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A New Approach to Stockout Penalties

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  • Benjamin L. Schwartz

    (Institute for Defense Analyses)

Abstract

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
    DOI: 10.1287/mnsc.12.12.B538
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    Cited by:

    1. Philipp Afèche & Mojtaba Araghi & Opher Baron, 2017. "Customer Acquisition, Retention, and Service Access Quality: Optimal Advertising, Capacity Level, and Capacity Allocation," Manufacturing & Service Operations Management, INFORMS, vol. 19(4), pages 674-691, October.
    2. Koos, Shelby E. & Shaikh, Nazrul I., 2019. "Dynamics of consumers' dissatisfaction due to stock-outs," International Journal of Production Economics, Elsevier, vol. 208(C), pages 461-471.
    3. 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.
    4. 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.
    5. L. San-José & J. García-Laguna & J. Sicilia, 2009. "An economic order quantity model with partial backlogging under general backorder cost function," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 366-384, December.
    6. Tava Lennon Olsen & Rodney P. Parker, 2008. "Inventory Management Under Market Size Dynamics," Management Science, INFORMS, vol. 54(10), pages 1805-1821, October.
    7. Vishal Gaur & Young-Hoon Park, 2007. "Asymmetric Consumer Learning and Inventory Competition," Management Science, INFORMS, vol. 53(2), pages 227-240, February.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Han, Xiaoya & Yu, Yugang & Hu, Guiping, 2019. "A dynamic newsvendor problem with goodwill-dependent demands and minimum commitment," Omega, Elsevier, vol. 89(C), pages 242-256.
    15. 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.
    16. 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.
    17. 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.
    18. Boutselis, Petros & McNaught, Ken, 2014. "Finite-Time Horizon Logistics Decision Making Problems: Consideration of a Wider Set of Factors," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Blecker, Thorsten & Kersten, Wolfgang & Ringle, Christian M. (ed.), Innovative Methods in Logistics and Supply Chain Management: Current Issues and Emerging Practices. Proceedings of the Hamburg International Conferenc, volume 19, pages 249-274, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    19. 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.
    20. Azeem, Muhammad Masood & Baker, Derek & Villano, Renato A. & Mounter, Stuart & Griffith, Garry, 2019. "Response to stockout in grocery stores: A small city case in a changing competitive environment," Journal of Retailing and Consumer Services, Elsevier, vol. 49(C), pages 242-252.
    21. 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.
    22. Liberopoulos, George & Deligiannis, Michalis, 2022. "Optimal supplier inventory control policies when buyer purchase incidence is driven by past service," European Journal of Operational Research, Elsevier, vol. 300(3), pages 917-936.

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