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The Finite Horizon Nonstationary Stochastic Inventory Problem: Near-Myopic Bounds, Heuristics, Testing

Author

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  • Thomas E. Morton

    (Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • David W. Pentico

    (A. J. Palumbo School of Business Administration, Duquesne University, Pittsburgh, Pennsylvania 15282)

Abstract

Nonstationary stochastic periodic review inventory problems with proportional costs occur in a number of industrial settings with seasonal patterns, trends, business cycles, and limited life items. Myopic policies for such problems order as if the salvage value in the current period for ending inventory were the full purchase price, so that information about the future would not be needed. They have been shown in the literature to be optimal when demand "is increasing over time," and to provide upper bounds for the stationary finite horizon problem (and in some other situations). Some results are also known, given special salvaging assumptions, about lower bounds on the optimal policy which are near-myopic. Here analogous but stronger bounds are derived for the general finite horizon problem, without such special assumptions. The best upper bound is an extension of the heuristic used by industry for some years for end of season (EOS) problems; the lower bound is an extension of earlier analytic methods. Four heuristics were tested against the optimal obtained by stochastic dynamic programming for 969 problems. The simplest heuristic is the myopic heuristic itself: it is good especially for moderately varying problems without heavy end of season salvage costs and averages only 2.75% in cost over the optimal. However, the best of the heuristics exceeds the optimal in cost by an average of only 0.02%, at about 0.5% of the computational cost of dynamic programming.

Suggested Citation

  • Thomas E. Morton & David W. Pentico, 1995. "The Finite Horizon Nonstationary Stochastic Inventory Problem: Near-Myopic Bounds, Heuristics, Testing," Management Science, INFORMS, vol. 41(2), pages 334-343, February.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:2:p:334-343
    DOI: 10.1287/mnsc.41.2.334
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    Cited by:

    1. Özen, Ulaş & Doğru, Mustafa K. & Armagan Tarim, S., 2012. "Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem," Omega, Elsevier, vol. 40(3), pages 348-357.
    2. 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.
    3. Ehrenthal, J.C.F. & Honhon, D. & Van Woensel, T., 2014. "Demand seasonality in retail inventory management," European Journal of Operational Research, Elsevier, vol. 238(2), pages 527-539.
    4. 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.
    5. 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.
    6. Cheaitou, Ali & van Delft, Christian, 2013. "Finite horizon stochastic inventory problem with dual sourcing: Near myopic and heuristics bounds," International Journal of Production Economics, Elsevier, vol. 143(2), pages 371-378.
    7. 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.
    8. Van-Anh Truong, 2014. "Approximation Algorithm for the Stochastic Multiperiod Inventory Problem via a Look-Ahead Optimization Approach," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1039-1056, November.
    9. Wang, Yunzeng, 2001. "The optimality of myopic stocking policies for systems with decreasing purchasing prices," European Journal of Operational Research, Elsevier, vol. 133(1), pages 153-159, August.
    10. 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.
    11. Joseph M. Milner & Panos Kouvelis, 2002. "On the Complementary Value of Accurate Demand Information and Production and Supplier Flexibility," Manufacturing & Service Operations Management, INFORMS, vol. 4(2), pages 99-113, December.
    12. Stephen C. Graves, 1999. "A Single-Item Inventory Model for a Nonstationary Demand Process," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 50-61.
    13. Karl Inderfurth & Rainer Kleber, 2010. "An Advanced Heuristic for Multiple-Option Spare Parts Procurement after End-of-Production," FEMM Working Papers 100005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    14. Sirong Luo & Jianrong Wang, 2017. "A technical note on the dynamic nonstationary inventory-pricing control model with lost sale," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5816-5825, October.
    15. Philip Kaminsky & Jayashankar M. Swaminathan, 2004. "Effective Heuristics for Capacitated Production Planning with Multiperiod Production and Demand with Forecast Band Refinement," Manufacturing & Service Operations Management, INFORMS, vol. 6(2), pages 184-194, March.
    16. 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.
    17. Iida, Tetsuo, 2001. "The infinite horizon non-stationary stochastic multi-echelon inventory problem and near-myopic policies," European Journal of Operational Research, Elsevier, vol. 134(3), pages 525-539, November.
    18. John J. Neale & Sean P. Willems, 2009. "Managing Inventory in Supply Chains with Nonstationary Demand," Interfaces, INFORMS, vol. 39(5), pages 388-399, October.
    19. Philip Kaminsky & Jayashankar M. Swaminathan, 2001. "Utilizing Forecast Band Refinement for Capacitated Production Planning," Manufacturing & Service Operations Management, INFORMS, vol. 3(1), pages 68-81, August.
    20. Stephen C. Graves & Sean P. Willems, 2008. "Strategic Inventory Placement in Supply Chains: Nonstationary Demand," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 278-287, March.
    21. Nasr, Walid W. & Elshar, Ibrahim J., 2018. "Continuous inventory control with stochastic and non-stationary Markovian demand," European Journal of Operational Research, Elsevier, vol. 270(1), pages 198-217.
    22. Argon, Nilay Tanik & Gullu, Refik & Erkip, Nesim, 2001. "Analysis of an inventory system under backorder correlated deterministic demand and geometric supply process," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 247-254, May.
    23. Chen, Frank Y. & Krass, Dmitry, 2001. "Inventory models with minimal service level constraints," European Journal of Operational Research, Elsevier, vol. 134(1), pages 120-140, October.
    24. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    25. 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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