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Single vehicle routing problems with a predefined customer sequence, compartmentalized load and stochastic demands

Author

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  • Pandelis, D.G.
  • Kyriakidis, E.G.
  • Dimitrakos, T.D.

Abstract

We consider the problem of finding the optimal routing of a single vehicle that delivers K different products to N customers according to a particular customer order. The demands of the customers for each product are assumed to be random variables with known distributions. Each product type is stored in its dedicated compartment in the vehicle. Using a suitable dynamic programming algorithm we find the policy that satisfies the demands of the customers with the minimum total expected cost. We also prove that this policy has a specific threshold-type structure. Furthermore, we investigate a corresponding infinite-time horizon problem in which the service of the customers does not stop when the last customer has been serviced but it continues indefinitely with the same customer order. It is assumed that the demands of the customers at different tours have the same distributions. It is shown that the discounted-cost optimal policy and the average-cost optimal policy have the same threshold-type structure as the optimal policy in the original problem. The theoretical results are illustrated by numerical examples.

Suggested Citation

  • Pandelis, D.G. & Kyriakidis, E.G. & Dimitrakos, T.D., 2012. "Single vehicle routing problems with a predefined customer sequence, compartmentalized load and stochastic demands," European Journal of Operational Research, Elsevier, vol. 217(2), pages 324-332.
  • Handle: RePEc:eee:ejores:v:217:y:2012:i:2:p:324-332
    DOI: 10.1016/j.ejor.2011.09.027
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    References listed on IDEAS

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    1. G. B. Dantzig & J. H. Ramser, 1959. "The Truck Dispatching Problem," Management Science, INFORMS, vol. 6(1), pages 80-91, October.
    2. Tsirimpas, P. & Tatarakis, A. & Minis, I. & Kyriakidis, E.G., 2008. "Single vehicle routing with a predefined customer sequence and multiple depot returns," European Journal of Operational Research, Elsevier, vol. 187(2), pages 483-495, June.
    3. Tatarakis, A. & Minis, I., 2009. "Stochastic single vehicle routing with a predefined customer sequence and multiple depot returns," European Journal of Operational Research, Elsevier, vol. 197(2), pages 557-571, September.
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    Citations

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    Cited by:

    1. Pandelis, D.G. & Karamatsoukis, C.C. & Kyriakidis, E.G., 2013. "Finite and infinite-horizon single vehicle routing problems with a predefined customer sequence and pickup and delivery," European Journal of Operational Research, Elsevier, vol. 231(3), pages 577-586.
    2. repec:eee:ejores:v:268:y:2018:i:2:p:613-623 is not listed on IDEAS
    3. Dimitrakos, T.D. & Kyriakidis, E.G., 2015. "A single vehicle routing problem with pickups and deliveries, continuous random demands and predefined customer order," European Journal of Operational Research, Elsevier, vol. 244(3), pages 990-993.
    4. Zhang, Junlong & Lam, William H.K. & Chen, Bi Yu, 2016. "On-time delivery probabilistic models for the vehicle routing problem with stochastic demands and time windows," European Journal of Operational Research, Elsevier, vol. 249(1), pages 144-154.
    5. Goodson, Justin C., 2015. "A priori policy evaluation and cyclic-order-based simulated annealing for the multi-compartment vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 241(2), pages 361-369.

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