Multi-depot vehicle scheduling problems with time windows and waiting costs

The multi-depot vehicle scheduling problem with time windows (MDVSPTW) consists of scheduling a fleet of vehicles to cover a set of tasks at minimum cost. Each task is restricted to begin within a prescribed time interval and vehicles are supplied by different depots. The problem is formulated as an integer nonlinear multi-commodity network flow model with time variables and is solved using a column generation approach embedded in a branch-and-bound framework. This paper breaks new ground by considering costs on exact waiting times between two consecutive tasks instead of minimal waiting times. This new and more realistic cost structure gives rise to a nonlinear objective function in the model. Optimal and heuristic versions of the algorithm have been extensively tested on randomly generated urban bus scheduling problem (UBSP) and freight transport scheduling problem (FTSP). The results show that such a general solution methodology outperforms specialized algorithms when minimal waiting costs are used, and can efficiently treat the case with exact waiting costs.

[1]  Jacques Desrosiers,et al.  A Unified Framework for Deterministic Time Constrained Vehicle Routing and Crew Scheduling Problems , 1998 .

[2]  Lucio Bianco,et al.  An Exact Algorithm for Combining Vehicle Trips , 1995 .

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

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

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

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

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

[8]  Michael Forbes,et al.  An exact algorithm for multiple depot bus scheduling , 1994 .

[9]  Matteo Fischetti,et al.  A branch and bound algorithm for the multiple depot vehicle scheduling problem , 1989, Networks.

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

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

[12]  Guy Desaulniers,et al.  The Shortest Path Problem with Time Windows and Linear Waiting Costs , 1997, Transp. Sci..

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

[14]  L. Bianco,et al.  A set partitioning approach to the multiple depot vehicle scheduling problem , 1994 .

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

[16]  Sylvie Gélinas,et al.  A dynamic programming algorithm for the shortest path problem with time windows and linear node costs , 1994, Networks.

[17]  Jacques Desrosiers,et al.  Time Constrained Routing and Scheduling , 1992 .