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A Simple Heuristic for Computing Nonstationary (s, S) Policies

Author

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  • Srinivas Bollapragada

    (GE Corporate Research and Development Center, 1 Research Circle, Schenectady, New York 12309)

  • Thomas E. Morton

    (Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

Nonstationary inventory problems with set-up costs, proportional ordering costs, and stochastic demands occur in a large number of industrial, distribution, and service contexts. It is well known that nonstationary ( s , S ) policies are optimal for such problems. In this paper, we propose a simple, myopic heuristic for computing the policies. The heuristic involves approximating the future problem at each period by a stationary one and obtaining the solution to the corresponding stationary problem. We numerically compare our heuristic with an earlier myopic heuristic and the optimal dynamic programming solution procedure. Over all problems tested, the new heuristic averaged 1.7% error, compared with 2.0% error for the old procedure, and is on average 399 times as fast as the D.P. and 2062 as fast as the old heuristic. Moreover, our heuristic, owing to its myopic nature, requires the demand data only a few periods into the future, while the dynamic programming solution needs the demand data for the entire time horizon—which are typically not available in most practical situations.

Suggested Citation

  • Srinivas Bollapragada & Thomas E. Morton, 1999. "A Simple Heuristic for Computing Nonstationary (s, S) Policies," Operations Research, INFORMS, vol. 47(4), pages 576-584, August.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:4:p:576-584
    DOI: 10.1287/opre.47.4.576
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    References listed on IDEAS

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    1. Yu-Sheng Zheng & A. Federgruen, 1991. "Finding Optimal (s, S) Policies Is About As Simple As Evaluating a Single Policy," Operations Research, INFORMS, vol. 39(4), pages 654-665, August.
    2. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    3. Arthur F. Veinott, Jr. & Harvey M. Wagner, 1965. "Computing Optimal (s, S) Inventory Policies," Management Science, INFORMS, vol. 11(5), pages 525-552, March.
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    Cited by:

    1. Daniel Y. Mo & Stephen C. H. Ng & David Tai, 2019. "Revamping NetApp’s Service Parts Operations by Process Optimization," Service Science, INFORMS, vol. 49(6), pages 407-421, November.
    2. John J. Neale & Sean P. Willems, 2009. "Managing Inventory in Supply Chains with Nonstationary Demand," Interfaces, INFORMS, vol. 39(5), pages 388-399, October.
    3. Gah-Yi Ban, 2020. "Confidence Intervals for Data-Driven Inventory Policies with Demand Censoring," Operations Research, INFORMS, vol. 68(2), pages 309-326, March.
    4. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
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    6. 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.
    7. Ma, Xiyuan & Rossi, Roberto & Archibald, Thomas Welsh, 2022. "Approximations for non-stationary stochastic lot-sizing under (s,Q)-type policy," European Journal of Operational Research, Elsevier, vol. 298(2), pages 573-584.
    8. Tarim, S. Armagan & Smith, Barbara M., 2008. "Constraint programming for computing non-stationary (R, S) inventory policies," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1004-1021, September.
    9. Visentin, Andrea & Prestwich, Steven & Rossi, Roberto & Tarim, S. Armagan, 2021. "Computing optimal (R,s,S) policy parameters by a hybrid of branch-and-bound and stochastic dynamic programming," European Journal of Operational Research, Elsevier, vol. 294(1), pages 91-99.
    10. Amiri-Aref, Mehdi & Klibi, Walid & Babai, M. Zied, 2018. "The multi-sourcing location inventory problem with stochastic demand," European Journal of Operational Research, Elsevier, vol. 266(1), pages 72-87.
    11. Cong Shi & Huanan Zhang & Xiuli Chao & Retsef Levi, 2014. "Approximation algorithms for capacitated stochastic inventory systems with setup costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(4), pages 304-319, June.
    12. J. A. O. Magbagbeola & O. M. Ayinde & E. A. Alo & A. I. Akosile & E. O. Magbagbeola, 2012. "Operations Research Approach to Enhancing Enterprise through Alliances: A case study of Mowe Town, Ogun State, Nigeria," International Journal of Business Administration, International Journal of Business Administration, Sciedu Press, vol. 3(3), pages 2-10, May.
    13. 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.
    14. Retsef Levi & Cong Shi, 2013. "Approximation Algorithms for the Stochastic Lot-Sizing Problem with Order Lead Times," Operations Research, INFORMS, vol. 61(3), pages 593-602, June.
    15. Xiang, Mengyuan & Rossi, Roberto & Martin-Barragan, Belen & Tarim, S. Armagan, 2018. "Computing non-stationary (s, S) policies using mixed integer linear programming," European Journal of Operational Research, Elsevier, vol. 271(2), pages 490-500.
    16. Chen, Zhen & Rossi, Roberto, 2021. "A dynamic ordering policy for a stochastic inventory problem with cash constraints," Omega, Elsevier, vol. 102(C).
    17. Dural-Selcuk, Gozdem & Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2020. "The benefit of receding horizon control: Near-optimal policies for stochastic inventory control," Omega, Elsevier, vol. 97(C).

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