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Tractable (Q, R) Heuristic Models for Constrained Service Levels

Author

Listed:
  • David E. Platt

    (College of Business Administration, University of Texas, Austin, Texas 78712-1172)

  • Lawrence W. Robinson

    (Johnson Graduate School of Management, Cornell University, Ithaca, New York 14853-4201)

  • Robert B. Freund

    (College of Business Administration, University of Texas, Austin, Texas 78712-1172)

Abstract

The fill rate (the proportion of demand that is satisfied from stock) is a viable alternative in inventory models to the hard-to-quantify penalty cost. However, a number of difficulties have impeded its implementation, among them that the existing cycle-based approximate solutions do not reflect the possibility of multiple outstanding orders and that the optimal policy cannot be found directly, but must be iteratively calculated. We show that for a large family of leadtime demand distributions, the optimal policy depends on only two parameters: the fill rate and the economic order quantity (EOQ) scaled by the standard deviation of demand over the constant leadtime. If we then assume that the leadtime demand is normally distributed, we can use the asymptotic results as the EOQ goes to zero and to positive infinity to fit atheoretic curves for the order quantity Q and the reorder point R. These fitted curves yield a good (Q, R) policy without iteration. We also find that, among the set of simple heuristics, the limit form as EOQ goes to positive infinity provides a better alternative to simply setting Q equal to the EOQ.

Suggested Citation

  • David E. Platt & Lawrence W. Robinson & Robert B. Freund, 1997. "Tractable (Q, R) Heuristic Models for Constrained Service Levels," Management Science, INFORMS, vol. 43(7), pages 951-965, July.
  • Handle: RePEc:inm:ormnsc:v:43:y:1997:i:7:p:951-965
    DOI: 10.1287/mnsc.43.7.951
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    Citations

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    Cited by:

    1. Strijbosch, L.W.G. & Moors, J.J.A., 1999. "Simple Expressions for Safety Factors in Inventory Control," Discussion Paper 1999-112, Tilburg University, Center for Economic Research.
    2. Chiang, Chi, 2010. "An order expediting policy for continuous review systems with manufacturing lead-time," European Journal of Operational Research, Elsevier, vol. 203(2), pages 526-531, June.
    3. Eynan, Amit & Kropp, Dean H., 2007. "Effective and simple EOQ-like solutions for stochastic demand periodic review systems," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1135-1143, August.
    4. Amy Hing‐Ling Lau & Hon‐Shiang Lau & David F. Pyke, 2002. "Degeneracy in inventory models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(7), pages 686-705, October.
    5. Eugenia Babiloni & Ester Guijarro & Juan R. Trapero, 2023. "Stock control analytics: a data-driven approach to compute the fill rate considering undershoots," Operational Research, Springer, vol. 23(1), pages 1-25, March.
    6. Vipul Agrawal & Sridhar Seshadri, 2000. "Distribution free bounds for service constrained (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 635-656, December.
    7. Lau, Amy Hing Ling & Lau, Hon-Shiang, 2008. "An improved (Q, R) formulation when the stockout cost is incurred on a per-stockout basis," International Journal of Production Economics, Elsevier, vol. 111(2), pages 421-434, February.
    8. Hon‐Shiang Lau & Amy Hing‐Ling Lau, 2003. "Nonrobustness of the normal approximation of lead‐time demand in a (Q, R) system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(2), pages 149-166, March.
    9. Lee, Jun-Yeon & Schwarz, Leroy B., 2007. "Leadtime reduction in a (Q,r) inventory system: An agency perspective," International Journal of Production Economics, Elsevier, vol. 105(1), pages 204-212, January.
    10. Matthew J. Sobel, 2004. "Fill Rates of Single-Stage and Multistage Supply Systems," Manufacturing & Service Operations Management, INFORMS, vol. 6(1), pages 41-52, June.
    11. Tamer Boyacı & Guillermo Gallego, 2002. "Managing waiting times of backordered demands in single‐stage (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 557-573, September.
    12. Halkos, George & Kevork, Ilias & Tziourtzioumis, Chris, 2014. "Optimal inventory policies with an exact cost function under large demand uncertainty," MPRA Paper 60545, University Library of Munich, Germany.
    13. Lau, Amy Hing-Ling & Lau, Hon-Shiang, 2002. "A comparison of different methods for estimating the average inventory level in a (Q,R) system with backorders," International Journal of Production Economics, Elsevier, vol. 79(3), pages 303-316, October.
    14. Eugenia Babiloni & Ester Guijarro, 2020. "Fill rate: from its definition to its calculation for the continuous (s, Q) inventory system with discrete demands and lost sales," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 35-43, March.
    15. Rego, José Roberto do & Mesquita, Marco Aurélio de, 2015. "Demand forecasting and inventory control: A simulation study on automotive spare parts," International Journal of Production Economics, Elsevier, vol. 161(C), pages 1-16.
    16. Shore, Haim, 1999. "Optimal solutions for stochastic inventory models when the lead-time demand distribution is partially specified," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 477-485, March.
    17. Lee, Chung-Yee & Lee, Hau L. & Zhang, Jiheng, 2015. "The impact of slow ocean steaming on delivery reliability and fuel consumption," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 76(C), pages 176-190.
    18. Ting-Chen Hu & Kuo-Chen Hung & Kuo-Lung Yang, 2019. "The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    19. Marcus Ang & Karl Sigman & Jing-Sheng Song & Hanqin Zhang, 2017. "Closed-Form Approximations for Optimal ( r , q ) and ( S , T ) Policies in a Parallel Processing Environment," Operations Research, INFORMS, vol. 65(5), pages 1414-1428, October.

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