Chapter 2 Time constrained routing and scheduling

Publisher Summary Time constrained routing and scheduling problems are encountered in a variety of industrial and service sector applications, ranging from logistics and transportation systems to material handling systems in manufacturing. The traveling salesman problem with time windows has applications in single and multiple vehicle problems. The vehicle routing problem with time windows has many industrial applications including those where dock availability is a bottleneck such as for distribution centers. This chapter describes the significant advances made in time constrained routing and scheduling. In terms of solution methodology capable of solving realistic size problems, this field has seen a natural progression from ad-hoc methods to simple heuristics, to optimization-based heuristics and recently optimal algorithms. The chapter discusses fixed schedule problems and develops in detail the Dantzig-Wolfe decomposition/column generation approach which will then be applied to many of the other problem types. The vehicle routing problem with time windows and several important problem variants including the multiple traveling salesman problems is explored. The chapter examines a unified framework for fleet and crew scheduling problems.

[1]  H. G. M. Pullen,et al.  A computer application to a transport scheduling problem , 1967, Comput. J..

[2]  Alexander H. G. Rinnooy Kan,et al.  Vehicle Routing with Time Windows , 1987, Oper. Res..

[3]  Roy E. Marsten,et al.  Crew Planning at Flying Tiger: A Successful Application of Integer Programming , 1979 .

[4]  Achim Lamatsch,et al.  An Approach to Vehicle Scheduling with Depot Capacity Constraints , 1992 .

[5]  Edith Heurgon Un problème de recouvrement : l'habillage des horaires d'une ligne d'autobus , 1972 .

[6]  Arthur J. Swersey,et al.  Scheduling School Buses , 1984 .

[7]  H. Psaraftis An Exact Algorithm for the Single Vehicle Many-to-Many Dial-A-Ride Problem with Time Windows , 1983 .

[8]  Roy E. Marsten,et al.  Exact solution of crew scheduling problems using the set partitioning model: Recent successful applications , 1981, Networks.

[9]  E. Martins On a multicriteria shortest path problem , 1984 .

[10]  Celso C. Ribeiro,et al.  A Column Generation Approach to the Multiple-Depot Vehicle Scheduling Problem , 1991, Oper. Res..

[11]  Gilbert Laporte,et al.  Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints , 1991, Oper. Res. Lett..

[12]  Matteo Fischetti,et al.  The Fixed Job Schedule Problem with Spread-Time Constraints , 1987, Oper. Res..

[13]  Cynthia Barnhart,et al.  A column-generation technique for the long-haul crew-assignment problem , 1994 .

[14]  Y. P. Aneja,et al.  Shortest chain subject to side constraints , 1983, Networks.

[15]  André Langevin,et al.  A two-commodity flow formulation for the traveling salesman and the makespan problems with time windows , 1990, Networks.

[16]  Martin Desrochers,et al.  CREW-OPT: Subproblem Modeling in a Column Generation Approach to Urban Crew Scheduling , 1992 .

[17]  Louis M. Dalberto,et al.  Improving the Distribution of Industrial Gases with an On-Line Computerized Routing and Scheduling Optimizer , 1983 .

[18]  Jacques Desrosiers,et al.  Survey Paper - Time Window Constrained Routing and Scheduling Problems , 1988, Transp. Sci..

[19]  Cynthia Barnhart,et al.  Deadhead Selection for the Long-Haul Crew Pairing Problem , 1995, Oper. Res..

[20]  Mwp Martin Savelsbergh,et al.  VEHICLE ROUTING WITH TIME WINDOWS: OPTIMIZATION AND APPROXIMATION. VEHICLE ROUTING: METHOD AND STUDIES. STUDIES IN MANAGEMENT SCIENCE AND SYSTEMS - VOLUME 16 , 1987 .

[21]  Giorgio Gallo,et al.  Network models for vehicle and crew scheduling , 1984 .

[22]  George B. Dantzig,et al.  Decomposition Principle for Linear Programs , 1960 .

[23]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[24]  Anthony Wren,et al.  A bus crew scheduling system using a set covering formulation , 1988 .

[25]  Ulf Bokinge,et al.  Improved vehicle scheduling in public transport through systematic changes in the time-table , 1980 .

[26]  Martin Desrochers,et al.  A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows , 1990, Oper. Res..

[27]  Edward K. Baker,et al.  Technical Note - An Exact Algorithm for the Time-Constrained Traveling Salesman Problem , 1983, Oper. Res..

[28]  Grant Edmund Martin Aircraft Scheduling Considered As An N-Task, M-Parallel Machine Problem With Start-Times And Deadlines , 1981 .

[29]  M. Minoux,et al.  A new approach for crew pairing problems by column generation with an application to air transportation , 1988 .

[30]  M. Padberg,et al.  Solving airline crew scheduling problems by branch-and-cut , 1993 .

[31]  J. Desrosiers,et al.  Plus court chemin avec contraintes d'horaires , 1983 .

[32]  J. P. Arabeyre,et al.  The Airline Crew Scheduling Problem: A Survey , 1969 .

[33]  Derek Graham,et al.  A COMPARISON OF HEURISTICS FOR A SCHOOL BUS SCHEDULING PROBLEM , 1986 .

[34]  G. Laporte,et al.  Exact Algorithms for the Vehicle Routing Problem , 1987 .

[35]  D. I. Calvert,et al.  Computer Scheduling of Public Transport 2 , 1986 .

[36]  Thomas L. Magnanti,et al.  Combinatorial optimization and vehicle fleet planning: Perspectives and prospects , 1981, Networks.

[37]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[38]  M. Goetschalckx,et al.  The vehicle routing problem with backhauls , 1989 .

[39]  L. R. Ford,et al.  NETWORK FLOW THEORY , 1956 .

[40]  Jean-Yves Potvin,et al.  A parallel route building algorithm for the vehicle routing and scheduling problem with time windows , 1993 .

[41]  Lucena Filho,et al.  Exact solution approaches for the vehicle routing problem , 1986 .

[42]  Paolo Toth,et al.  State-space relaxation procedures for the computation of bounds to routing problems , 1981, Networks.

[43]  Sylvie Gélinas,et al.  A new branching strategy for time constrained routing problems with application to backhauling , 1992, Ann. Oper. Res..

[44]  D. R. Fulkerson Flow Networks and Combinatorial Operations Research , 1966 .

[45]  Jacques Desrosiers,et al.  Technical Note - Optimizing the Schedule for a Fixed Vehicle Path with Convex Inconvenience Costs , 1989, Transp. Sci..

[46]  François Soumis,et al.  A model for large-scale aircraft routing and scheduling problems , 1980 .

[47]  Stefano Pallottino,et al.  Shortest-path methods: Complexity, interrelations and new propositions , 1984, Networks.

[48]  Jan Karel Lenstra,et al.  Variable-Depth Search for the Single-Vehicle Pickup and Delivery Problem with Time Windows , 1993, Transp. Sci..

[49]  M. Minoux,et al.  Plus court chemin avec contraintes : Algorithmes et applications , 1975 .

[50]  Clifford S. Orloff,et al.  Route Constrained Fleet Scheduling , 1976 .

[51]  M. Fischetti,et al.  Heuristic algorithms for the multiple depot vehicle scheduling problem , 1993 .

[52]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[53]  Jacques Desrosiers,et al.  Routing with time windows by column generation , 1983, Networks.

[54]  Jonathan F. Bard,et al.  A GRASP for the Vehicle Routing Problem with Time Windows , 1995, INFORMS J. Comput..

[55]  Martin W. P. Savelsbergh,et al.  The Vehicle Routing Problem with Time Windows: Minimizing Route Duration , 1992, INFORMS J. Comput..

[56]  Jacques Desrosiers,et al.  An Algorithm for Mini-Clustering in Handicapped Transport , 1991 .

[57]  Marius M. Solomon,et al.  Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints , 1987, Oper. Res..

[58]  Shen Lin Computer solutions of the traveling salesman problem , 1965 .

[59]  Martin Desrochers,et al.  A Column Generation Approach to the Urban Transit Crew Scheduling Problem , 1987, Transp. Sci..

[60]  Pierre Hansen,et al.  Bicriterion Path Problems , 1980 .

[61]  Lawrence Bodin,et al.  Routing and Scheduling of School Buses by Computer , 1979 .

[62]  Jacques Desrosiers,et al.  Large Scale Multi-Vehicle Dial-a-Ride Problems , 1989 .

[63]  Paul M. Thompson,et al.  Cyclic Transfer Algorithm for Multivehicle Routing and Scheduling Problems , 1993, Oper. Res..

[64]  Jacques Desrosiers,et al.  An Optimal Algorithm for the Traveling Salesman Problem with Time Windows , 1991, Oper. Res..

[65]  P. Toth,et al.  Some New Branching and Bounding Criteria for the Asymmetric Travelling Salesman Problem , 1980 .

[66]  Martin Desrochers,et al.  Optimal urban bus routing with scheduling flexibilities , 1984 .

[67]  D. R. Fulkerson,et al.  MINIMIZING THE NUMBER OF CARRIERS TO MEET A FIXED SCHEDULE , 1954 .

[68]  Jacques Desrosiers,et al.  An Application of Vehicle-Routing Methodology to Large-Scale Larvicide Control Programs , 1990 .

[69]  Richard D. McBride,et al.  Flight crew scheduling , 1993 .

[70]  Bruce L. Golden,et al.  VEHICLE ROUTING: METHODS AND STUDIES , 1988 .

[71]  D. M. Ryan,et al.  Express: Set Partitioning for Bus Crew Scheduling in Christchurch , 1992 .

[72]  George Papageorgiou,et al.  The Complexity of the Travelling Repairman Problem , 1986, RAIRO Theor. Informatics Appl..

[73]  L. Appelgren Integer Programming Methods for a Vessel Scheduling Problem , 1971 .

[74]  Leif H. Appelgren,et al.  A Column Generation Algorithm for a Ship Scheduling Problem , 1969 .

[75]  H. Joksch The shortest route problem with constraints , 1966 .

[76]  Ira Gershkoff,et al.  Optimizing Flight Crew Schedules , 1989 .

[77]  Christos H. Papadimitriou,et al.  The Euclidean Traveling Salesman Problem is NP-Complete , 1977, Theor. Comput. Sci..

[78]  J F Barutt,et al.  AIRLINE CREW SCHEDULING : SUPERCOMPUTERS AND ALGORITHMS , 1990 .

[79]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[80]  Matteo Fischetti,et al.  An Additive Bounding Procedure for Combinatorial Optimization Problems , 1989, Oper. Res..

[81]  Paolo Toth,et al.  Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations , 1981, Math. Program..

[82]  Marius M. Solomon,et al.  Routing and scheduling on a shoreline with release times , 1990 .

[83]  Teodor Gabriel Crainic,et al.  The Column Generation Principle And The Airline Crew Scheduling Problem , 1987 .

[84]  José M. P. Paixão,et al.  Multiple Depot Vehicle Scheduling Problem: A New Heuristic Based on Quasi-Assignment Algorithms , 1992 .

[85]  Martin Desrochers,et al.  A Breakthrough in Airline Crew Scheduling , 1991 .

[86]  H. Stern,et al.  DEFICIT FUNCTION BUS SCHEDULING WITH DEADHEADING TRIP INSERTIONS FOR FLEET SIZE REDUCTION , 1981 .

[87]  Harilaos N. Psaraftis,et al.  A Dynamic Programming Solution to the Single Vehicle Many-to-Many Immediate Request Dial-a-Ride Problem , 1980 .

[88]  Moshe B. Rosenwein,et al.  An interactive optimization system for bulk-cargo ship scheduling , 1989 .

[89]  Jacques Desrosiers,et al.  A Dynamic Programming Solution of the Large-Scale Single-Vehicle Dial-A-Ride Problem with Time Windows , 1984 .

[90]  Dag Wedelin Efficient Algorithms for Probabilistic Inference, Combinatorial Optimization and the Discovery of Causal Structure from Data , 1993 .

[91]  Marius M. Solomon,et al.  On the worst-case performance of some heuristics for the vehicle routing and scheduling problem with time window constraints , 1986, Networks.

[92]  Martin W. P. Savelsbergh,et al.  Local search in routing problems with time windows , 1984 .

[93]  Rajendra S. Solanki,et al.  An Execution Planning Algorithm for Military Airlift , 1991 .

[94]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[95]  Monique Guignard-Spielberg,et al.  Lagrangean decomposition: A model yielding stronger lagrangean bounds , 1987, Math. Program..

[96]  Eric Gelman,et al.  Recent Advances in Crew-Pairing Optimization at American Airlines , 1991 .

[97]  John N. Tsitsiklis,et al.  Special cases of traveling salesman and repairman problems with time windows , 1992, Networks.

[98]  Matteo Fischetti,et al.  A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem , 2001 .

[99]  Thomas M. Cook,et al.  A SIMULATION AND STATISTICAL ANALYSIS OF STOCHASTIC VEHICLE ROUTING WITH TIMING CONSTRAINTS , 1978 .

[100]  G. Dantzig,et al.  THE DECOMPOSITION ALGORITHM FOR LINEAR PROGRAMS , 1961 .

[101]  Helman Stern,et al.  Minimal Resources for Fixed and Variable Job Schedules , 1978, Oper. Res..

[102]  Nigel Hamer,et al.  The HASTUS System: New Algorithms and Modules for the 90s , 1992 .

[103]  M. Desrochers,et al.  A reoptimization algorithm for the shortest path problem with time windows , 1988 .

[104]  J. Desrosiers,et al.  Methods for routing with time windows , 1986 .

[105]  J. Ferland,et al.  Vehicles scheduling with sliding time windows , 1989 .

[106]  G. Mitra,et al.  Computer Scheduling of Public Transport , 1982 .

[107]  K. W. Knight,et al.  Vehicle Scheduling with Timed and Connected Calls: A Case Study , 1968 .

[108]  L. Bodin ROUTING AND SCHEDULING OF VEHICLES AND CREWS–THE STATE OF THE ART , 1983 .

[109]  Lawrence Bodin,et al.  Optimizing Single Vehicle Many-to-Many Operations with Desired Delivery Times: I. Scheduling , 1985, Transp. Sci..

[110]  U. Pape,et al.  Algorithm 562: Shortest Path Lengths [H] , 1980, TOMS.

[111]  Robert A. Russell,et al.  Technical Note - An Effective Heuristic for the M-Tour Traveling Salesman Problem with Some Side Conditions , 1977, Oper. Res..

[112]  Marshall L. Fisher,et al.  A generalized assignment heuristic for vehicle routing , 1981, Networks.

[113]  Jacques Desrosiers,et al.  Daily Aircraft Routing and Scheduling , 1994 .

[114]  Candace Arai Yano,et al.  Vehicle Routing at Quality Stores , 1987 .

[115]  M. Desrochers,et al.  A Generalized Permanent Labelling Algorithm For The Shortest Path Problem With Time Windows , 1988 .

[116]  Nigel H. M. Wilson,et al.  A heuristic algorithm for the multi-vehicle advance request dial-a-ride problem with time windows , 1986 .

[117]  Harilaos N. Psaraftis,et al.  Scheduling Large-Scale Advance-Request Dial-A-Ride Systems , 1986 .

[118]  Bruce L. Golden,et al.  A Planning Heuristic for Military Airlift , 1992 .

[119]  Jean-Yves Potvin,et al.  A Generalized K-Opt Exchange Procedure For The MTSP , 1989 .

[120]  Jacques Desrosiers,et al.  The Pickup and Delivery Problem with Time Windows , 1989 .

[121]  Mathieu Willem Paul Savelsbergh,et al.  Computer aided routing , 1992 .

[122]  Warren B. Powell,et al.  An Optimization-Based Heuristic for Vehicle Routing and Scheduling with Soft Time Window Constraints , 1992, Transp. Sci..

[123]  J Potvin,et al.  A tabu search heuristic for the vehicle routing problem with time windows , 1992 .

[124]  J. K. Lenstra,et al.  Complexity of vehicle routing and scheduling problems , 1981, Networks.

[125]  M. Fisher,et al.  Optimal solution of set covering/partitioning problems using dual heuristics , 1990 .

[126]  Anthony Wren,et al.  Computer Scheduling of Public Transportation: Urban Passenger Vehicle and Crew Scheduling , 1981 .

[127]  Michel Gendreau,et al.  Single-vehicle routing and scheduling to minimize the number of missed deadlines , 1992 .

[128]  R. P. Dilworth,et al.  A DECOMPOSITION THEOREM FOR PARTIALLY ORDERED SETS , 1950 .

[129]  Amos Levin Scheduling and Fleet Routing Models for Transportation Systems , 1971 .

[130]  José Pinto Paixão,et al.  A quasi-assignment algorithm for bus scheduling , 1987, Networks.

[131]  R Genser,et al.  Optimization Applied to Transportation Systems , 1977 .

[132]  Gilbert Laporte,et al.  The vehicle routing problem: An overview of exact and approximate algorithms , 1992 .

[133]  E. Denardo,et al.  Shortest-Route Methods: 1. Reaching, Pruning, and Buckets , 1979, Oper. Res..

[134]  E Heurgon,et al.  PREPARING DUTY ROSTERS FOR BUS ROUTES BY COMPUTER , 1975 .

[135]  M M Solomon,et al.  VEHICLE ROUTING AND SCHEDULING PROBLEMS WITH TIME WINDOW CONSTRAINTS: EFFICIENT IMPLEMENTATIONS OF SOLUTION IMPROVEMENT PROCEDURES , 1988 .

[136]  Jacques Desrosiers,et al.  A Request Clustering Algorithm for Door-to-Door Handicapped Transportation , 1991, Transp. Sci..

[137]  Marshall L. Fisher,et al.  Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees , 1994, Oper. Res..

[138]  Dennis F. X. Mathaisel,et al.  Airline Scheduling: An Overview , 1985, Transp. Sci..

[139]  Jeffrey M. Jaffe,et al.  Algorithms for finding paths with multiple constraints , 1984, Networks.

[140]  Richard Bellman,et al.  ON A ROUTING PROBLEM , 1958 .

[141]  Pierre Hansen,et al.  Un algorithme primal de programmation linéaire généralisée pour les programmes mixtes , 1991 .

[142]  Bruce L. Golden,et al.  A transportation problem formulation for the MAC Airlift Planning problem , 1994, Ann. Oper. Res..

[143]  Moshe Dror,et al.  Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW , 1994, Oper. Res..

[144]  Paul M. Thompson,et al.  Analysis and solution algorithms of sealift routing and scheduling problems : final report , 1985 .

[145]  Jean-Yves Blais,et al.  THE HASTUS VEHICLE AND MANPOWER SCHEDULING SYSTEM AT THE SOCIETE DE TRANSPORT DE LA COMMUNAUTE URBAINE DE MONTREAL , 1990 .

[146]  M. Wagner,et al.  Generalized Linear Programming Solves the Dual , 1976 .

[147]  François Soumis,et al.  Minimisation d'une fonction convexe séparable avec contraintes de rapport entre les variables , 1988 .

[148]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[149]  Alan A. Bertossi,et al.  On some matching problems arising in vehicle scheduling models , 1987, Networks.

[150]  Lawrence Bodin,et al.  Classification in vehicle routing and scheduling , 1981, Networks.

[151]  J. Desrosiers,et al.  Lagrangian relaxation methods for solving the minimum fleet size multiple traveling salesman problem with time windows , 1988 .

[152]  Michael Forbes,et al.  Exact Solution of Locomotive Scheduling Problems , 1991 .