The Pickup and Delivery Problem with Time Windows

Abstract The vehicle routing problem ( vrp ) involves the design of a set of minimum cost routes for a fleet of vehicles which services exactly once a set of customers with known demands. The pickup and delivery problem with time windows ( pdptw ) is a generalization of the vrp which is concerned with the construction of optimal routes to satisfy transportation requests, each requiring both pickup and delivery under capacity, time window and precedence constraints. This paper presents an exact algorithm which solves the pickup and delivery problem when transporting goods. This algorithm uses a column generation scheme with a constrained shortest path as a subproblem. The algorithm can handle multiple depots and different types of vehicles.

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

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

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

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

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

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

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

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

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

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

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

[12]  Thomas R. Sexton,et al.  Pickup and Delivery of Partial Loads with “Soft” Time Windows , 1986 .

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

[14]  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 .

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

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

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

[18]  Jacques Desrosiers,et al.  THE MULTIPLE VEHICLE DIAL-A-RIDE PROBLEM , 1988 .

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

[20]  R. A. Zemlin,et al.  Integer Programming Formulation of Traveling Salesman Problems , 1960, JACM.

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

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