Integrating routing decisions in public transportation problems

235 Pages·2014·3.251 MB·English

by  Marie E. Schmidt (auth.)

Springer Optimization and Its Applications 89
Marie E. Schmidt
Integrating
Routing Decisions
in Public
Transportation
Problems
Springer Optimization and Its Applications
VOLUME89
ManagingEditor
PanosM.Pardalos(UniversityofFlorida)
Editor–CombinatorialOptimization
Ding-ZhuDu(UniversityofTexasatDallas)
AdvisoryBoard
J.Birge(UniversityofChicago)
C.A.Floudas(PrincetonUniversity)
F.Giannessi(UniversityofPisa)
H.D.Sherali(VirginiaPolytechnicandStateUniversity)
T.Terlaky(McMasterUniversity)
Y.Ye(StanfordUniversity)
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Optimization has been expanding in all directions at an astonishing rate
during the last few decades. New algorithmic and theoretical techniques
havebeendeveloped,thediffusionintootherdisciplineshasproceededata
rapidpace,andourknowledgeofallaspectsofthefieldhasgrownevenmore
profound.Atthesametime,oneofthemoststrikingtrendsinoptimization
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engineering,medicine,economics,andothersciences.
The series Springer Optimization and Its Applications publishes under-
graduate and graduate textbooks, monographs and state-of-the-art exposi-
tory work that focus on algorithms for solving optimization problems and
alsostudyapplicationsinvolvingsuchproblems.Someofthetopicscovered
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multi-objectiveprogramming,descriptionofsoftwarepackages,approxima-
tiontechniquesandheuristicapproaches.
Forfurthervolumes:
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Marie E. Schmidt
Integrating Routing
Decisions in Public
Transportation Problems
123
MarieE.Schmidt
InstituteforNumericalandAppliedMathematics
Göttingen,Germany
ISSN1931-6828 ISSN1931-6836(electronic)
ISBN978-1-4614-9565-9 ISBN978-1-4614-9566-6(eBook)
DOI10.1007/978-1-4614-9566-6
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2013957935
MathematicsSubjectClassification(2010):90-02
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Preface
Tomodelandsolveoptimizationproblemsarisinginpublictransportationplanning,
dataaboutthepassengersisnecessaryandhastobeincludedinthemodelsinany
phase of the planning process. In particular, when aiming at minimizing the pas-
sengers’ travel time, information about passengers’ travel routes is indispensable.
Forexample,ifmanypassengerstravelbetweentwostationsusingthesameroute,
it may be beneficial to establish a high-speed line on this route; a good timetable
shouldofferlowwaitingtimesforconnectionswithhighpassengernumbers.
For this reason, many solution approaches assume a two-step procedure: in
the first step, passenger routes are determined using shortest path, flow, or traffic
assignmentprocedures.Inthesecondstep,theactualplanningoflines,timetables,
etc.,isdone.Thisapproachignoresthatformostpassengerstherearemanypossible
waystoreachtheirdestinationsinthepublictransportationnetwork;thus,theactual
connectionsthepassengerswilltakedependstronglyonthedecisionsmadeduring
theplanningphase.
In this book we aim at integrating the route determination procedure in the
optimizationprocessofpublictransportationproblems.Weconsiderthreeplanning
problems arising in public transportation planning: line planning specifies the
paths and frequencies of the train lines to be established based on data about
the infrastructure; timetabling determines arrival and departure times of trains at
stations;andthetaskofdelaymanagement istodecidewhethertrainsshouldwait
for feeder trains or depart on time in case of delays. In order to maximize the
passengers’ benefit, our objective is the minimization of the passengers’ overall
traveltime.
After formulating suitable network models for the considered problems with
integrated routing, we investigate the computational complexity of the integrated
problems. We prove NP-hardness results and derive polynomial algorithms for
special cases, furthermore we investigate the approximability of some of the
v
vi Preface
consideredproblems.Forsolvingtheintegratedproblems,wepresentexactinteger
programming approaches as well as a heuristic approach which alternates route
determinationandoptimizationsteps.
Göttingen,Germany MarieE.Schmidt
Contents
1 Introduction .................................................................. 1
1.1 Overview ................................................................ 1
1.2 Outline................................................................... 4
1.3 BasicConceptsUsedinThisBook .................................... 5
2 LinePlanning................................................................. 9
2.1 IntroductiontoLinePlanning .......................................... 9
2.1.1 LinePlanningProblems........................................ 9
2.1.2 LiteratureOverview ............................................ 12
2.1.3 TheLinePlanningProblemsConsideredinThisBook....... 14
2.1.4 OutlineoftheLinePlanningChapter.......................... 20
2.2 ModelingLinePlanningwithRouting................................. 20
2.2.1 TheChange-and-GoNetwork.................................. 21
2.2.2 LinePlanningintheChange-and-GoNetwork................ 23
2.2.3 TheLineNetwork .............................................. 25
2.2.4 UncapacitatedLinePlanningintheLineNetwork............ 28
2.3 SolvingLinePlanningWhenPartoftheSolutionIsFixed........... 30
2.3.1 SolvingUncapacitatedLinePlanningWhenPart
oftheSolutionIsFixed......................................... 30
2.3.2 SolvingCapacitatedLinePlanningWhenPart
oftheSolutionIsFixed......................................... 31
2.4 ClassificationofLinePlanningProblemswithRouting .............. 33
2.5 UncapacitatedLinePlanningwithRouting............................ 35
2.5.1 UncapacitatedLinePlanninginGeneralNetworks........... 35
2.5.2 UncapacitatedLinePlanninginLinearNetworks ............ 44
2.6 CapacitatedLinePlanningwithRouting .............................. 60
2.6.1 ComplexityofCapacitatedLinePlanningwithRouting ..... 60
2.6.2 IntegerProgrammingFormulations............................ 64
vii
viii Contents
3 Timetabling................................................................... 73
3.1 IntroductiontoTimetabling ............................................ 73
3.1.1 TimetablingProblems .......................................... 73
3.1.2 LiteratureOverview ............................................ 76
3.1.3 TheTimetablingProblemConsideredinThisBook.......... 79
3.1.4 OutlineoftheTimetablingChapter............................ 81
3.2 ModelingTimetablingwithRoutingUsing
Event-ActivityNetworks ............................................... 82
3.3 SolvingTimetablingWhenPartoftheSolutionIsFixed............. 85
3.4 ComplexityofTimetablingwithRouting ............................. 88
3.4.1 NP-HardnessofTimetablingwithRouting ................... 88
3.4.2 InapproximabilityofTimetablingwithRouting .............. 92
3.5 TimetablingwithRoutingBetweenEvents ........................... 97
3.6 AnExactAlgorithmforTimetablingwithRouting ................... 99
3.7 IntegerProgrammingFormulations.................................... 101
3.7.1 Flow-BasedFormulation....................................... 102
3.7.2 Virtual-Activity-BasedFormulation........................... 108
4 DelayManagement .......................................................... 113
4.1 IntroductiontoDelayManagement.................................... 113
4.1.1 DelayManagementProblems.................................. 113
4.1.2 LiteratureOverview ............................................ 117
4.1.3 TheDelayManagementProblemConsidered
inThisBook .................................................... 120
4.1.4 OutlineoftheDelayManagementChapter.................... 122
4.2 Modeling Delay Management with Routing Using
Event-ActivityNetworks ............................................... 123
4.3 SolvingDelayManagementWhenPartoftheSolutionIsFixed..... 126
4.4 ComplexityofDelayManagementwithRouting ..................... 130
4.4.1 NP-HardnessofDelayManagementwithRouting
forOneOD-Pair ................................................ 131
4.4.2 AnAlgorithmforDelayManagementwithRouting
withOneOD-Pair............................................... 136
4.4.3 NP-HardnessofDelayManagementwithRouting
forInstanceswithNTTProperty .............................. 151
4.4.4 InapproximabilityofDelayManagementwithRouting...... 155
4.5 IntegerProgrammingFormulation..................................... 162
5 An Iterative Solution Approach for General Network
ProblemswithRouting ..................................................... 167
5.1 ClassificationofNetworkProblemswithRouting .................... 167
5.2 AnIterativeHeuristic .................................................. 173
5.3 ThePriceofSequentiality ............................................. 175
5.4 AnalysisoftheIterativeHeuristicforTimetablingwithRouting .... 176
Contents ix
5.5 AnalysisoftheIterativeHeuristicforArcSpeed-Up................. 181
5.5.1 DefinitionoftheProblemArcSpeed-Up...................... 181
5.5.2 TheIterativeHeuristicforArcSpeed-Up ..................... 183
5.5.3 SolvingArcSpeed-UpExactly ................................ 185
5.5.4 ThePriceofSequentialityforArcSpeed-Up ................. 186
6 ConclusionsandOutlook ................................................... 207
FrequentlyUsedNotation....................................................... 213
References......................................................................... 217
Index............................................................................... 225