Title: Hybrid model for the vehicle routing problem with stochastic demand

Authors: Keisuke Murakami, Hiroshi Morita

Addresses: Department of Information Physics and Sciences, Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan. ' Department of Information Physics and Sciences, Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan

Abstract: The vehicle routing problem with stochastic demand (VRPSD) is one of the most important problems in distribution and transportation. The classical models for the vehicle routing problem with stochastic demand are the chance-constrained model and the penalty model. This paper proposes the hybrid model which combines the chance-constrained model and the penalty model. The travel cost of the hybrid model is less than that of the chance-constrained model and the worst case is guaranteed though the hybrid model may have more travel cost than the penalty model. We formulate the VRPSD as a set covering problem and this problem is solved using a column generation approach. We propose the solution methods for the hybrid model. The solution method is based on saving algorithm. In numerical results, we compare the results of the chance-constrained model, the penalty model and the hybrid model.

Keywords: vehicle routing problem; stochastic demand; VRPSD; transport; set covering models; column generation method; distribution; transportation; chance-constrained models; penalty models; travel costs; hybrid models; worst case; saving algorithms.

DOI: 10.1504/IJAMS.2010.033566

International Journal of Applied Management Science, 2010 Vol.2 No.3, pp.224 - 238

Published online: 06 Jun 2010 *

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