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The Nonstationary Stochastic Lead-Time Inventory Problem: Near-Myopic Bounds, Heuristics, and Testing

Author

Listed:
  • Ravi Anupindi

    (J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60208)

  • Thomas E. Morton

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

  • David Pentico

    (School of Business, Duquesne University, Pittsburgh, Pennsylvania 15282)

Abstract

The purpose of the current paper is to combine the classical results of Kaplan (Kaplan, R. 1970. Dynamic inventory model with stochastic lead times. Management Sci. 16(2) 491--507.) and Ehrhardt (Ehrhardt, R. 1984. (s, S) Policies for a dynamic inventory model with stochastic lead times. Oper. Res. 32(1) 121--132.) for stochastic leadtime problems with recent work of Morton and Pentico (Morton, T., D. Pentico. 1995. The finite horizon nonstationary stochastic inventory problem near-myopic bounds, heuristics, testing. Management Sci. 41(2) 334--343.), which assumed zero lag, to obtain near-myopic bounds and heuristics for the nonstationary stochastic leadtime problem with arbitrary sequences of demand distributions, and to obtain planning horizon results. Four heuristics have been tested on a number of different demand scenarios over a number of random trials for four different leadtime distributions. The myopic (simplest) heuristic performs well only for moderately varying problems without heavy end of season salvaging, giving errors for this type of problem that are less than 1.5%. However, the average error for the myopic heuristic over all scenarios tested is 20.0%. The most accurate heuristic is the near-myopic heuristic which averages 0.5% form optimal across all leadtime distributions with a maximum error of 4.7%. The average error with increases in variance of the leadtime distribution.

Suggested Citation

  • Ravi Anupindi & Thomas E. Morton & David Pentico, 1996. "The Nonstationary Stochastic Lead-Time Inventory Problem: Near-Myopic Bounds, Heuristics, and Testing," Management Science, INFORMS, vol. 42(1), pages 124-129, January.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:1:p:124-129
    DOI: 10.1287/mnsc.42.1.124
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    Cited by:

    1. Zolfagharinia, Hossein & Haughton, Michael, 2014. "The benefit of advance load information for truckload carriers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 70(C), pages 34-54.
    2. Zolfagharinia, Hossein & Haughton, Michael, 2016. "Effective truckload dispatch decision methods with incomplete advance load information," European Journal of Operational Research, Elsevier, vol. 252(1), pages 103-121.
    3. James T. Treharne & Charles R. Sox, 2002. "Adaptive Inventory Control for Nonstationary Demand and Partial Information," Management Science, INFORMS, vol. 48(5), pages 607-624, May.
    4. 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.
    5. Asadi, Amin & Nurre Pinkley, Sarah, 2021. "A stochastic scheduling, allocation, and inventory replenishment problem for battery swap stations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 146(C).
    6. 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.
    7. 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.
    8. 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.
    9. Srinivas Bollapragada & Thomas E. Morton, 1999. "Myopic Heuristics for the Random Yield Problem," Operations Research, INFORMS, vol. 47(5), pages 713-722, October.
    10. Ningyuan Chen & Steven Kou & Chun Wang, 2018. "A Partitioning Algorithm for Markov Decision Processes with Applications to Market Microstructure," Management Science, INFORMS, vol. 64(2), pages 784-803, February.
    11. Jing-Sheng Song & Candace A. Yano & Panupol Lerssrisuriya, 2000. "Contract Assembly: Dealing with Combined Supply Lead Time and Demand Quantity Uncertainty," Manufacturing & Service Operations Management, INFORMS, vol. 2(3), pages 287-296, July.
    12. 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.
    13. Jodlbauer, Herbert & Reitner, Sonja, 2012. "Optimizing service-level and relevant cost for a stochastic multi-item cyclic production system," International Journal of Production Economics, Elsevier, vol. 136(2), pages 306-317.
    14. 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.

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