New exact algorithms for the vehicle routing problem
We consider the problem in which a fleet of M vehicles stationed at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. This problem is referred as the Vehicle Routing Problem (VRP). In this paper we present two exact branch and bound algorithms for solving the VRP based on a Set Partitioning formulation of the problem. The first algorithm is based on a bounding procedure that finds a heuristic solution of the dual of the LP-relaxation of the Set Partitioning formulation without generating the entire set partitioning matrix. The dual solution obtained is then used to limit the set of the feasible routes containing the optimal VRP solution. The resulting Set Partitioning problem is solved by using a branch and bound method. The second algorithm is based on a lower bound that makes use of a new surrogate relaxation of the Set Partitioning problem. The two algorithms can solve both symmetric and asymmetric VRPS. Computational results are presented for a number of problems derived from the literature.
- OSTI ID:
- 36283
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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