A Bus Driver Scheduling Problem: a new mathematical model and a GRASP approximate solution

Authors:
Renato Leone;Paola Festa;Emilia Marchitto
Affiliations:
School of Science and Technology, University of Camerino, Camerino, Italy 62032;Department of Mathematics and Applications, University of Napoli Federico II, Naples, Italy;School of Science and Technology, University of Camerino, Camerino, Italy 62032
Venue:
Journal of Heuristics
Year:
2011

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Abstract

This paper addresses the problem of determining the best scheduling for Bus Drivers, a $\mathcal{NP}$ -hard problem consisting of finding the minimum number of drivers to cover a set of Pieces-Of-Work (POWs) subject to a variety of rules and regulations that must be enforced such as spreadover and working time. This problem is known in literature as Crew Scheduling Problem and, in particular in public transportation, it is designated as Bus Driver Scheduling Problem. We propose a new mathematical formulation of a Bus Driver Scheduling Problem under special constraints imposed by Italian transportation rules. Unfortunately, this model can only be usefully applied to small or medium size problem instances. For large instances, a Greedy Randomized Adaptive Search Procedure (GRASP) is proposed. Results are reported for a set of real-word problems and comparison is made with an exact method. Moreover, we report a comparison of the computational results obtained with our GRASP procedure with the results obtained by Huisman et al. (Transp. Sci. 39(4):491---502, 2005).