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Optimal control of a production-inventory system with productreturns

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  • Vercraene, Samuel
  • Gayon, Jean-Philippe

Abstract

We consider a production-inventory system that consists of n stages. Each stage has a finite production capacity modelled by an exponential server. The downstream stage faces a Poisson demand. Each stage receives returns of products according to independent Poisson processes that can be used to serve demand. The problem is to control production to minimize discounted (or average) holding and backordering costs. For the single-stage problem (n=1), we fully characterize the optimal policy. We show that the optimal policy is base-stock and we derive an explicit formula for the optimal base-stock level. For the general n-stage problem, we show that the optimal policy is characterized by state-dependent base-stock levels. In a numerical study, we investigate three heuristic policies: the base-stock policy, the Kanban policy and the fixed buffer policy. The fixed-buffer policy obtains poor results while the relative performances of base-stock and Kanban policies depend on bottlenecks. We also show that returns have a non-monotonic effect on average costs and strongly affect the performances of heuristics. Finally, we observe that having returns at the upstream stage is preferable in some situations.

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  • Vercraene, Samuel & Gayon, Jean-Philippe, 2013. "Optimal control of a production-inventory system with productreturns," International Journal of Production Economics, Elsevier, vol. 142(2), pages 302-310.
    • Handle: RePEc:eee:proeco:v:142:y:2013:i:2:p:302-310
    DOI: 10.1016/j.ijpe.2012.11.012
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    References listed on IDEAS

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    Cited by:

    1. Samuel Vercraene & Jean-Philippe Gayon & Fikri Karaesmen, 2018. "Effects of System Parameters on the Optimal Cost and Policy in a Class of Multidimensional Queueing Control Problems," Operations Research, INFORMS, vol. 66(1), pages 150-162, January.
    2. Sagawa, Juliana Keiko & Mušič, Gašper, 2019. "Towards the use of bond graphs for manufacturing control: Design of controllers," International Journal of Production Economics, Elsevier, vol. 214(C), pages 53-72.
    3. Zolfagharinia, Hossein & Hafezi, Maryam & Farahani, Reza Zanjirani & Fahimnia, Behnam, 2014. "A hybrid two-stock inventory control model for a reverse supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 67(C), pages 141-161.
    4. Gayon, Jean-Philippe & Vercraene, Samuel & Flapper, Simme Douwe P., 2017. "Optimal control of a production-inventory system with product returns and two disposal options," European Journal of Operational Research, Elsevier, vol. 262(2), pages 499-508.
    5. Flapper, Simme Douwe & Gayon, Jean-Philippe & Lim, Lâm Laurent, 2014. "On the optimal control of manufacturing and remanufacturing activities with a single shared server," European Journal of Operational Research, Elsevier, vol. 234(1), pages 86-98.
    6. Alireza Pooya & Morteza Pakdaman, 2019. "Optimal control model for finite capacity continuous MRP with deteriorating items," Journal of Intelligent Manufacturing, Springer, vol. 30(5), pages 2203-2215, June.

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