A dynamic day-ahead paratransit planning problem

Abstract We consider a dynamic planning problem for the transport of elderly and disabled people. The focus is on a decision to make one day ahead: which requests to serve with own vehicles, and which ones to assign to subcontractors, under uncertainty of late requests which are gradually revealed during the day of operation. We call this problem the Dynamic Day-ahead Paratransit Planning problem. The developed model is a nonstandard two-stage recourse model in which ideas from stochastic programming and online optimization are combined: in the first stage clustered requests are assigned to vehicles, and in the dynamic second-stage problem an event-driven approach is used to cluster the late requests once they are revealed and subsequently assign them to vehicles. A genetic algorithm is used to solve the model. Computational results are presented for randomly generated data sets. Furthermore, a comparison is made to a similar problem we studied earlier in which the simplifying but unrealistic assumption has been made that all late requests are revealed at the beginning of the day of operation.

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

[2]  Martin Grötschel,et al.  Combinatorial Online Optimization in Real Time , 2001 .

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

[4]  Maged Dessouky,et al.  A new regret insertion heuristic for solving large-scale dial-a-ride problems with time windows , 2004 .

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

[6]  Susanne Albers,et al.  Online algorithms: a survey , 2003, Math. Program..

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

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

[9]  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..

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

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

[12]  Maarten H. van der Vlerk,et al.  A two-stage model for a day-ahead paratransit planning problem , 2006, Math. Methods Oper. Res..

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

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

[15]  Michael G. H. Bell,et al.  Solution of the Dial-a-Ride Problem with multi-dimensional capacity constraints , 2006, Int. Trans. Oper. Res..

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

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

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