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Managing Inventory with Multiple Products, Lags in Delivery, Resource Constraints, and Lost Sales: A Mathematical Programming Approach

Author

Listed:
  • Brian Downs

    (Supply Chain Division, Aspen Technology, Inc., 1293 Eldridge Parkway, Houston, Texas 77077)

  • Richard Metters

    (Department of Information Systems and Operations Management, Edwin L. Cox School of Business, Southern Methodist University, Post Office Box 750333, Dallas, Texas 75275-0333)

  • John Semple

    (Department of Information Systems and Operations Management, Edwin L. Cox School of Business, Southern Methodist University, Post Office Box 750333, Dallas, Texas 75275-0333)

Abstract

This paper develops an order-up-to S inventory model that is designed to handle multiple items, resource constraints, lags in delivery, and lost sales without sacrificing computational simplicity. Mild conditions are shown to ensure that the expected average holding cost and the expected average shortage cost are separable convex functions of the order-up-to levels. We develop nonparametric estimates of these costs and use them in conjunction with linear programming to produce what is termed the "LP policy." The LP policy has two major advantages over traditional methods: first, it can be computed in complex environments such as the one described above; and second, it does not require an explicit functional form of demand, something that is difficult to specify accurately in practice. In two numerical experiments designed so that optimal policies could be computed, the LP policy fared well, differing from the optimal profit by an average of 2.20% and 1.84%, respectively. These results compare quite favorably with the errors incurred in traditional methods when a correctly specified distribution uses estimated parameters. Our findings support the effectiveness of this mathematical programming technique for approximating complex, real-world inventory control problems.

Suggested Citation

  • Brian Downs & Richard Metters & John Semple, 2001. "Managing Inventory with Multiple Products, Lags in Delivery, Resource Constraints, and Lost Sales: A Mathematical Programming Approach," Management Science, INFORMS, vol. 47(3), pages 464-479, March.
    • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:3:p:464-479
    DOI: 10.1287/mnsc.47.3.464.9774
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    References listed on IDEAS

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    Cited by:

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    3. Yanyi Xu & Sang-Phil Kim & Arnab Bisi & Maqbool Dada & Suresh Chand, 2018. "Base-Stock Models for Lost Sales: A Markovian Approach," Purdue University Economics Working Papers 1305, Purdue University, Department of Economics.
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    6. Cai, Gangshu (George) & Chiang, Wen-Chyuan & Chen, Xiangfeng, 2011. "Game theoretic pricing and ordering decisions with partial lost sales in two-stage supply chains," International Journal of Production Economics, Elsevier, vol. 130(2), pages 175-185, April.
    7. Paul Zipkin, 2008. "Old and New Methods for Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1256-1263, October.
    8. Ertogral, Kadir & Rahim, M.A., 2005. "Replenish-up-to inventory control policy with random replenishment intervals," International Journal of Production Economics, Elsevier, vol. 93(1), pages 399-405, January.
    9. Johansen, Soren Glud, 2005. "Base-stock policies for the lost sales inventory system with Poisson demand and Erlangian lead times," International Journal of Production Economics, Elsevier, vol. 93(1), pages 429-437, January.
    10. Bijvank, Marco & Vis, Iris F.A., 2012. "Lost-sales inventory systems with a service level criterion," European Journal of Operational Research, Elsevier, vol. 220(3), pages 610-618.
    11. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    12. Yanyi Xu & Doğan A. Serel & Arnab Bisi & Maqbool Dada, 2022. "Coping with Demand Uncertainty: The Interplay between Dual Sourcing and Endogenous Partial Backordering," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1560-1575, April.
    13. Bijvank, Marco & Johansen, Søren Glud, 2012. "Periodic review lost-sales inventory models with compound Poisson demand and constant lead times of any length," European Journal of Operational Research, Elsevier, vol. 220(1), pages 106-114.
    14. Schneider, Frank & Klabjan, Diego, 2013. "Inventory control in multi-channel retail," European Journal of Operational Research, Elsevier, vol. 227(1), pages 101-111.
    15. Lin, X. & Basten, R.J.I. & Kranenburg, A.A. & van Houtum, G.J., 2017. "Condition based spare parts supply," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 240-248.
    16. Woonghee Tim Huh & Ganesh Janakiraman, 2010. "Base‐stock policies in capacitated assembly systems: Convexity properties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(2), pages 109-118, March.
    17. Druehl, Cheryl T. & Schmidt, Glen M. & Souza, Gilvan C., 2009. "The optimal pace of product updates," European Journal of Operational Research, Elsevier, vol. 192(2), pages 621-633, January.
    18. Marco Bijvank & Woonghee Tim Huh & Ganesh Janakiraman & Wanmo Kang, 2014. "Robustness of Order-Up-to Policies in Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 62(5), pages 1040-1047, October.
    19. A. Gürhan Kök & Marshall L. Fisher, 2007. "Demand Estimation and Assortment Optimization Under Substitution: Methodology and Application," Operations Research, INFORMS, vol. 55(6), pages 1001-1021, December.
    20. Anshul Sheopuri & Ganesh Janakiraman & Sridhar Seshadri, 2010. "New Policies for the Stochastic Inventory Control Problem with Two Supply Sources," Operations Research, INFORMS, vol. 58(3), pages 734-745, June.
    21. David A. Goldberg & Dmitriy A. Katz-Rogozhnikov & Yingdong Lu & Mayank Sharma & Mark S. Squillante, 2016. "Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead Times," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 898-913, August.
    22. Ganesh Janakiraman & Robin O. Roundy, 2004. "Lost-Sales Problems with Stochastic Lead Times: Convexity Results for Base-Stock Policies," Operations Research, INFORMS, vol. 52(5), pages 795-803, October.

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