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Hybrid model for the vehicle routing problem with stochastic demand


  • Keisuke Murakami
  • Hiroshi Morita


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.

Suggested Citation

  • Keisuke Murakami & Hiroshi Morita, 2010. "Hybrid model for the vehicle routing problem with stochastic demand," International Journal of Applied Management Science, Inderscience Enterprises Ltd, vol. 2(3), pages 224-238.
  • Handle: RePEc:ids:injams:v:2:y:2010:i:3:p:224-238

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    References listed on IDEAS

    1. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    2. Halkos, George & Salamouris, Dimitrios, 2001. "Efficiency Measures of the Greek Banking Sector: A Non-Parametric Approach for the Period 1997-1999," MPRA Paper 2858, University Library of Munich, Germany.
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