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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.

Abstract

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.

Suggested Citation

  • van Wijk, A.C.C. & Adan, I.J.B.F. & van Houtum, G.J., 2012. "Approximate evaluation of multi-location inventory models with lateral transshipments and hold back levels," European Journal of Operational Research, Elsevier, vol. 218(3), pages 624-635.
    • Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:624-635
    DOI: 10.1016/j.ejor.2011.12.004
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    2. van Wingerden, E. & Tan, T. & Van Houtum, G.J., 2019. "The impact of an emergency warehouse in a two-echelon spare parts network," European Journal of Operational Research, Elsevier, vol. 276(3), pages 983-997.
    3. Cem Deniz Caglar Bozkir & O. Erhun Kundakcioglu & Andrea C. Henry, 2022. "Hospital service levels during drug shortages: Stocking and transshipment policies for pharmaceutical inventory," Journal of Global Optimization, Springer, vol. 83(3), pages 565-584, July.
    4. Liao, Yi & Shen, Wenjing & Hu, Xinxin & Yang, Shilei, 2014. "Optimal responses to stockouts: Lateral transshipment versus emergency order policies," Omega, Elsevier, vol. 49(C), pages 79-92.
    5. Rahimi-Ghahroodi, S. & Al Hanbali, A. & Vliegen, I.M.H. & Cohen, M.A., 2019. "Joint optimization of spare parts inventory and service engineers staffing with full backlogging," International Journal of Production Economics, Elsevier, vol. 212(C), pages 39-50.
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    7. 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.
    8. 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.
    9. Johansson, Lina & Olsson, Fredrik, 2018. "Age-based inventory control in a multi-echelon system with emergency replenishments," European Journal of Operational Research, Elsevier, vol. 265(3), pages 951-961.
    10. S. Rahimi-Ghahroodi & A. Al Hanbali & W. H. M. Zijm & J. K. W. Ommeren & A. Sleptchenko, 2017. "Integrated planning of spare parts and service engineers with partial backlogging," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 711-748, July.
    11. Zümbül Atan & Lawrence V. Snyder & George R. Wilson, 2018. "Transshipment policies for systems with multiple retailers and two demand classes," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 159-186, January.

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