IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v67y2020i7p487-502.html
   My bibliography  Save this article

Optimal policies for stochastic clearing systems with time‐dependent delay penalties

Author

Listed:
  • Qi‐Ming He
  • James H. Bookbinder
  • Qishu Cai

Abstract

We study stochastic clearing systems with a discrete‐time Markovian input process, and an output mechanism that intermittently and instantaneously clears the system partially or completely. The decision to clear the system depends on both quantities and delays of outstanding inputs. Clearing the system incurs a fixed cost, and outstanding inputs are charged a delay penalty, which is a general increasing function of the quantities and delays of individual inputs. By recording the quantities and delays of outstanding inputs in a sequence, we model the clearing system as a tree‐structured Markov decision process over both a finite and infinite horizon. We show that the optimal clearing policies, under realistic conditions, are of the on‐off type or the threshold type. Based on the characterization of the optimal policies, we develop efficient algorithms to compute parameters of the optimal policies for such complex clearing systems for the first time. We conduct a numerical analysis on the impact of the nonlinear delay penalty cost function, the comparison of the optimal policy and the classical hybrid policy (ie, quantity and age thresholds), and the impact of the state of the input process. Our experiments demonstrate that (a) the classical linear approximation of the cost function can lead to significant performance differences; (b) the classical hybrid policy may perform poorly (as compared to the optimal policies); and (c) the consideration of the state of the input process makes significant improvement in system performance.

Suggested Citation

  • Qi‐Ming He & James H. Bookbinder & Qishu Cai, 2020. "Optimal policies for stochastic clearing systems with time‐dependent delay penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 487-502, October.
  • Handle: RePEc:wly:navres:v:67:y:2020:i:7:p:487-502
    DOI: 10.1002/nav.21931
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21931
    Download Restriction: no

    File URL: https://libkey.io/10.1002/nav.21931?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. Shaler Stidham, 1977. "Cost Models for Stochastic Clearing Systems," Operations Research, INFORMS, vol. 25(1), pages 100-127, February.
    2. Donald L. Iglehart, 1963. "Optimality of (s, S) Policies in the Infinite Horizon Dynamic Inventory Problem," Management Science, INFORMS, vol. 9(2), pages 259-267, January.
    3. 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.
    4. Shaler Stidham, 1986. "Clearing Systems and ( s , S ) Inventory Systems with Nonlinear Costs and Positive Lead Times," Operations Research, INFORMS, vol. 34(2), pages 276-280, April.
    5. Arthur F. Veinott, Jr. & Harvey M. Wagner, 1965. "Computing Optimal (s, S) Inventory Policies," Management Science, INFORMS, vol. 11(5), pages 525-552, March.
    6. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    7. Qing Li & Peiwen Yu & Xiaoli Wu, 2016. "Managing Perishable Inventories in Retailing: Replenishment, Clearance Sales, and Segregation," Operations Research, INFORMS, vol. 64(6), pages 1270-1284, December.
    8. Bookbinder, James H. & Higginson, James K., 2002. "Probabilistic modeling of freight consolidation by private carriage," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 38(5), pages 305-318, September.
    9. Stidham, Shaler, 1974. "Stochastic clearing systems," Stochastic Processes and their Applications, Elsevier, vol. 2(1), pages 85-113, January.
    10. James K. Higginson & James H. Bookbinder, 1995. "Markovian Decision Processes in Shipment Consolidation," Transportation Science, INFORMS, vol. 29(3), pages 242-255, August.
    11. Dirk Beyer & Feng Cheng & Suresh P. Sethi & Michael Taksar, 2010. "Markovian Demand Inventory Models," International Series in Operations Research and Management Science, Springer, number 978-0-387-71604-6, April.
    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. Nurehemaiti Yiming, 2024. "Dynamic Analysis of the M/G/1 Stochastic Clearing Queueing Model in a Three-Phase Environment," Mathematics, MDPI, vol. 12(6), pages 1-26, March.
    2. Wei, Bo & Çetinkaya, Sıla & Cline, Daren B.H., 2023. "Inbound replenishment and outbound dispatch decisions under hybrid shipment consolidation policies: An analytical model and comparison," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).
    3. Feray Tunçalp & Lerzan Örmeci & Evrim D. Güneş, 2024. "Capacity allocation in a two-channel service system from a social planner’s perspective," Queueing Systems: Theory and Applications, Springer, vol. 108(1), pages 185-213, October.

    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. 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.
    2. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    3. Walid W. Nasr, 2022. "Inventory systems with stochastic and batch demand: computational approaches," Annals of Operations Research, Springer, vol. 309(1), pages 163-187, February.
    4. Yee, Hannah & van Staden, Heletjé E. & Boute, Robert N., 2024. "Dual sourcing under non-stationary demand and partial observability," European Journal of Operational Research, Elsevier, vol. 314(1), pages 94-110.
    5. Alain Bensoussan & Lama Moussawi-Haidar & Metin Çakanyıldırım, 2010. "Inventory control with an order-time constraint: optimality, uniqueness and significance," Annals of Operations Research, Springer, vol. 181(1), pages 603-640, December.
    6. Oded Berman & Mahmut Parlar & David Perry & M. J. M. Posner, 2005. "Production/Clearing Models Under Continuous and Sporadic Reviews," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 203-224, June.
    7. Jinhui Han & Suresh P. Sethi & Chi Chung Siu & Sheung Chi Phillip Yam, 2023. "Co‐op advertising in randomly fluctuating markets," Production and Operations Management, Production and Operations Management Society, vol. 32(6), pages 1617-1635, June.
    8. Arnoud den Boer & Ohad Perry & Bert Zwart, 2018. "Dynamic pricing policies for an inventory model with random windows of opportunities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 660-675, December.
    9. Li, Xiaoming, 2010. "Optimal inventory policies in decentralized supply chains," International Journal of Production Economics, Elsevier, vol. 128(1), pages 303-309, November.
    10. Guillermo Gallego & Özalp Özer, 2003. "Optimal Replenishment Policies for Multiechelon Inventory Problems Under Advance Demand Information," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 157-175, February.
    11. David Perry & Wolfgang Stadje & Shelemyahu Zacks, 2005. "Sporadic and Continuous Clearing Policies for a Production/Inventory System Under an M / G Demand Process," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 354-368, May.
    12. Lee, Jun-Yeon & Ren, Louie, 2011. "Vendor-managed inventory in a global environment with exchange rate uncertainty," International Journal of Production Economics, Elsevier, vol. 130(2), pages 169-174, April.
    13. Satya S. Malladi & Alan L. Erera & Chelsea C. White, 2023. "Inventory control with modulated demand and a partially observed modulation process," Annals of Operations Research, Springer, vol. 321(1), pages 343-369, February.
    14. Tunc, Huseyin & Kilic, Onur A. & Tarim, S. Armagan & Eksioglu, Burak, 2011. "The cost of using stationary inventory policies when demand is non-stationary," Omega, Elsevier, vol. 39(4), pages 410-415, August.
    15. Hong-Qiao Chen & Xiao-Song Ding & Ji-Hong Zhang & Hua-Yi Li, 2020. "Optimal Production-Inventory Policy for a Periodic-Review Energy Buy-Back System over an Infinite Planning Horizon," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(02), pages 1-32, March.
    16. Lagodimos, A.G. & Christou, I.T. & Skouri, K., 2012. "Computing globally optimal (s,S,T) inventory policies," Omega, Elsevier, vol. 40(5), pages 660-671.
    17. Satır, Benhür & Erenay, Fatih Safa & Bookbinder, James H., 2018. "Shipment consolidation with two demand classes: Rationing the dispatch capacity," European Journal of Operational Research, Elsevier, vol. 270(1), pages 171-184.
    18. 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.
    19. Yonit Barron & Dror Hermel, 2017. "Shortage decision policies for a fluid production model with MAP arrivals," International Journal of Production Research, Taylor & Francis Journals, vol. 55(14), pages 3946-3969, July.
    20. Awi Federgruen & Min Wang, 2015. "Inventory Models with Shelf-Age and Delay-Dependent Inventory Costs," Operations Research, INFORMS, vol. 63(3), pages 701-715, June.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:67:y:2020:i:7:p:487-502. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.