ALLOCATED 130 130 130Page 142APPENDIX 14TRANSIT CENTRE ALLOCATIONS FOR DRIVER RELIEFThe weights used to represent the proportion of a route's buses allocated between alternative transitcentres should not be employed when examining driver relief. The aforementioned weights considered all buses,both peak and all-day vehicles. However, peak service buses do not require driver relief. Therefore, theproportions used to reflect assignment of a route's buses between multiple transit centres should examine onlyall-day trips.The following is a list of the routes which will be examined for their implication on driver relief:Route Current Garage Optimal Garage4 OTC MN/TRM9 OTC OTC^(0.91)MN/TRM^0.09)10 OTC OTC (0.33)MN/TRM^0.67)16 OTC OTC (0.86)MN/TRM^0.14)19 OTC OTC (0.76)MN/TRM^0.24)22B OTC BTC^(0.71)MN/TRM^0.29)41 OTC SIC^(0.75)OTC (0.25)413 OTC BCRTC601 OTC OTC^(1.00)MN/TRM (0.00)The Main & Terminal^location is onlyallocated AM peak assignments.1 BTC OTC31 BTC BTCMN/TRMThis route only offers peak service,^sodriver relief^is not a consideration.49 SIC OTC50 BTC MN/TRM101 BTC BCRTC102 BTC SIC^(0.71)BCRTC (0.29)106 SIC BCRTC108 SIC SIC (0.83)BCRTC^(0.17)110 BTC BCRTC^(0.17)BTC (0.83)114 SIC BCRTC^(0.17)BTC (0.83)115 BTC BCRTC116 BTC BCRTC^(0.17)SIC (0.83)112 SIC BCRTCPage 143Route Current Garage Optimal Garage120 BTC BCRTC (0.24)BTC (0.76)MN/TRM (0.00)The Main & Terminal^location is onlyallocated PM peak assignments.142 BTC BCRTC (0.00)BTC^(1.00)The BCRTC location is only allocated AMpeak assignments.410 BTC BCRTC100 PCT OTC154 PCT PCT (0.80)BCRTC (0.20)210 NVT NVT (0.38)BTC (0.58)MN/TRM (0.04)240 NVT NVT^(0.83)BTC^(0.17)241/42 NVT BTC247 NVT BTC292 NVT BTC740 NVT NVTMN/TRMThis route only offers peak service, sodriver relief^is not a consideration.340 STC SIC (0.77)BCRTC^(0.23)353 SIC SIC^(0.75)BCRTC (0.25)507 SIC PCTPage 144APPENDIX 15CALCULATION OF WEEKLY DRIVER RELIEFSRouteDaily Driver Reliefs WeeklyM-F M-F Sat Sat Sun/HolSun/Holdriverreliefs1 2 1 2 1 24 6 5 3 5 2 5 1059 20 3 4 8 6 6 16810 10 4 6 5 4 5 12016 7 2 4 5 1 4 7819 6 4 5 4 2 5 9522B 4 0 5 3 0 0 3141 4 6 4 6 2 5 108413 0 0 0 0 0 0 01 6 2 6 2 0 0 6049 3 4 4 3 2 5 7750 0 0 0 0 0 2 4101 2 2 2 2 0 2 40102 1 0 1 0 0 1 8106 6 3 4 4 1 4 81108 0 1 0 1 0 0 12110 1 1 0 1 0 1 19114 1 1 0 1 0 1 19115 0 0 0 1 0 1 4116 2 0 0 1 1 0 13112 3 1 1 2 0 2 34120 3 4 5 3 0 3 72410 0 0 0 0 0 0 0100 2 1 2 1 0 2 28Page 145RouteDaily Driver Reliefs WeeklyM-F M-F Sat Sat Sun/HolSun/Holdriverreliefs1 2 1 2 1 2154 7 4 4 5 0 5 99210 4 5 0 4 0 4 86240 6 0 1 2 0 3 41241/42 0 0 0 0 0 0 0247 0 0 0 0 0 0 0292 0 0 0 0 0 0 0340 2 2 2 2 0 2 40353 2 1 2 1 2 0 26507 0 0 1 0 1 0 2Page 146APPENDIX 16CALCULATION OF DRIVER RELIEF SAVINGSRoute Currentdist.(cm's)Optimaldist.(cm's)Currentdist.(km's)Optimaldist.(km's)CurrentHoursOptimalHoursWeeklyDriverReliefsWeeklyCurrentCostWeeklyOptimalCostAnnualCurrentCostAnnualOptimalCost($) ($) ($) ($)4 6.5 5 4.063 3.125 0.163 0.125 105 $341.25 $262.50 $17,745 $13,6509 5.5 5.5 3.438 3.438 0.138 0.138 168 $462.00 $462.00 $24,024 $24,02410 6.5 5.5 4.063 3.438 0.163 0.138 120 $390.00 $330.00 $20,280 $17,16016 11.5 10.52 7.188 6.575 0.288 0.263 78 $448.50 $410.28 $23,322 $21,33519 6.5 5.66 4.063 3.538 0.163 0.142 95 $308.75 $268.85 $16,055 $13,98022B 7 11.18 4.375 6.988 0.175 0.280 31 $108.50 $173.29 $5,642 $9,01141 3 13.125 1.875 8.203 0.075 0.328 108 $162.00 $708.75 $8,424 $36,855413 16 10.5 10.000 6.563 0.400 0.263 0 $0.00 $0.00 $0 $01 12.5 8 7.813 5.000 0.313 0.200 60 $375.00 $240.00 $19,500 $12,48049 11.5 4.5 7.188 2.813 0.288 0.113 77 $442.75 $173.25 $23,023 $9,00950 13 4.5 8.125 2.813 0.325 0.113 4 $26.00 $9.00 $1,352 $468101 14 5 8.750 3.125 0.350 0.125 40 $280.00 $100.00 $14,560 $5,200102 16.5 11.54 10.313 7.213 0.413 0.289 8 $66.00 $46.16 $3,432 $2,400106 11.5 3 7.188 1.875 0.288 0.075 81 $465.75 $121.50 $24,219 $6,318108 16 12.89 10.000 8.056 0.400 0.322 12 $96.00 $77.34 $4,992 $4,022110 8 8.34 5.000 5.213 0.200 0.209 19 $76.00 $79.23 $3,952 $4,120114 10.5 9.57 6.563 5.981 0.263 0.239 19 $99.75 $90.62 $5,187 $4,728115 11 3.5 6.875 2.188 0.275 0.088 4 $22.00 $7.00 $1,144 $364116 10 9.41 6.250 5.881 0.250 0.235 13 $65.00 $61.17 $3,380 $3,181112 15.5 3 9.688 1.875 0.388 0.075 34 $263.50 $51.00 $13,702 $2,652Page 147Route Currentdist.(cm's)Optimaldist.(cm's)Currentdist.(km's)Optimaldist.(km's)CurrentHoursOptimalHoursWeeklyDriverReliefsWeeklyCurrentCostWeeklyOptimalCostAnnualCurrentCostAnnualOptimalCost($) ($) ($) ($)120 3.5 5.3 2.188 3.313 0.088 0.133 72 $126.00 $190.80 $6,552 $9,922410 17 11 10.625 6.875 0.425 0.275 0 $0.00 $0.00 $0 $0100 33 10 20.625 6.250 0.825 0.250 28 $462.00 $140.00 $24,024 $7,280154 9.5 10.4 5.938 6.500 0.238 0.260 99 $470.25 $514.80 $24,453 $26,770210 5.5 4.75 3.438 2.969 0.138 0.119 86 $236.50 $204.25 $12,298 $10,621240 8.5 8.93 5.313 5.581 0.213 0.223 41 $174.25 $183.07 $9,061 $9,519241/42 7 14.5 4.375 9.063 0.175 0.363 0 $0.00 $0.00 $0 $0247 9 16 5.625 10.000 0.225 0.400 0 $0.00 $0.00 $0 $0292 5.5 3 3.438 1.875 0.138 0.075 0 $0.00 $0.00 $0 $0340 3 5.88 1.875 3.675 0.075 0.147 40 $60.00 $117.60 $3,120 $6,115353 9.5 12.38 5.938 7.738 0.238 0.310 26 $123.50 $160.94 $6,422 $8,369507 29 24 18.125 15.000 0.725 0.600 2 $29.00 $24.00 $1,508 $1,248TOTAL DRIVER RELIEF COSTS $321,373 $270,800ANNUAL SAVINGS $50,573PERCENTAGE SAVINGS 15.74%NOTE:1) According to the scale of the BC Transit route map, one cm = 0.625 kms.2) The average speed used for driver relief is 25 km/h.3)^The driver salary for calculating driver relief cost is $20 per hour.

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