An exact solution framework for a broad class of vehicle routing problems

This paper presents an exact solution framework for solving some variants of the vehicle routing problem (VRP) that can be modeled as set partitioning (SP) problems with additional constraints. The method consists in combining different dual ascent procedures to find a near optimal dual solution of the SP model. Then, a column-and-cut generation algorithm attempts to close the integrality gap left by the dual ascent procedures by adding valid inequalities to the SP formulation. The final dual solution is used to generate a reduced problem containing all optimal integer solutions that is solved by an integer programming solver. In this paper, we describe how this solution framework can be extended to solve different variants of the VRP by tailoring the different bounding procedures to deal with the constraints of the specific variant. We describe how this solution framework has been recently used to derive exact algorithms for a broad class of VRPs such as the capacitated VRP, the VRP with time windows, the pickup and delivery problem with time windows, R. Baldacci (B) Department of Electronics, Computer Science and Systems (DEIS), University of Bologna, Via Venezia 52, 47521 Cesena, Italy e-mail: [email protected] E. Bartolini Department of Computer Science, University of Bologna, Mura Anteo Zamboni 7, 40127 Bologna, Italy e-mail: [email protected] A. Mingozzi Department of Mathematics, University of Bologna, Via Sacchi 3, 47521 Cesena, Italy e-mail: [email protected] R. Roberti Department of Electronics, Computer Science and Systems (DEIS), University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy e-mail: [email protected]