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A New Approach to Stockout Penalties


  • Benjamin L. Schwartz

    (Institute for Defense Analyses)


Classical inventory theory considers that stockouts generate penalty costs to the firm, often assumed to be proportional to the excess of demand over supply. While such a concept is sometimes appropriate, it does not correctly reflect the effect of loss of goodwill. The latter is characterized by the fact that a disappointed customer reacts in the future to change his purchasing habits. Thus the nature of the effect is that subsequent demand is perturbed, a phenomenon quite different from having an immediate penalty cost imposed. Models with this property are termed perturbed demand, abbreviated PD. In this paper, this concept is defined precisely, and some of its properties are developed. Some typical cases are solved to determine optimal policies when PD prevails.

Suggested Citation

  • Benjamin L. Schwartz, 1966. "A New Approach to Stockout Penalties," Management Science, INFORMS, vol. 12(12), pages 538-544, August.
  • Handle: RePEc:inm:ormnsc:v:12:y:1966:i:12:p:b538-b544

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    Cited by:

    1. Fernando Bernstein & Awi Federgruen, 2004. "A General Equilibrium Model for Industries with Price and Service Competition," Operations Research, INFORMS, vol. 52(6), pages 868-886, December.
    2. Karthik Balasubramanian & David F. Drake, 2015. "Service Quality, Inventory and Competition: An Empirical Analysis of Mobile Money Agents in Africa," Harvard Business School Working Papers 15-059, Harvard Business School, revised Oct 2015.
    3. repec:eee:proeco:v:208:y:2019:i:c:p:461-471 is not listed on IDEAS
    4. repec:eee:jomega:v:89:y:2019:i:c:p:242-256 is not listed on IDEAS
    5. Ernst, Ricardo & Powell, Stephen G., 1998. "Manufacturer incentives to improve retail service levels," European Journal of Operational Research, Elsevier, vol. 104(3), pages 437-450, February.
    6. Ryan W. Buell & Dennis Campbell & Frances X. Frei, 2016. "How Do Customers Respond to Increased Service Quality Competition?," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 585-607, October.
    7. Junmin Shi & Michael Katehakis & Benjamin Melamed, 2013. "Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands," Annals of Operations Research, Springer, vol. 208(1), pages 593-612, September.
    8. Tava Lennon Olsen & Rodney P. Parker, 2008. "Inventory Management Under Market Size Dynamics," Management Science, INFORMS, vol. 54(10), pages 1805-1821, October.
    9. Vishal Gaur & Young-Hoon Park, 2007. "Asymmetric Consumer Learning and Inventory Competition," Management Science, INFORMS, vol. 53(2), pages 227-240, February.
    10. Liming Liu & Weixin Shang & Shaohua Wu, 2007. "Dynamic Competitive Newsvendors with Service-Sensitive Demands," Manufacturing & Service Operations Management, INFORMS, vol. 9(1), pages 84-93, June.
    11. Tianhu Deng & Zuo-Jun Max Shen & J. George Shanthikumar, 2014. "Statistical Learning of Service-Dependent Demand in a Multiperiod Newsvendor Setting," Operations Research, INFORMS, vol. 62(5), pages 1064-1076, October.
    12. Liberopoulos, George & Tsikis, Isidoros & Delikouras, Stefanos, 2010. "Backorder penalty cost coefficient "b": What could it be?," International Journal of Production Economics, Elsevier, vol. 123(1), pages 166-178, January.
    13. Eugene Khmelnitsky & Gonen Singer, 2015. "An optimal inventory management problem with reputation-dependent demand," Annals of Operations Research, Springer, vol. 231(1), pages 305-316, August.
    14. Dana, James D, Jr, 2001. "Competition in Price and Availability When Availability is Unobservable," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 497-513, Autumn.
    15. Ernst, Ricardo & Powell, Stephen G., 1995. "Optimal inventory policies under service-sensitive demand," European Journal of Operational Research, Elsevier, vol. 87(2), pages 316-327, December.
    16. repec:eee:joreco:v:49:y:2019:i:c:p:242-252 is not listed on IDEAS
    17. Lawrence W. Robinson & Rachel R. Chen, 2011. "Estimating the Implied Value of the Customer's Waiting Time," Manufacturing & Service Operations Management, INFORMS, vol. 13(1), pages 53-57, February.
    18. James D. Dana, Jr. & Nicholas C. Petruzzi, 2001. "Note: The Newsvendor Model with Endogenous Demand," Management Science, INFORMS, vol. 47(11), pages 1488-1497, November.

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