IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v66y2019i3p193-212.html
   My bibliography  Save this article

Optimal control policies for an inventory system with commitment lead time

Author

Listed:
  • Taher Ahmadi
  • Zümbül Atan
  • Ton de Kok
  • Ivo Adan

Abstract

We consider a firm which faces a Poisson customer demand and uses a base‐stock policy to replenish its inventories from an outside supplier with a fixed lead time. The firm can use a preorder strategy which allows the customers to place their orders before their actual need. The time from a customer's order until the date a product is actually needed is called commitment lead time. The firm pays a commitment cost which is strictly increasing and convex in the length of the commitment lead time. For such a system, we prove the optimality of bang‐bang and all‐or‐nothing policies for the commitment lead time and the base‐stock policy, respectively. We study the case where the commitment cost is linear in the length of the commitment lead time in detail. We show that there exists a unit commitment cost threshold which dictates the optimality of either a buy‐to‐order (BTO) or a buy‐to‐stock strategy. The unit commitment cost threshold is increasing in the unit holding and backordering costs and decreasing in the mean lead time demand. We determine the conditions on the unit commitment cost for profitability of the BTO strategy and study the case with a compound Poisson customer demand.

Suggested Citation

  • Taher Ahmadi & Zümbül Atan & Ton de Kok & Ivo Adan, 2019. "Optimal control policies for an inventory system with commitment lead time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(3), pages 193-212, April.
    • Handle: RePEc:wly:navres:v:66:y:2019:i:3:p:193-212
    DOI: 10.1002/nav.21835
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21835
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21835?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. Cuihong Li & Fuqiang Zhang, 2013. "Advance Demand Information, Price Discrimination, and Preorder Strategies," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 57-71, September.
    2. Mohammed Hichame Benbitour & Evren Sahin, 2015. "Evaluation of the Impact of Uncertain Advance Demand Information on Production/Inventory Systems," Post-Print hal-01199290, HAL.
    3. Kevin McCardle & Kumar Rajaram & Christopher S. Tang, 2004. "Advance Booking Discount Programs Under Retail Competition," Management Science, INFORMS, vol. 50(5), pages 701-708, May.
    4. Saif Benjaafar & William L. Cooper & Setareh Mardan, 2011. "Production‐inventory systems with imperfect advance demand information and updating," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 88-106, March.
    5. Yimin Wang & Brian Tomlin, 2009. "To wait or not to wait: Optimal ordering under lead time uncertainty and forecast updating," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 766-779, December.
    6. Tan, Tarkan & Gullu, Refik & Erkip, Nesim, 2007. "Modelling imperfect advance demand information and analysis of optimal inventory policies," European Journal of Operational Research, Elsevier, vol. 177(2), pages 897-923, March.
    7. Tetsuo Iida & Paul Zipkin, 2010. "Competition and Cooperation in a Two-Stage Supply Chain with Demand Forecasts," Operations Research, INFORMS, vol. 58(5), pages 1350-1363, October.
    8. Özalp Özer, 2003. "Replenishment Strategies for Distribution Systems Under Advance Demand Information," Management Science, INFORMS, vol. 49(3), pages 255-272, March.
    9. Zümbül Atan & Ton de Kok & Nico P. Dellaert & Richard van Boxel & Fred Janssen, 2016. "Setting Planned Leadtimes in Customer-Order-Driven Assembly Systems," Manufacturing & Service Operations Management, INFORMS, vol. 18(1), pages 122-140, February.
    10. Özalp Özer & Wei Wei, 2004. "Inventory Control with Limited Capacity and Advance Demand Information," Operations Research, INFORMS, vol. 52(6), pages 988-1000, December.
    11. Christopher S. Tang & Kumar Rajaram & Ayd{i}n Alptekinou{g}lu & Jihong Ou, 2004. "The Benefits of Advance Booking Discount Programs: Model and Analysis," Management Science, INFORMS, vol. 50(4), pages 465-478, April.
    12. Jansen, Sjors & Atan, Zümbül & Adan, Ivo & Kok, Ton de, 2019. "Setting optimal planned leadtimes in configure-to-order assembly systems," European Journal of Operational Research, Elsevier, vol. 273(2), pages 585-595.
    13. Geert-Jan van Houtum & Bram Kranenburg, 2015. "Spare Parts Inventory Control under System Availability Constraints," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4899-7609-3, December.
    14. Rema Hariharan & Paul Zipkin, 1995. "Customer-Order Information, Leadtimes, and Inventories," Management Science, INFORMS, vol. 41(10), pages 1599-1607, October.
    15. Guillermo Gallego & Özalp Özer, 2001. "Integrating Replenishment Decisions with Advance Demand Information," Management Science, INFORMS, vol. 47(10), pages 1344-1360, October.
    16. Kaijie Zhu & Ulrich W. Thonemann, 2004. "Modeling the Benefits of Sharing Future Demand Information," Operations Research, INFORMS, vol. 52(1), pages 136-147, February.
    17. Fikri Karaesmen & George Liberopoulos & Yves Dallery, 2004. "The Value of Advance Demand Information in Production/Inventory Systems," Annals of Operations Research, Springer, vol. 126(1), pages 135-157, February.
    18. Taher Ahmadi & Zumbul Atan & Ton de Kok & Ivo Adan, 2019. "Optimal control policies for assemble-to-order systems with commitment lead time," IISE Transactions, Taylor & Francis Journals, vol. 51(12), pages 1365-1382, December.
    19. Atan, Zümbül & Ahmadi, Taher & Stegehuis, Clara & Kok, Ton de & Adan, Ivo, 2017. "Assemble-to-order systems: A review," European Journal of Operational Research, Elsevier, vol. 261(3), pages 866-879.
    20. Ananth V. Iyer & Vinayak Deshpande & Zhengping Wu, 2003. "A Postponement Model for Demand Management," Management Science, INFORMS, vol. 49(8), pages 983-1002, August.
    21. G. J. Feeney & C. C. Sherbrooke, 1966. "The (S - 1, S) Inventory Policy Under Compound Poisson Demand," Management Science, INFORMS, vol. 12(5), pages 391-411, January.
    22. Thonemann, U. W., 2002. "Improving supply-chain performance by sharing advance demand information," European Journal of Operational Research, Elsevier, vol. 142(1), pages 81-107, October.
    23. 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.
    24. Felix Papier, 2016. "Supply Allocation Under Sequential Advance Demand Information," Operations Research, INFORMS, vol. 64(2), pages 341-361, April.
    25. Jean-Philippe Gayon & Saif Benjaafar & Francis de Véricourt, 2009. "Using Imperfect Advance Demand Information in Production-Inventory Systems with Multiple Customer Classes," Manufacturing & Service Operations Management, INFORMS, vol. 11(1), pages 128-143, July.
    26. Iida, Tetsuo, 2015. "Benefits of leadtime information and of its combination with demand forecast information," International Journal of Production Economics, Elsevier, vol. 163(C), pages 146-156.
    27. Felix Papier & Ulrich W. Thonemann, 2010. "Capacity Rationing in Stochastic Rental Systems with Advance Demand Information," Operations Research, INFORMS, vol. 58(2), pages 274-288, April.
    28. Tong Wang & Beril L. Toktay, 2008. "Inventory Management with Advance Demand Information and Flexible Delivery," Management Science, INFORMS, vol. 54(4), pages 716-732, 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. Liu, Liming & Xu, He & Zhu, Stuart X., 2020. "Push verse pull: Inventory-leadtime tradeoff for managing system variability," European Journal of Operational Research, Elsevier, vol. 287(1), pages 119-132.
    2. Jana Ralfs & Gudrun P. Kiesmüller, 2022. "Inventory management with advance demand information and flexible shipment consolidation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1009-1044, December.

    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. Alım, Muzaffer & Beullens, Patrick, 2022. "Improving inventory system performance by selective purchasing of buyers’ willingness to wait," European Journal of Operational Research, Elsevier, vol. 300(1), pages 124-136.
    2. Jana Ralfs & Gudrun P. Kiesmüller, 2022. "Inventory management with advance demand information and flexible shipment consolidation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1009-1044, December.
    3. Taher Ahmadi & Zümbül Atan & Ton Kok & Ivo Adan, 2020. "Time-based service constraints for inventory systems with commitment lead time," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 355-395, June.
    4. Fernando Bernstein & Gregory A. DeCroix, 2015. "Advance Demand Information in a Multiproduct System," Manufacturing & Service Operations Management, INFORMS, vol. 17(1), pages 52-65, February.
    5. Tong Wang & Beril L. Toktay, 2008. "Inventory Management with Advance Demand Information and Flexible Delivery," Management Science, INFORMS, vol. 54(4), pages 716-732, April.
    6. Rippe, Christoph & Kiesmüller, Gudrun P., 2023. "The repair kit problem with imperfect advance demand information," European Journal of Operational Research, Elsevier, vol. 304(2), pages 558-576.
    7. Choi, Tsan-Ming & Sethi, Suresh, 2010. "Innovative quick response programs: A review," International Journal of Production Economics, Elsevier, vol. 127(1), pages 1-12, September.
    8. Liberopoulos, George, 2008. "On the tradeoff between optimal order-base-stock levels and demand lead-times," European Journal of Operational Research, Elsevier, vol. 190(1), pages 136-155, October.
    9. Christoph Rippe & Gudrun P. Kiesmüller, 2023. "The added value of advance demand information for the planning of a repair kit," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(1), pages 311-335, March.
    10. Alexandar Angelus & Özalp Özer, 2016. "Knowledge You Can Act on: Optimal Policies for Assembly Systems with Expediting and Advance Demand Information," Operations Research, INFORMS, vol. 64(6), pages 1338-1371, December.
    11. Cuihong Li & Fuqiang Zhang, 2013. "Advance Demand Information, Price Discrimination, and Preorder Strategies," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 57-71, September.
    12. Zhu, Sha & Jaarsveld, Willem van & Dekker, Rommert, 2020. "Spare parts inventory control based on maintenance planning," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    13. Saif Benjaafar & William L. Cooper & Setareh Mardan, 2011. "Production‐inventory systems with imperfect advance demand information and updating," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 88-106, March.
    14. Michelle M. H. Şeref & Onur Şeref & Aydın Alptekinoğlu & S. Selçuk Erengüç, 2016. "Advance selling to strategic consumers," Computational Management Science, Springer, vol. 13(4), pages 597-626, October.
    15. Du, Bisheng & Larsen, Christian, 2017. "Reservation policies of advance orders in the presence of multiple demand classes," European Journal of Operational Research, Elsevier, vol. 256(2), pages 430-438.
    16. Oguzhan Vicil, 2021. "Optimizing stock levels for service-differentiated demand classes with inventory rationing and demand lead times," Flexible Services and Manufacturing Journal, Springer, vol. 33(2), pages 381-424, June.
    17. Feng, Haofang & Zhang, Sheng Hao & Zhang, Yong, 2023. "Managing production-inventory-maintenance systems with condition monitoring," European Journal of Operational Research, Elsevier, vol. 310(2), pages 698-711.
    18. Long Gao & Susan H. Xu & Michael O. Ball, 2012. "Managing an Available-to-Promise Assembly System with Dynamic Short-Term Pseudo-Order Forecast," Management Science, INFORMS, vol. 58(4), pages 770-790, April.
    19. Xu, Haoxuan & Gong, Yeming (Yale) & Chu, Chengbin & Zhang, Jinlong, 2017. "Dynamic lot-sizing models for retailers with online channels," International Journal of Production Economics, Elsevier, vol. 183(PA), pages 171-184.
    20. Siawsolit, Chokdee & Gaukler, Gary M., 2021. "Offsetting omnichannel grocery fulfillment cost through advance ordering of perishables," International Journal of Production Economics, Elsevier, vol. 239(C).

    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:66:y:2019:i:3:p:193-212. 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.