A two-stage model for a day-ahead paratransit planning problem

We consider a dynamic planning problem for paratransit transportation. The focus is on a decision to take one day ahead: which requests to serve with own vehicles, and which requests to subcontract to taxis? We call this problem the day-ahead paratransit planning problem. The developed model is a non-standard two-stage integer recourse model. Both stages consist of two consecutive optimization problems: the clustering of requests into routes, and the assignment of these routes to vehicles. To solve this model, a genetic algorithm approach is used. Computational results are presented for randomly generated data sets.

[1]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[2]  Gilbert Laporte,et al.  The Dial-a-Ride Problem (DARP): Variants, modeling issues and algorithms , 2003, 4OR.

[3]  John E. Beasley,et al.  A Genetic Algorithm for the Multidimensional Knapsack Problem , 1998, J. Heuristics.

[4]  Geir Dahl,et al.  LP based heuristics for the multiple knapsack problem with assignment restrictions , 2006, Ann. Oper. Res..

[5]  John E. Beasley,et al.  A genetic algorithm for the generalised assignment problem , 1997, Comput. Oper. Res..

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

[7]  F. Glover,et al.  In Modern Heuristic Techniques for Combinatorial Problems , 1993 .

[8]  Paolo Toth,et al.  Heuristic Algorithms for the Handicapped Persons Transportation Problem , 1997, Transp. Sci..

[9]  Gilbert Laporte,et al.  Parallel Tabu search heuristics for the dynamic multi-vehicle dial-a-ride problem , 2004, Parallel Comput..

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

[11]  Hasan Pirkul,et al.  Algorithms for the multi-resource generalized assignment problem , 1991 .

[12]  Joseph B. Mazzola,et al.  Heuristics for the multi‐resource generalized assignment problem , 2001 .

[13]  Günther R. Raidl,et al.  An improved hybrid genetic algorithm for the generalized assignment problem , 2004, SAC '04.

[14]  A. Ruszczynski Stochastic Programming Models , 2003 .

[15]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[16]  Milind Dawande,et al.  Approximation Algorithms for the Multiple Knapsack Problem with Assignment Restrictions , 2000, J. Comb. Optim..

[17]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[18]  Peter Kall,et al.  Stochastic Linear Programming , 1975 .

[19]  Oli B. G. Madsen,et al.  A heuristic algorithm for a dial-a-ride problem with time windows, multiple capacities, and multiple objectives , 1995, Ann. Oper. Res..

[20]  Martin Grötschel,et al.  Telebus Berlin: Vehicle Scheduling in a Dial-a-Ride System , 1999 .

[21]  R M Jorgensen,et al.  Solving the Dial-a-Ride problem using genetic algorithms , 2007, J. Oper. Res. Soc..

[22]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Static Multi-Vehicle Dial-a-Ride Problem , 2002 .

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

[24]  Barrie M. Baker,et al.  A genetic algorithm for the vehicle routing problem , 2003, Comput. Oper. Res..