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Approximate evaluation of multi-location inventory models with lateral transshipments and hold back levels


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  • van Wijk, A.C.C.
  • Adan, I.J.B.F.
  • van Houtum, G.J.
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    We consider a continuous-time, single-echelon, multi-location inventory model with Poisson demand processes. In case of a stock-out at a local warehouse, a demand can be fulfilled via a lateral transshipment (LT). Each warehouse is assigned a pre-determined sequence of other warehouses where it will request for an LT. However, a warehouse can hold its last part(s) back from such a request. This is called a hold back pooling policy, where each warehouse has hold back levels determining whether a request for an LT by another warehouse is satisfied. We are interested in the fractions of demand satisfied from stock (fill rate), via an LT, and via an emergency procedure from an external source. From these, the average costs of a policy can be determined. We present a new approximation algorithm for the evaluation of a given policy, approximating the above mentioned fractions. Whereas algorithms currently known in the literature approximate the stream of LT requests from a warehouse by a Poisson process, we use an interrupted Poisson process. This is a process that is turned alternatingly On and Off for exponentially distributed durations. This leads to the On/Off overflow algorithm. In a numerical study we show that this algorithm is significantly more accurate than the algorithm based on Poisson processes, although it requires a longer computation time. Furthermore, we show the benefits of hold back levels, and we illustrate how our algorithm can be used in a heuristic search for the setting of the hold back levels.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 218 (2012)
    Issue (Month): 3 ()
    Pages: 624-635

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    Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:624-635

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    Keywords: Inventory; Lateral transshipment; Approximation algorithm; Interrupted Poisson process;


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    14. Xu, Kefeng & Evers, Philip T. & Fu, Michael C., 2003. "Estimating customer service in a two-location continuous review inventory model with emergency transshipments," European Journal of Operational Research, Elsevier, vol. 145(3), pages 569-584, March.
    15. Kutanoglu, Erhan & Mahajan, Mohit, 2009. "An inventory sharing and allocation method for a multi-location service parts logistics network with time-based service levels," European Journal of Operational Research, Elsevier, vol. 194(3), pages 728-742, May.
    16. Wong, H. & van Houtum, G.J. & Cattrysse, D. & Oudheusden, D. Van, 2006. "Multi-item spare parts systems with lateral transshipments and waiting time constraints," European Journal of Operational Research, Elsevier, vol. 171(3), pages 1071-1093, June.
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    Cited by:
    1. Deflem, Yannick & Van Nieuwenhuyse, Inneke, 2013. "Managing inventories with one-way substitution: A newsvendor analysis," European Journal of Operational Research, Elsevier, vol. 228(3), pages 484-493.
    2. Alvarez, E.M. & van der Heijden, M.C. & Vliegen, I.M.H. & Zijm, W.H.M., 2014. "Service differentiation through selective lateral transshipments," European Journal of Operational Research, Elsevier, vol. 237(3), pages 824-835.


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