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. 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

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


    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. 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. 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.
    8. Yiwei Chen & Cong Shi, 2019. "Joint Pricing and Inventory Management with Strategic Customers," Operations Research, INFORMS, vol. 67(6), pages 1610-1627, November.
    9. 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.
    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.
    11. Kilic, Onur A. & Tarim, S. Armagan, 2024. "A simple heuristic for computing non-stationary inventory policies based on function approximation," European Journal of Operational Research, Elsevier, vol. 316(3), pages 899-905.

    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. 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).
    4. 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.
    5. 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).
    6. 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.
    7. 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.
    8. Wang, Xiaolin & Liu, Bin & Zhao, Xiujie, 2021. "A performance-based warranty for products subject to competing hard and soft failures," International Journal of Production Economics, Elsevier, vol. 233(C).
    9. Nicolai, R.P. & Frenk, J.B.G. & Dekker, R., 2007. "Modelling and Optimizing Imperfect Maintenance of Coatings on Steel Structures," ERIM Report Series Research in Management ERS-2007-043-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    10. Kevin H. Shang & Sean X. Zhou & Geert-Jan van Houtum, 2010. "Improving Supply Chain Performance: Real-Time Demand Information and Flexible Deliveries," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 430-448, May.
    11. Lin Wang & Zhiqiang Lu & Yifei Ren, 2019. "A rolling horizon approach for production planning and condition-based maintenance under uncertain demand," Journal of Risk and Reliability, , vol. 233(6), pages 1014-1028, December.
    12. Liang, Qingzhu & Yang, Yinghao & Peng, Changhong, 2023. "A reliability model for systems subject to mutually dependent degradation processes and random shocks under dynamic environments," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    13. Shen, Jingyuan & Cui, Lirong & Ma, Yizhong, 2019. "Availability and optimal maintenance policy for systems degrading in dynamic environments," European Journal of Operational Research, Elsevier, vol. 276(1), pages 133-143.
    14. Safaei, Fatemeh & Taghipour, Sharareh, 2024. "Integrated degradation-based burn-in and maintenance model for heterogeneous and highly reliable items," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    15. Maxim Finkelstein & Ji Hwan Cha, 2022. "Reducing degradation and age of items in imperfect repair modeling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1058-1081, December.
    16. Lu, Biao & Zhou, Xiaojun, 2017. "Opportunistic preventive maintenance scheduling for serial-parallel multistage manufacturing systems with multiple streams of deterioration," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 116-127.
    17. Xudan Chen & Guoxun Ji & Xinli Sun & Zhen Li, 2019. "Inverse Gaussian–based model with measurement errors for degradation analysis," Journal of Risk and Reliability, , vol. 233(6), pages 1086-1098, December.
    18. Liu, Xingheng & Matias, José & Jäschke, Johannes & Vatn, Jørn, 2022. "Gibbs sampler for noisy Transformed Gamma process: Inference and remaining useful life estimation," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    19. Giorgio, Massimiliano & Pulcini, Gianpaolo, 2018. "A new state-dependent degradation process and related model misidentification problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1027-1038.

    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.