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Stock Rationing in an M/E k /1 Make-to-Stock Queue


  • Albert Y. Ha

    () (Yale School of Management, 135 Prospect Street, New Haven, Connecticut 06511)


This paper considers the stock rationing problem of a single-item, make-to-stock production system with several demand classes and lost sales. When demand is Poisson and processing time has an Erlang distribution, we show that a single-state variable called work storage level can be employed to completely capture the information regarding inventory level and the status of current production. The optimal rationing policy can be characterized by a sequence of monotone critical work storage levels. For each demand class, there exists a work storage level at or below which it is optimal to start rejecting the demand of this class in anticipation of future arrival of higher-priority demands. The optimal production policy can also be characterized by a critical work storage level. Our numerical examples indicate that a critical stock level policy, which ignores information on the status of current production, performs very well.

Suggested Citation

  • Albert Y. Ha, 2000. "Stock Rationing in an M/E k /1 Make-to-Stock Queue," Management Science, INFORMS, vol. 46(1), pages 77-87, January.
  • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:1:p:77-87

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    References listed on IDEAS

    1. Morris A. Cohen & Paul R. Kleindorfer & Hau L. Lee, 1988. "Service Constrained (s, S) Inventory Systems with Priority Demand Classes and Lost Sales," Management Science, INFORMS, vol. 34(4), pages 482-499, April.
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    8. Albert Y. Ha, 1997. "Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales," Management Science, INFORMS, vol. 43(8), pages 1093-1103, August.
    9. Kenneth R. Baker & Michael J. Magazine & Henry L. W. Nuttle, 1986. "The Effect of Commonality on Safety Stock in a Simple Inventory Model," Management Science, INFORMS, vol. 32(8), pages 982-988, August.
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    Cited by:

    1. Lee, Jeong Eun & Hong, Yushin, 2003. "A stock rationing policy in a (s,S)-controlled stochastic production system with 2-phase Coxian processing times and lost sales," International Journal of Production Economics, Elsevier, vol. 83(3), pages 299-307, March.
    2. 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.
    3. 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.
    4. repec:spr:annopr:v:241:y:2016:i:1:d:10.1007_s10479-013-1311-x is not listed on IDEAS
    5. 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.
    6. ElHafsi, Mohsen & Camus, Herve & Craye, Etienne, 2010. "Managing an integrated production inventory system with information on the production and demand status and multiple non-unitary demand classes," European Journal of Operational Research, Elsevier, vol. 207(2), pages 986-1001, December.
    7. Foreest, N. D. van & Wijngaard, J., 2010. "On the Optimal Policy for the Single-product Inventory Problem with Set-up Cost and a Restricted Production Capacity," Research Report 10005, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    8. Xu, Jianjun & Serrano, Alejandro & Lin, Bing, 2017. "Optimal production and rationing policy of two-stage tandem production system," International Journal of Production Economics, Elsevier, vol. 185(C), pages 100-112.
    9. Akinc, Umit & Meredith, Jack, 2009. "Modeling the manager's match-or-wait dilemma in a make-to-forecast production situation," Omega, Elsevier, vol. 37(2), pages 300-311, April.
    10. Jang, Wooseung & Kim, Dongwon, 2007. "Integrated production and allocation policies with one direct shipping option," European Journal of Operational Research, Elsevier, vol. 181(2), pages 716-732, September.
    11. Feng, Jiejian & Zhang, Michael, 2017. "Dynamic quotation of leadtime and price for a Make-To-Order system with multiple customer classes and perfect information on customer preferences," European Journal of Operational Research, Elsevier, vol. 258(1), pages 334-342.
    12. repec:dgr:rugsom:10005 is not listed on IDEAS
    13. Samii, Amir-Behzad, 2016. "Impact of nested inventory allocation policies in a newsvendor setting," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 247-256.
    14. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    15. P. Escalona & F. Ordóñez & I. Kauak, 2017. "Critical level rationing in inventory systems with continuously distributed demand," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 273-301, January.
    16. Kim, Eungab & Park, Taeho, 2016. "Admission and inventory control of a single-component make-to-order production system with replenishment setup cost and lead time," European Journal of Operational Research, Elsevier, vol. 255(1), pages 91-102.


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