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A note on the rationing policies of multiple demand classes with lost sales

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  • Wang, Daqin
  • Tang, Ou
  • Zhang, Lihua

Abstract

We study inventory rationing in a system with multiple demand classes and lost sales. It is assumed to have at most one outstanding order, resulting in two periods in an order cycle separated by the time of order release. We review the most related work by Melchiors (2001, 2003) (Ph.D. thesis, University of Aarhus, Int. J. Prod. Econ. 81–82, (11), 461–468), and find that the existing approximated and optimal policies are not easy to obtain due to computational complexity. Also as the rationing issue before order release is not well addressed in literature, in this paper we prove the static rationing being optimal. Furthermore in such a system with two distinct periods, the optimal rationing policy is a combination of a dynamic policy during the replenishment lead time and a static policy before order release. In order to make the rationing policies to be readily used in practice, we introduce two approximated methods for calculating the rationing levels in two periods, respectively. The results, in particular the combination of static and dynamic rationing, outperform the existing approximations in literature. In addition, the computation is obviously simplified due to the efficient algorithm of dynamic rationing and the explicit expressions of static rationing.

Suggested Citation

  • Wang, Daqin & Tang, Ou & Zhang, Lihua, 2015. "A note on the rationing policies of multiple demand classes with lost sales," International Journal of Production Economics, Elsevier, vol. 165(C), pages 145-154.
    • Handle: RePEc:eee:proeco:v:165:y:2015:i:c:p:145-154
    DOI: 10.1016/j.ijpe.2015.03.029
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    References listed on IDEAS

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    1. Melchiors, Philip, 2003. "Restricted time-remembering policies for the inventory rationing problem," International Journal of Production Economics, Elsevier, vol. 81(1), pages 461-468, January.
    2. P Melchiors & R Dekker & M J Kleijn, 2000. "Inventory rationing in an (s, Q) inventory model with lost sales and two demand classes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(1), pages 111-122, January.
    3. Vinayak Deshpande & Morris A. Cohen & Karen Donohue, 2003. "A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes," Management Science, INFORMS, vol. 49(6), pages 683-703, June.
    4. Steven Nahmias & W. Steven Demmy, 1981. "Operating Characteristics of an Inventory System with Rationing," Management Science, INFORMS, vol. 27(11), pages 1236-1245, November.
    5. Liu, Shudong & Song, Miao & Tan, Kok Choon & Zhang, Changyong, 2015. "Multi-class dynamic inventory rationing with stochastic demands and backordering," European Journal of Operational Research, Elsevier, vol. 244(1), pages 153-163.
    6. FadIloglu, Mehmet Murat & Bulut, Önder, 2010. "A dynamic rationing policy for continuous-review inventory systems," European Journal of Operational Research, Elsevier, vol. 202(3), pages 675-685, May.
    7. Wang, Daqin & Tang, Ou, 2014. "Dynamic inventory rationing with mixed backorders and lost sales," International Journal of Production Economics, Elsevier, vol. 149(C), pages 56-67.
    8. Arthur F. Veinott, 1965. "Optimal Policy in a Dynamic, Single Product, Nonstationary Inventory Model with Several Demand Classes," Operations Research, INFORMS, vol. 13(5), pages 761-778, October.
    9. Teunter, Ruud H. & Klein Haneveld, Willem K., 2008. "Dynamic inventory rationing strategies for inventory systems with two demand classes, Poisson demand and backordering," European Journal of Operational Research, Elsevier, vol. 190(1), pages 156-178, October.
    10. Hung, Yi-Feng & Hsiao, Jui-Yi, 2013. "Inventory rationing decision models during replenishment lead time," International Journal of Production Economics, Elsevier, vol. 144(1), pages 290-300.
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    Cited by:

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    2. 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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