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IMA Journal of Management Mathematics Advance Access published online on June 19, 2009
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpp007
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© The authors 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A dynamic day-ahead paratransit planning problem

Maria L. A. G. Cremers{dagger}, Willem K. Klein Haneveld and Maarten H. van der Vlerk

Department of Operations, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands

{dagger} Email: m.l.a.g.cremers{at}rug.nl

Received on 15 June 2007. Accepted on 19 May 2008.

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 that are gradually revealed during the day of operation. We call this problem the dynamic day-ahead paratransit planning problem. The developed model is a non-standard 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 simulation 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.

Keywords: paratransit transport; stochastic programming; online optimization


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