IDEAS home Printed from https://ideas.repec.org/a/inm/ormsom/v14y2012i1p42-49.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/msom.1110.0353
    Download Restriction: no
    File URL: https://libkey.io/10.1287/msom.1110.0353?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. 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).
    4. 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.
    5. 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.
    6. 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.
    7. Yiwei Chen & Cong Shi, 2019. "Joint Pricing and Inventory Management with Strategic Customers," Operations Research, INFORMS, vol. 67(6), pages 1610-1627, November.
    8. 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.
    9. 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.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," Working Papers - Mathematical Economics 2012-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    2. Laura Ballotta & Ioannis Kyriakou, 2015. "Convertible bond valuation in a jump diffusion setting with stochastic interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 115-129, January.
    3. Maxim Finkelstein & Ji Hwan Cha, 2021. "On degradation-based imperfect repair and induced generalized renewal processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1026-1045, December.
    4. Song, Kai & Cui, Lirong, 2022. "A common random effect induced bivariate gamma degradation process with application to remaining useful life prediction," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    5. Shafiee, Mahmood & Finkelstein, Maxim & Bérenguer, Christophe, 2015. "An opportunistic condition-based maintenance policy for offshore wind turbine blades subjected to degradation and environmental shocks," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 463-471.
    6. Antonio Romero-Medina & Matteo Triossi, 2013. "Games with capacity manipulation: incentives and Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 701-720, September.
    7. Vale, Cecília & M. Lurdes, Simões, 2013. "Stochastic model for the geometrical rail track degradation process in the Portuguese railway Northern Line," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 91-98.
    8. Song, Kai & Shi, Jian & Yi, Xiaojian, 2020. "A time-discrete and zero-adjusted gamma process model with application to degradation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    9. Olde Keizer, Minou C.A. & Teunter, Ruud H. & Veldman, Jasper, 2016. "Clustering condition-based maintenance for systems with redundancy and economic dependencies," European Journal of Operational Research, Elsevier, vol. 251(2), pages 531-540.
    10. Cholette, Michael E. & Yu, Hongyang & Borghesani, Pietro & Ma, Lin & Kent, Geoff, 2019. "Degradation modeling and condition-based maintenance of boiler heat exchangers using gamma processes," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 184-196.
    11. Giorgio, Massimiliano & Pulcini, Gianpaolo, 2024. "The effect of model misspecification of the bounded transformed gamma process on maintenance optimization," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    12. Hatem Ben‐Ameur & Rim Chérif & Bruno Rémillard, 2020. "Dynamic programming for valuing American options under a variance‐gamma process," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(10), pages 1548-1561, October.
    13. Thomas Michael Welte & Iver Bakken Sperstad & Espen Høegh Sørum & Magne Lorentzen Kolstad, 2017. "Integration of Degradation Processes in a Strategic Offshore Wind Farm O&M Simulation Model," Energies, MDPI, vol. 10(7), pages 1-18, July.
    14. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2023. "Improving classical optimal age-replacement policies for degrading items," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    15. Elisa Luciano, 2007. "Copula-Based Default Dependence Modelling: Where Do We Stand?," ICER Working Papers - Applied Mathematics Series 21-2007, ICER - International Centre for Economic Research.
    16. Michiel A. J. uit het Broek & Ruud H. Teunter & Bram de Jonge & Jasper Veldman & Nicky D. Van Foreest, 2020. "Condition-Based Production Planning: Adjusting Production Rates to Balance Output and Failure Risk," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 792-811, July.
    17. MERCIER, Sophie & CASTRO, I.T., 2019. "Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system," European Journal of Operational Research, Elsevier, vol. 273(1), pages 237-248.
    18. Zhao, Xuejing & Fouladirad, Mitra & Bérenguer, Christophe & Bordes, Laurent, 2010. "Condition-based inspection/replacement policies for non-monotone deteriorating systems with environmental covariates," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 921-934.
    19. E Deloux & B Castanier & C Bérenguer, 2008. "Maintenance policy for a deteriorating system evolving in a stressful environment," Journal of Risk and Reliability, , vol. 222(4), pages 613-622, December.
    20. Phuc Do & Christophe Bérenguer, 2022. "Residual life-based importance measures for predictive maintenance decision-making," Journal of Risk and Reliability, , vol. 236(1), pages 98-113, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormsom:v:14:y:2012:i:1:p:42-49. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.