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A zero-inventory production and distribution problem with a fixed customer sequence

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  • Ronald Armstrong
  • Su Gao
  • Lei Lei

Abstract

In this paper, we study the zero-inventory production and distribution problem with a single transporter and a fixed sequence of customers. The production facility has a limited production rate, and the delivery truck has non-negligible traveling times between locations. The order in which customers may receive deliveries is fixed. Each customer requests a delivery quantity and a time window for receiving the delivery. The lifespan of the product starts as soon as the production for a customer’s order is finished, which makes the product expire in a constant time. Since the production facility and the shipping truck are limited resources, not all the customers may receive the delivery within their specified time windows and/or within product lifespan. The problem is then to choose a subset of customers from the given sequence to receive the deliveries to maximize the total demand satisfied, without violating the product lifespan, the production/distribution capacity, and the delivery time window constraints. We analyze several fundamental properties of the problem and show that these properties can lead to a fast branch and bound search procedure for practical problems. A heuristic lower bound on the optimal solution is developed to accelerate the search. Empirical studies on the computational effort required by the proposed search procedure comparing to that required by CPLEX on randomly generated test cases are reported. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Ronald Armstrong & Su Gao & Lei Lei, 2008. "A zero-inventory production and distribution problem with a fixed customer sequence," Annals of Operations Research, Springer, vol. 159(1), pages 395-414, March.
    • Handle: RePEc:spr:annopr:v:159:y:2008:i:1:p:395-414:10.1007/s10479-007-0272-3
    DOI: 10.1007/s10479-007-0272-3
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    References listed on IDEAS

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    Cited by:

    1. Iman Dayarian & Guy Desaulniers, 2019. "A Branch-Price-and-Cut Algorithm for a Production-Routing Problem with Short-Life-Span Products," Transportation Science, INFORMS, vol. 53(3), pages 829-849, May.
    2. Ling Liu & Sen Liu, 2020. "Integrated Production and Distribution Problem of Perishable Products with a Minimum Total Order Weighted Delivery Time," Mathematics, MDPI, vol. 8(2), pages 1-18, January.
    3. Ali Gharaei & Fariborz Jolai, 2021. "A Pareto approach for the multi-factory supply chain scheduling and distribution problem," Operational Research, Springer, vol. 21(4), pages 2333-2364, December.
    4. Gao, Su & Qi, Lian & Lei, Lei, 2015. "Integrated batch production and distribution scheduling with limited vehicle capacity," International Journal of Production Economics, Elsevier, vol. 160(C), pages 13-25.
    5. Wang, Yu & Ropke, Stefan & Wen, Min & Bergh, Simon, 2023. "The mobile production vehicle routing problem: Using 3D printing in last mile distribution," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1407-1423.
    6. Christian Viergutz & Sigrid Knust, 2014. "Integrated production and distribution scheduling with lifespan constraints," Annals of Operations Research, Springer, vol. 213(1), pages 293-318, February.
    7. Berghman, Lotte & Kergosien, Yannick & Billaut, Jean-Charles, 2023. "A review on integrated scheduling and outbound vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 1-23.
    8. Azeddine Cheref & Alessandro Agnetis & Christian Artigues & Jean-Charles Billaut, 2017. "Complexity results for an integrated single machine scheduling and outbound delivery problem with fixed sequence," Journal of Scheduling, Springer, vol. 20(6), pages 681-693, December.
    9. Lei Lei & Hua Zhong & W. Art Chaovalitwongse, 2009. "On the Integrated Production and Distribution Problem with Bidirectional Flows," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 585-598, November.
    10. Mohammadi, S. & Al-e-Hashem, S.M.J. Mirzapour & Rekik, Y., 2020. "An integrated production scheduling and delivery route planning with multi-purpose machines: A case study from a furniture manufacturing company," International Journal of Production Economics, Elsevier, vol. 219(C), pages 347-359.
    11. Bachtenkirch, David & Bock, Stefan, 2022. "Finding efficient make-to-order production and batch delivery schedules," European Journal of Operational Research, Elsevier, vol. 297(1), pages 133-152.
    12. Zhi-Long Chen, 2010. "Integrated Production and Outbound Distribution Scheduling: Review and Extensions," Operations Research, INFORMS, vol. 58(1), pages 130-148, February.

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