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Good and Bad News About the ( S , T ) Policy

Author

Listed:
  • Fang Liu

    (Nanyang Business School, Nanyang Technological University, Singapore 639798)

  • Jing-Sheng Song

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708; and School of Management, Fudan University, Shanghai 200433, China)

Abstract

This paper studies the optimization of the ( S , T ) inventory policy, where T is the replenishment interval and S is the order-up-to level. First, we demonstrate that the previously established joint convexity of the long-run average cost is false. Hence, the optimization is not straightforward. We then point out that the joint convexity concept depends on whether S and T are continuous or discrete variables, and in some situations it may not even be well defined. Nonetheless, we are able to identify several useful properties of the cost function, such as submodularity and coordinatewise convexity. Based on these properties, we develop efficient algorithms to compute the optimal policy for continuous and discrete demands.

Suggested Citation

  • Fang Liu & Jing-Sheng Song, 2012. "Good and Bad News About the ( S , T ) Policy," Manufacturing & Service Operations Management, INFORMS, vol. 14(1), pages 42-49, January.
    • Handle: RePEc:inm:ormsom:v:14:y:2012:i:1:p:42-49
    DOI: 10.1287/msom.1110.0353
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    References listed on IDEAS

    as
    1. Filippo Fiorani & Elisa Luciano & Patrizia Semeraro, 2007. "Single and joint default in a structural model with purely discontinuous assets," Carlo Alberto Notebooks 41, Collegio Carlo Alberto.
    2. Filippo Fiorani & Elisa Luciano & Patrizia Semeraro, 2010. "Single and joint default in a structural model with purely discontinuous asset prices," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 249-263.
    3. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
    4. Uday S. Rao, 2003. "Properties of the Periodic Review (R, T) Inventory Control Policy for Stationary, Stochastic Demand," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 37-53, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Lagodimos, A.G. & Skouri, K. & Christou, I.T. & Chountalas, P.T., 2018. "The discrete-time EOQ model: Solution and implications," European Journal of Operational Research, Elsevier, vol. 266(1), pages 112-121.
    2. Qinan Wang & Sven Axsäter, 2013. "Fixed‐interval joint‐replenishment policies for distribution systems with multiple retailers and stochastic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 637-651, December.
    3. Ang, Marcus & Song, Jing-Sheng & Wang, Mingzheng & Zhang, Hanqin, 2013. "On properties of discrete (r, q) and (s, T) inventory systems," European Journal of Operational Research, Elsevier, vol. 229(1), pages 95-105.
    4. Kevin H. Shang & Zhijie Tao & Sean X. Zhou, 2015. "Optimizing Reorder Intervals for Two-Echelon Distribution Systems with Stochastic Demand," Operations Research, INFORMS, vol. 63(2), pages 458-475, April.
    5. Prak, Derk & Teunter, Rudolf & Babai, M. Z. & Syntetos, A. A. & Boylan, D, 2018. "Forecasting and Inventory Control with Compound Poisson Demand Using Periodic Demand Data," Research Report 2018010, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    6. Yiwei Chen & Cong Shi, 2019. "Joint Pricing and Inventory Management with Strategic Customers," Operations Research, INFORMS, vol. 67(6), pages 1610-1627, November.
    7. Apurva Jain & Kamran Moinzadeh & Yong-Pin Zhou, 2012. "A Single-Supplier, Multiple-Retailer Model with Single-Season, Multiple-Ordering Opportunities, and Fixed Ordering Cost," Operations Research, INFORMS, vol. 60(5), pages 1098-1110, October.
    8. Dina Smirnov & Yale T. Herer & Assaf Avrahami, 2021. "Two‐Phase Newsvendor with Optimally Timed Additional Replenishment: Model, Algorithm, Case Study," Production and Operations Management, Production and Operations Management Society, vol. 30(9), pages 2871-2889, September.
    9. Wang, Qinan & Wan, Guangyu, 2023. "Fixed-interval order-up-to policies and myopic optimal warehouse stock allocation for one-warehouse multiple-retailer systems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1112-1124.
    10. Wang, Qinan, 2013. "A periodic-review inventory control policy for a two-level supply chain with multiple retailers and stochastic demand," European Journal of Operational Research, Elsevier, vol. 230(1), pages 53-62.

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