IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v261y2017i3p880-892.html
   My bibliography  Save this article

Optimizing (s, S) policies for multi-period inventory models with demand distribution uncertainty: Robust dynamic programing approaches

Author

Listed:
  • Qiu, Ruozhen
  • Sun, Minghe
  • Lim, Yun Fong

Abstract

This study considers a finite-horizon single-product periodic-review inventory management problem with demand distribution uncertainty. The problem is formulated as a dynamic program and the existence of an optimal (s, S) policy is proved. The corresponding dynamic robust counterpart models are then developed for the box and the ellipsoid uncertainty sets. These counterpart models are transformed into tractable linear and second-order cone programs, respectively. The effectiveness and practicality of the proposed robust optimization approaches are validated through a numerical study.

Suggested Citation

  • Qiu, Ruozhen & Sun, Minghe & Lim, Yun Fong, 2017. "Optimizing (s, S) policies for multi-period inventory models with demand distribution uncertainty: Robust dynamic programing approaches," European Journal of Operational Research, Elsevier, vol. 261(3), pages 880-892.
    • Handle: RePEc:eee:ejores:v:261:y:2017:i:3:p:880-892
    DOI: 10.1016/j.ejor.2017.02.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717301492
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.02.027?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hossein Abouee-Mehrizi & Oded Berman & Shrutivandana Sharma, 2015. "Optimal Joint Replenishment and Transshipment Policies in a Multi-Period Inventory System with Lost Sales," Operations Research, INFORMS, vol. 63(2), pages 342-350, April.
    2. Lin, Jun & Ng, Tsan Sheng, 2011. "Robust multi-market newsvendor models with interval demand data," European Journal of Operational Research, Elsevier, vol. 212(2), pages 361-373, July.
    3. Alfares, Hesham K. & Elmorra, Hassan H., 2005. "The distribution-free newsboy problem: Extensions to the shortage penalty case," International Journal of Production Economics, Elsevier, vol. 93(1), pages 465-477, January.
    4. Andersson, Jonas & Jörnsten, Kurt & Nonås, Sigrid Lise & Sandal, Leif & Ubøe, Jan, 2013. "A maximum entropy approach to the newsvendor problem with partial information," European Journal of Operational Research, Elsevier, vol. 228(1), pages 190-200.
    5. Dimitris Bertsimas & Aurélie Thiele, 2006. "A Robust Optimization Approach to Inventory Theory," Operations Research, INFORMS, vol. 54(1), pages 150-168, February.
    6. Liu, Yong & Qin, Fei & Fry, Michael J. & Raturi, Amitabh S., 2012. "Multi-period modeling of two-way price commitment under price-dependent demand," European Journal of Operational Research, Elsevier, vol. 221(3), pages 546-556.
    7. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    8. Pooya Farahvash & Tayfur Altiok, 2011. "A multi-period inventory model with multi-dimensional procurement bidding," Annals of Operations Research, Springer, vol. 186(1), pages 101-118, June.
    9. Fangruo Chen & Jing-Sheng Song, 2001. "Optimal Policies for Multiechelon Inventory Problems with Markov-Modulated Demand," Operations Research, INFORMS, vol. 49(2), pages 226-234, April.
    10. Ventura, José A. & Valdebenito, Victor A. & Golany, Boaz, 2013. "A dynamic inventory model with supplier selection in a serial supply chain structure," European Journal of Operational Research, Elsevier, vol. 230(2), pages 258-271.
    11. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    12. Jinfeng Yue & Bintong Chen & Min-Chiang Wang, 2006. "Expected Value of Distribution Information for the Newsvendor Problem," Operations Research, INFORMS, vol. 54(6), pages 1128-1136, December.
    13. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    14. Disney, Stephen M. & Maltz, Arnold & Wang, Xun & Warburton, Roger D.H., 2016. "Inventory management for stochastic lead times with order crossovers," European Journal of Operational Research, Elsevier, vol. 248(2), pages 473-486.
    15. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    16. Editors, 2014. "International Journal of Systems Science," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 1-1, December.
    17. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    18. Wang, Haifeng & Chen, Bocheng & Yan, Houmin, 2010. "Optimal inventory decisions in a multiperiod newsvendor problem with partially observed Markovian supply capacities," European Journal of Operational Research, Elsevier, vol. 202(2), pages 502-517, April.
    19. Chuen-Teck See & Melvyn Sim, 2010. "Robust Approximation to Multiperiod Inventory Management," Operations Research, INFORMS, vol. 58(3), pages 583-594, June.
    20. Song, Yuyue & Wang, Yunzeng, 2017. "Periodic review inventory systems with fixed order cost and uniform random yield," European Journal of Operational Research, Elsevier, vol. 257(1), pages 106-117.
    21. Lin, Yu-Jen, 2008. "Minimax distribution free procedure with backorder price discount," International Journal of Production Economics, Elsevier, vol. 111(1), pages 118-128, January.
    22. Wei, Cansheng & Li, Yongjian & Cai, Xiaoqiang, 2011. "Robust optimal policies of production and inventory with uncertain returns and demand," International Journal of Production Economics, Elsevier, vol. 134(2), pages 357-367, December.
    23. Aharon Ben-Tal & Boaz Golany & Arkadi Nemirovski & Jean-Philippe Vial, 2005. "Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach," Manufacturing & Service Operations Management, INFORMS, vol. 7(3), pages 248-271, February.
    24. Vlajic, Jelena V. & van der Vorst, Jack G.A.J. & Haijema, René, 2012. "A framework for designing robust food supply chains," International Journal of Production Economics, Elsevier, vol. 137(1), pages 176-189.
    25. Noblesse, Ann M. & Boute, Robert N. & Lambrecht, Marc R. & Van Houdt, Benny, 2014. "Characterizing order processes of continuous review (s,S) and (r,nQ) policies," European Journal of Operational Research, Elsevier, vol. 236(2), pages 534-547.
    26. Shushang Zhu & Masao Fukushima, 2009. "Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management," Operations Research, INFORMS, vol. 57(5), pages 1155-1168, October.
    27. Ahmed, Shabbir & Cakmak, Ulas & Shapiro, Alexander, 2007. "Coherent risk measures in inventory problems," European Journal of Operational Research, Elsevier, vol. 182(1), pages 226-238, October.
    28. Seong-Cheol Kang & Theodora Brisimi & Ioannis Paschalidis, 2015. "Distribution-dependent robust linear optimization with applications to inventory control," Annals of Operations Research, Springer, vol. 231(1), pages 229-263, August.
    29. Matsuyama, Keisuke, 2006. "The multi-period newsboy problem," European Journal of Operational Research, Elsevier, vol. 171(1), pages 170-188, May.
    30. Zhang, Dali & Xu, Huifu & Wu, Yue, 2009. "Single and multi-period optimal inventory control models with risk-averse constraints," European Journal of Operational Research, Elsevier, vol. 199(2), pages 420-434, December.
    31. Yun Fong Lim & Chen Wang, 2017. "Inventory Management Based on Target-Oriented Robust Optimization," Management Science, INFORMS, vol. 63(12), pages 4409-4427, December.
    32. Kwon, Kysang & Cheong, Taesu, 2014. "A minimax distribution-free procedure for a newsvendor problem with free shipping," European Journal of Operational Research, Elsevier, vol. 232(1), pages 234-240.
    33. Noblesse, Ann M. & Boute, Robert N. & Lambrecht, Marc R. & Van Houdt, Benny, 2014. "Lot sizing and lead time decisions in production/inventory systems," International Journal of Production Economics, Elsevier, vol. 155(C), pages 351-360.
    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. Qiu, Ruozhen & Ma, Lin & Sun, Minghe, 2023. "A robust omnichannel pricing and ordering optimization approach with return policies based on data-driven support vector clustering," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1337-1354.
    2. Zahra Mohammadnazari & Seyed Farid Ghannadpour, 2021. "Sustainable construction supply chain management with the spotlight of inventory optimization under uncertainty," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(7), pages 10937-10972, July.
    3. Chia-Nan Wang & Thanh-Tuan Dang & Ngoc-Ai-Thy Nguyen, 2020. "A Computational Model for Determining Levels of Factors in Inventory Management Using Response Surface Methodology," Mathematics, MDPI, vol. 8(8), pages 1-23, July.
    4. Xiang, Mengyuan & Rossi, Roberto & Martin-Barragan, Belen & Tarim, S. Armagan, 2018. "Computing non-stationary (s, S) policies using mixed integer linear programming," European Journal of Operational Research, Elsevier, vol. 271(2), pages 490-500.
    5. Ehsan Ahmadi & Dale T. Masel & Seth Hostetler & Reza Maihami & Iman Ghalehkhondabi, 2020. "A centralized stochastic inventory control model for perishable products considering age-dependent purchase price and lead time," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 231-269, April.
    6. Liu, Xinbao & Yang, Tianji & Pei, Jun & Liao, Haitao & Pohl, Edward A., 2019. "Replacement and inventory control for a multi-customer product service system with decreasing replacement costs," European Journal of Operational Research, Elsevier, vol. 273(2), pages 561-574.
    7. Zheng, Meimei & Su, Zhiyun & Wang, Dong & Pan, Ershun, 2024. "Joint maintenance and spare part ordering from multiple suppliers for multicomponent systems using a deep reinforcement learning algorithm," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    8. Nasr, Walid W. & Elshar, Ibrahim J., 2018. "Continuous inventory control with stochastic and non-stationary Markovian demand," European Journal of Operational Research, Elsevier, vol. 270(1), pages 198-217.
    9. Bao, Xing & Diabat, Ali & Zheng, Zhongliang, 2020. "An ambiguous manager's disruption decisions with insufficient data in recovery phase," International Journal of Production Economics, Elsevier, vol. 221(C).

    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. Qiu, Ruozhen & Shang, Jennifer & Huang, Xiaoyuan, 2014. "Robust inventory decision under distribution uncertainty: A CVaR-based optimization approach," International Journal of Production Economics, Elsevier, vol. 153(C), pages 13-23.
    2. Mengshi Lu & Zuo‐Jun Max Shen, 2021. "A Review of Robust Operations Management under Model Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1927-1943, June.
    3. Xin, Linwei & Goldberg, David A., 2021. "Time (in)consistency of multistage distributionally robust inventory models with moment constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1127-1141.
    4. Xie, Chen & Wang, Liangquan & Yang, Chaolin, 2021. "Robust inventory management with multiple supply sources," European Journal of Operational Research, Elsevier, vol. 295(2), pages 463-474.
    5. Thevenin, Simon & Ben-Ammar, Oussama & Brahimi, Nadjib, 2022. "Robust optimization approaches for purchase planning with supplier selection under lead time uncertainty," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1199-1215.
    6. Shin, Youngchul & Lee, Sangyoon & Moon, Ilkyeong, 2021. "Robust multiperiod inventory model with a new type of buy one get one promotion: “My Own Refrigerator”," Omega, Elsevier, vol. 99(C).
    7. Guo, Min & Chen, Yu-wang & Wang, Hongwei & Yang, Jian-Bo & Zhang, Keyong, 2019. "The single-period (newsvendor) problem under interval grade uncertainties," European Journal of Operational Research, Elsevier, vol. 273(1), pages 198-216.
    8. Bai, Qingguo & Xu, Jianteng & Gong, Yeming & Chauhan, Satyaveer S., 2022. "Robust decisions for regulated sustainable manufacturing with partial demand information: Mandatory emission capacity versus emission tax," European Journal of Operational Research, Elsevier, vol. 298(3), pages 874-893.
    9. Kamburowski, Jerzy, 2014. "The distribution-free newsboy problem under the worst-case and best-case scenarios," European Journal of Operational Research, Elsevier, vol. 237(1), pages 106-112.
    10. Hamed Mamani & Shima Nassiri & Michael R. Wagner, 2017. "Closed-Form Solutions for Robust Inventory Management," Management Science, INFORMS, vol. 63(5), pages 1625-1643, May.
    11. Viktoryia Buhayenko & Dick den Hertog, 2017. "Adjustable Robust Optimisation approach to optimise discounts for multi-period supply chain coordination under demand uncertainty," International Journal of Production Research, Taylor & Francis Journals, vol. 55(22), pages 6801-6823, November.
    12. Wang, Charles X. & Webster, Scott & Zhang, Sidong, 2014. "Robust price-setting newsvendor model with interval market size and consumer willingness-to-pay," International Journal of Production Economics, Elsevier, vol. 154(C), pages 100-112.
    13. Andreas Thorsen & Tao Yao, 2017. "Robust inventory control under demand and lead time uncertainty," Annals of Operations Research, Springer, vol. 257(1), pages 207-236, October.
    14. Akartunalı, Kerem & Dauzère-Pérès, Stéphane, 2022. "Dynamic lot sizing with stochastic demand timing," European Journal of Operational Research, Elsevier, vol. 302(1), pages 221-229.
    15. Karthik Natarajan & Dongjian Shi & Kim-Chuan Toh, 2014. "A Probabilistic Model for Minmax Regret in Combinatorial Optimization," Operations Research, INFORMS, vol. 62(1), pages 160-181, February.
    16. Zheng Cui & Jianpeng Ding & Daniel Zhuoyu Long & Lianmin Zhang, 2023. "Target‐based resource pooling problem," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1187-1204, April.
    17. Chan, Rebecca & Li, Zhaolin & Matsypura, Dmytro, 2020. "Assortment optimisation problem: A distribution-free approach," Omega, Elsevier, vol. 95(C).
    18. Zhi Chen & Weijun Xie, 2021. "Regret in the Newsvendor Model with Demand and Yield Randomness," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4176-4197, November.
    19. Michael R. Wagner, 2010. "Fully Distribution-Free Profit Maximization: The Inventory Management Case," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 728-741, November.
    20. Meng Qi & Ying Cao & Zuo-Jun (Max) Shen, 2022. "Distributionally Robust Conditional Quantile Prediction with Fixed Design," Management Science, INFORMS, vol. 68(3), pages 1639-1658, March.

    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:eee:ejores:v:261:y:2017:i:3:p:880-892. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.