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Optimising reorder intervals and order-up-to levels in guaranteed service supply chains

Author

Listed:
  • Zied Jemai

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

  • Ayse Sena Eruguz

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

  • Evren Sahin

    (Ecole Centrale Paris)

  • Yves Dallery

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

Abstract

We consider the problem of determining the optimal reorder intervals R and order-up-to levels S in a multi-echelon supply chain system where all echelons are assumed to have fixed ordering costs and to operate with a (R, S) policy with stationary nested power-of-two reorder intervals. By using the guaranteed service approach to model the multi-echelon system facing a stochastic demand, we formulate the problem as a deterministic optimisation model in order to simultaneously determine the optimal R and S parameters as well as the guaranteed service times. The model is a non-linear integer programming (NLIP) problem with a non-convex and non-concave objective function including rational and square root terms. Then, we propose a sequential optimisation procedure (SOP) to obtain near-optimal solutions with reasonable computational time. The numerical study demonstrates that for a general acyclic multi-echelon system with randomly generated parameters, the SOP is able to obtain near-optimal solutions of about 0.46% optimality gap in average in a few seconds. Moreover, we propose an improved direct approach using a global optimiser, bounding the decision variables in the NLIP model and considering the SOP solution as an initial solution. Numerical examples illustrate that this reduces significantly the computational time.

Suggested Citation

  • Zied Jemai & Ayse Sena Eruguz & Evren Sahin & Yves Dallery, 2014. "Optimising reorder intervals and order-up-to levels in guaranteed service supply chains," Post-Print hal-01672392, HAL.
  • Handle: RePEc:hal:journl:hal-01672392
    DOI: 10.1080/00207543.2013.831188
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    Citations

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    Cited by:

    1. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    2. Achkar, Victoria G. & Brunaud, Braulio B. & Pérez, Héctor D. & Musa, Rami & Méndez, Carlos A. & Grossmann, Ignacio E., 2024. "Extensions to the guaranteed service model for industrial applications of multi-echelon inventory optimization," European Journal of Operational Research, Elsevier, vol. 313(1), pages 192-206.
    3. Liu, Weihua & Liang, Zhicheng & Ye, Zi & Liu, Liang, 2016. "The optimal decision of customer order decoupling point for order insertion scheduling in logistics service supply chain," International Journal of Production Economics, Elsevier, vol. 175(C), pages 50-60.
    4. Eruguz, Ayse Sena & Sahin, Evren & Jemai, Zied & Dallery, Yves, 2016. "A comprehensive survey of guaranteed-service models for multi-echelon inventory optimization," International Journal of Production Economics, Elsevier, vol. 172(C), pages 110-125.
    5. Weihua Liu & Shuqing Wang & DongLei Zhu & Di Wang & Xinran Shen, 2018. "Order allocation of logistics service supply chain with fairness concern and demand updating: model analysis and empirical examination," Annals of Operations Research, Springer, vol. 268(1), pages 177-213, September.

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