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

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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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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Florio, Alexandre M. & Hartl, Richard F. & Minner, Stefan, 2020. "Optimal a priori tour and restocking policy for the single-vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 285(1), pages 172-182.
    4. Kyriakidis, Epaminondas G. & Dimitrakos, Theodosis D. & Karamatsoukis, Constantinos C., 2019. "Optimal delivery of two similar products to N ordered customers with product preferences," International Journal of Production Economics, Elsevier, vol. 209(C), pages 194-204.
    5. 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.
    6. Zhu, Lin & Sheu, Jiuh-Biing, 2018. "Failure-specific cooperative recourse strategy for simultaneous pickup and delivery problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 271(3), pages 896-912.
    7. David Raba & Rafael D. Tordecilla & Pedro Copado & Angel A. Juan & Daniel Mount, 2022. "A Digital Twin for Decision Making on Livestock Feeding," Interfaces, INFORMS, vol. 52(3), pages 267-282, May.
    8. Jin, Ming & Li, Gang & Cheng, T.C.E., 2018. "Buy online and pick up in-store: Design of the service area," European Journal of Operational Research, Elsevier, vol. 268(2), pages 613-623.
    9. Epaminondas G. Kyriakidis & Theodosis D. Dimitrakos & Constantinos C. Karamatsoukis, 2020. "A Stochastic Single Vehicle Routing Problem with a Predefined Sequence of Customers and Collection of Two Similar Materials," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1559-1582, December.
    10. 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.
    11. Justin C. Goodson & Barrett W. Thomas & Jeffrey W. Ohlmann, 2016. "Restocking-Based Rollout Policies for the Vehicle Routing Problem with Stochastic Demand and Duration Limits," Transportation Science, INFORMS, vol. 50(2), pages 591-607, May.
    12. Soeffker, Ninja & Ulmer, Marlin W. & Mattfeld, Dirk C., 2022. "Stochastic dynamic vehicle routing in the light of prescriptive analytics: A review," European Journal of Operational Research, Elsevier, vol. 298(3), pages 801-820.

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