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Stopped Myopic Policies in Some Inventory Models with Generalized Demand Processes

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  • William S. Lovejoy

    (Graduate School of Business, Stanford University, Stanford, California 94305-5015)

Abstract

This paper considers single-item inventory systems with immediate delivery and no economies of scale. Bounds are provided on the value loss relative to optimal cost for restricting attention to the class of inventory stocking policies that behave myopically up to a specified stopping time. The stopping time may be random, and may depend on demand histories as well as information exogenous to the firm. The bounds are robust to the nature of the demand process faced after the stopping time, so are applicable when the statistics of demand after the stopping time are unknown. Stopping times that are large with high probability imply that near-term decisions are completely specified with high probability. The general bounding results allow one to consider demand processes that may otherwise be analytically intractable. It is shown that the class of demand models for which the assumption of additive i.i.d. shocks is appropriate is the same class admitting effective myopic stocking policies. The bounds also make rigorous the intuitive notion that myopic policies are least effective in systems with precipitous drops in demand coupled with an inability to recover cash invested in inventory. The option of selling inventory at discount is a reality in many real systems and enhances the attractiveness of the myopic stocking policy. In numerical examples, the myopic policy is shown to be an effective competitor in a range of systems for which optimal policies are not known. The results suggest that for systems with immediate delivery, no economies of scale, and no currently known optimal policy, the myopic stocking rule is a reasonable default policy to adopt.

Suggested Citation

  • William S. Lovejoy, 1992. "Stopped Myopic Policies in Some Inventory Models with Generalized Demand Processes," Management Science, INFORMS, vol. 38(5), pages 688-707, May.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:5:p:688-707
    DOI: 10.1287/mnsc.38.5.688
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    Cited by:

    1. Satya S. Malladi & Alan L. Erera & Chelsea C. White, 2023. "Inventory control with modulated demand and a partially observed modulation process," Annals of Operations Research, Springer, vol. 321(1), pages 343-369, February.
    2. Gah-Yi Ban & Cynthia Rudin, 2019. "The Big Data Newsvendor: Practical Insights from Machine Learning," Operations Research, INFORMS, vol. 67(1), pages 90-108, January.
    3. Lingxiu Dong & Hau L. Lee, 2003. "Optimal Policies and Approximations for a Serial Multiechelon Inventory System with Time-Correlated Demand," Operations Research, INFORMS, vol. 51(6), pages 969-980, December.
    4. Chad R. Larson & Danko Turcic & Fuqiang Zhang, 2015. "An Empirical Investigation of Dynamic Ordering Policies," Management Science, INFORMS, vol. 61(9), pages 2118-2138, September.
    5. Martinez de Albeniz, Victor & Lago, Alejandro, 2007. "Myopic inventory policies using individual customer arrival information," IESE Research Papers D/719, IESE Business School.
    6. Mor Armony & Erica L. Plambeck, 2005. "The Impact of Duplicate Orders on Demand Estimation and Capacity Investment," Management Science, INFORMS, vol. 51(10), pages 1505-1518, October.
    7. Fangruo Chen & Jing-Sheng Song, 2001. "Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand," Operations Research, INFORMS, vol. 49(2), pages 226-234, April.
    8. Gavirneni, Srinagesh & Bollapragada, Srinivas & E. Morton, Thomas, 1998. "Periodic review stochastic inventory problem with forecast updates: Worst-case bounds for the myopic solution," European Journal of Operational Research, Elsevier, vol. 111(2), pages 381-392, December.
    9. Lode Li & Martin Shubik & Matthew J. Sobel, 2013. "Control of Dividends, Capital Subscriptions, and Physical Inventories," Management Science, INFORMS, vol. 59(5), pages 1107-1124, May.
    10. Iida, Tetsuo, 2002. "A non-stationary periodic review production-inventory model with uncertain production capacity and uncertain demand," European Journal of Operational Research, Elsevier, vol. 140(3), pages 670-683, August.
    11. L. Beril Toktay & Lawrence M. Wein, 2001. "Analysis of a Forecasting-Production-Inventory System with Stationary Demand," Management Science, INFORMS, vol. 47(9), pages 1268-1281, September.
    12. Iida, Tetsuo, 1999. "The infinite horizon non-stationary stochastic inventory problem: Near myopic policies and weak ergodicity," European Journal of Operational Research, Elsevier, vol. 116(2), pages 405-422, July.
    13. Cetinkaya, S. & Parlar, M., 1998. "Optimal myopic policy for a stochastic inventory problem with fixed and proportional backorder costs," European Journal of Operational Research, Elsevier, vol. 110(1), pages 20-41, October.
    14. Amar Sapra & Van-Anh Truong & Rachel Q. Zhang, 2010. "How Much Demand Should Be Fulfilled?," Operations Research, INFORMS, vol. 58(3), pages 719-733, June.
    15. Xin, Linwei & Goldberg, David A., 2021. "Time (in)consistency of multistage distributionally robust inventory models with moment constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1127-1141.
    16. Torpong Cheevaprawatdomrong & Robert L. Smith, 2004. "Infinite Horizon Production Scheduling in Time-Varying Systems Under Stochastic Demand," Operations Research, INFORMS, vol. 52(1), pages 105-115, February.
    17. Disney, S.M. & Farasyn, I. & Lambrecht, M. & Towill, D.R. & de Velde, W. Van, 2006. "Taming the bullwhip effect whilst watching customer service in a single supply chain echelon," European Journal of Operational Research, Elsevier, vol. 173(1), pages 151-172, August.
    18. Harun Avci & Kagan Gokbayrak & Emre Nadar, 2020. "Structural Results for Average‐Cost Inventory Models with Markov‐Modulated Demand and Partial Information," Production and Operations Management, Production and Operations Management Society, vol. 29(1), pages 156-173, January.
    19. Xiangwen Lu & Jing-Sheng Song & Amelia Regan, 2006. "Inventory Planning with Forecast Updates: Approximate Solutions and Cost Error Bounds," Operations Research, INFORMS, vol. 54(6), pages 1079-1097, December.
    20. Pirayesh Neghab, Davood & Khayyati, Siamak & Karaesmen, Fikri, 2022. "An integrated data-driven method using deep learning for a newsvendor problem with unobservable features," European Journal of Operational Research, Elsevier, vol. 302(2), pages 482-496.
    21. Bazsa-Oldenkamp, E.M. & den Iseger, P., 2003. "Wide sense one-dependent processes with embedded Harris chains and their applications in inventory management," Econometric Institute Research Papers EI 2002-44, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    22. Victor Martínez-de-Albéniz & Alejandro Lago, 2010. "Myopic Inventory Policies Using Individual Customer Arrival Information," Manufacturing & Service Operations Management, INFORMS, vol. 12(4), pages 663-672, May.
    23. A. A. Tsay & W. S. Lovejoy, 1999. "Quantity Flexibility Contracts and Supply Chain Performance," Manufacturing & Service Operations Management, INFORMS, vol. 1(2), pages 89-111.
    24. Tetsuo Iida & Paul H. Zipkin, 2006. "Approximate Solutions of a Dynamic Forecast-Inventory Model," Manufacturing & Service Operations Management, INFORMS, vol. 8(4), pages 407-425, October.

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