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Multi-item two-echelon spare parts inventory control problem with batch ordering in the central warehouse under compound Poisson demand

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Journal of the Operational Research Society

Abstract

We consider a multi-item two-echelon spare part inventory system in which the central warehouse operates under an (nQ, R) policy and the local warehouses implement order-up-to S policy, each facing a compound Poisson demand. The objective is to find the policy parameters minimizing expected system-wide inventory holding and fixed ordering costs subject to an aggregate mean response time constraint at each warehouse. In this paper, we propose four alternative approximations for the steady state performance of the system; and extend a heuristic and a lower bound proposed under Poisson demand assumption to the compound Poisson setting. In a computational study, we show that the performances of the approximations, the heuristic, and the lower bound are quite satisfactory; and the relative cost saving of setting an aggregate service level rather than individually for each part is quite high.

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References

  • Al-Rifai MH and Rossetti MD (2007). An efficient heuristic optimization algorithm for a two-echelon (R, Q) inventory system. International Journal of Production Economics 109 (1–2): 195–213.

    Article  Google Scholar 

  • Axsäter S (1995). Approximate evaluation of batch-ordering policies for a one-warehouse, N non-identical retailer system under compound Poisson demand. Naval Research Logistics 42: 807–819.

    Article  Google Scholar 

  • Axsäter S (2000). Exact analysis of continuous review (R, Q) policies in two echelon inventory systems with compound Poisson demand. Operations Research 48 (5): 686–696.

    Article  Google Scholar 

  • Axsäter S (2001). Scaling down multi-echelon inventory problems. International Journal of Production Economics 71: 255–261.

    Article  Google Scholar 

  • Axsäter S and Zhang WF (1996). Recursive evaluation of order-up-to-S policies for two-echelon inventory systems with compound Poisson demand. Naval Research Logistics 43: 151–157.

    Article  Google Scholar 

  • Caggiano KE, Jackson PL, Muckstadt JA and Rappold JA (2007). Optimizing service parts inventory in a multiechelon, multi-item supply chain with time-based customer service-level agreements. Operations Research 55 (2): 303–318.

    Article  Google Scholar 

  • Çağlar D, Li CL and Simchi-Levi D (2004). Two-echelon spare parts inventory system subject to a service constraint. IIE Transactions 36: 655–666.

    Article  Google Scholar 

  • Eaves AHC (2002). Forecasting for the ordering and stock- holding of consumable spare parts. PhD Thesis, University of Lancaster.

  • Forsberg R (1995). Optimization of order-up-to-S policies for two-level inventory systems with compound Poisson demand. European Journal of Operational Research 81: 143–153.

    Article  Google Scholar 

  • Graves SC (1985). A multi-echelon inventory model for a repairable item with one-for-one replenishment. Management Science 31: 1247–1256.

    Article  Google Scholar 

  • Hopp WJ, Zhang RQ and Spearman ML (1999). An easily implementable hierarchical heuristic for a two-echelon spare parts distribution system. IIE Transactions 31: 977–988.

    Google Scholar 

  • Kaas K, Goovaerts M, Dhaene J and Denuit M (2001). Modern Actuarial Risk Theory. Kluwer Academic Publishers: London, New York.

  • Lübbecke ME and Desrosiers J (2002). Selected topics in column generation. Operations Research 53 (6): 1007–1023.

    Article  Google Scholar 

  • Özer Ö and Xiong H (2008). Stock positioning and performance estimation for distribution systems with service constraints. IIE Transactions 40 (12): 1141–1157.

    Article  Google Scholar 

  • Shanker K (1981). Exact analysis of a two-echelon inventory system for recoverable items under batch inspection policy. Naval Research Logistics Quarterly 28: 579–601.

    Article  Google Scholar 

  • Sherbrooke CC (1968). Metric: A multi-echelon technique for recoverable item control. Operations Research 16: 122–141.

    Article  Google Scholar 

  • Thonemann UW, Brown AO and Hausman WH (2002). Easy quantification of improved spare parts inventory policies. Management Science 48 (9): 1213–1225.

    Article  Google Scholar 

  • Topan E (2010). Multi-item two-echelon spare parts inventory control problem with batch ordering in the central warehouse. PhD Thesis, Middle East Technical University.

  • Topan E, Bayindir ZP and Tan T (2010). An exact solution procedure for multi-item two-echelon spare parts inventory control problem with batch ordering in the central warehouse. Operations Research Letters 38: 454–461.

    Article  Google Scholar 

  • Wong H, Kranenburg D, Van Houtum GJ and Cattrysse D (2007). Efficient heuristics for two-echelon spare parts inventory systems with an aggregate mean waiting time constraint per local warehouse. OR Spectrum 29: 699–722.

    Article  Google Scholar 

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Correspondence to Z P Bayindir.

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Topan, E., Bayindir, Z. Multi-item two-echelon spare parts inventory control problem with batch ordering in the central warehouse under compound Poisson demand. J Oper Res Soc 63, 1143–1152 (2012). https://doi.org/10.1057/jors.2011.125

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  • DOI: https://doi.org/10.1057/jors.2011.125

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