IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v270y2024ics0925527324000483.html
   My bibliography  Save this article

Maximizing the survival probability in a cash flow inventory problem with a joint service level constraint

Author

Listed:
  • Chen, Zhen
  • Archibald, Thomas W.

Abstract

This paper investigates a multi-period stochastic cash flow inventory problem with the aim of maximizing the long-term survival probability, which may be the objective of some retailers especially in periods of economic distress. Demand in each period is stochastic and can be non-stationary. In order to avoid too many lost sales under this objective, we introduce a joint chance constraint requiring the probability of no stockouts during the planning horizon to be higher than a specified service level. We develop a scenario-based model and a sample average approximation (SAA) model to solve the problem. A statistical upper bound on the survival probability based on SAA is provided and we discuss upper and lower bounds for the problem based on stochastic dynamic programming. We also propose a rolling horizon approach with service rate updating to test the out-of-sample performance of the two stochastic models and solve problems with long planning horizons. We test the two methods in large numerical tests and find that the rolling horizon approach together with the stochastic models can solve realistically sized problems in reasonable time.

Suggested Citation

  • Chen, Zhen & Archibald, Thomas W., 2024. "Maximizing the survival probability in a cash flow inventory problem with a joint service level constraint," International Journal of Production Economics, Elsevier, vol. 270(C).
    • Handle: RePEc:eee:proeco:v:270:y:2024:i:c:s0925527324000483
    DOI: 10.1016/j.ijpe.2024.109191
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527324000483
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijpe.2024.109191?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. Fehmi Tanrısever & S. Sinan Erzurumlu & Nitin Joglekar, 2012. "Production, Process Investment, and the Survival of Debt‐Financed Startup Firms," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 637-652, July.
    2. Bruce L. Miller & Harvey M. Wagner, 1965. "Chance Constrained Programming with Joint Constraints," Operations Research, INFORMS, vol. 13(6), pages 930-945, December.
    3. Andrieu, L. & Henrion, R. & Römisch, W., 2010. "A model for dynamic chance constraints in hydro power reservoir management," European Journal of Operational Research, Elsevier, vol. 207(2), pages 579-589, December.
    4. Thomas W Archibald & Edgar Possani & Lyn C Thomas, 2015. "Managing inventory and production capacity in start-up firms," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(10), pages 1624-1634, October.
    5. A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
    6. Ernest Benedito & Albert Corominas & Carme Martínez & Marta Mas-Machuca, 2016. "Single-site strategic capacity planning considering renewal, maintenance, inventory, taxes and cash flow management," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(7), pages 970-981, July.
    7. Robert Swinney & Gérard P. Cachon & Serguei Netessine, 2011. "Capacity Investment Timing by Start-ups and Established Firms in New Markets," Management Science, INFORMS, vol. 57(4), pages 763-777, April.
    8. Michael N. Katehakis & Benjamin Melamed & Jim (Junmin) Shi, 2016. "Cash-Flow Based Dynamic Inventory Management," Production and Operations Management, Production and Operations Management Society, vol. 25(9), pages 1558-1575, September.
    9. Gökçe Esenduran & John V. Gray & Burcu Tan, 2022. "A Dynamic Analysis of Supply Chain Risk Management and Extended Payment Terms," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1394-1417, March.
    10. Nathan Charles Craig & Nicole DeHoratius & Ananth Raman, 2010. "The Impact of Supplier Inventory Service Level on Retailer Demand," Harvard Business School Working Papers 11-034, Harvard Business School, revised Jan 2016.
    11. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    12. T. W. Archibald & L. C. Thomas & J. M. Betts & R. B. Johnston, 2002. "Should Start-up Companies Be Cautious? Inventory Policies Which Maximise Survival Probabilities," Management Science, INFORMS, vol. 48(9), pages 1161-1174, September.
    13. Ke Fu & Xiting Gong & Vernon N. Hsu & Jiye Xue, 2021. "Dynamic Inventory Management with Inventory‐based Financing," Production and Operations Management, Production and Operations Management Society, vol. 30(5), pages 1313-1330, May.
    14. S. Alex Yang & John R. Birge & Rodney P. Parker, 2015. "The Supply Chain Effects of Bankruptcy," Management Science, INFORMS, vol. 61(10), pages 2320-2338, October.
    15. Archibald, Thomas W. & Thomas, Lyn C. & Possani, Edgar, 2007. "Keep or return? Managing ordering and return policies in start-up companies," European Journal of Operational Research, Elsevier, vol. 179(1), pages 97-113, May.
    16. Nathan Craig & Nicole DeHoratius & Ananth Raman, 2016. "The Impact of Supplier Inventory Service Level on Retailer Demand," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 461-474, October.
    17. Y. Boulaksil & A.C.C. van Wijk, 2018. "A cash-constrained stochastic inventory model with consumer loans and supplier credits: the case of nanostores in emerging markets," International Journal of Production Research, Taylor & Francis Journals, vol. 56(15), pages 4983-5004, August.
    18. B. K. Pagnoncelli & S. Ahmed & A. Shapiro, 2009. "Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 399-416, August.
    19. Xiaodong Xu & John R. Birge, 2006. "Equity valuation, production, and financial planning: A stochastic programming approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(7), pages 641-655, October.
    20. Glomb, Lukas & Liers, Frauke & Rösel, Florian, 2022. "A rolling-horizon approach for multi-period optimization," European Journal of Operational Research, Elsevier, vol. 300(1), pages 189-206.
    21. Desheng Wu & Baofeng Zhang & Opher Baron, 2019. "A Trade Credit Model with Asymmetric Competing Retailers," Production and Operations Management, Production and Operations Management Society, vol. 28(1), pages 206-231, January.
    22. Panos Kouvelis & Wenhui Zhao, 2012. "Financing the Newsvendor: Supplier vs. Bank, and the Structure of Optimal Trade Credit Contracts," Operations Research, INFORMS, vol. 60(3), pages 566-580, June.
    23. Céline Gicquel & Jianqiang Cheng, 2018. "A joint chance-constrained programming approach for the single-item capacitated lot-sizing problem with stochastic demand," Annals of Operations Research, Springer, vol. 264(1), pages 123-155, May.
    24. Xiuli Chao & Jia Chen & Shouyang Wang, 2008. "Dynamic inventory management with cash flow constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 758-768, December.
    25. Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2015. "Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing," Omega, Elsevier, vol. 50(C), pages 126-140.
    26. Kajjoune, Oussama & Aouam, Tarik & Zouadi, Tarik & Dairi, Meriem, 2021. "Dynamic lot-sizing with short-term financing and external deposits for a capital-constrained manufacturer," International Journal of Production Economics, Elsevier, vol. 242(C).
    Full references (including those not matched with items on IDEAS)

    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. Chen, Zhen & Rossi, Roberto, 2021. "A dynamic ordering policy for a stochastic inventory problem with cash constraints," Omega, Elsevier, vol. 102(C).
    2. Kajjoune, Oussama & Aouam, Tarik & Zouadi, Tarik & Dairi, Meriem, 2021. "Dynamic lot-sizing with short-term financing and external deposits for a capital-constrained manufacturer," International Journal of Production Economics, Elsevier, vol. 242(C).
    3. Kajjoune, Oussama & Aouam, Tarik & Zouadi, Tarik & Ranjan, Ravi Prakash, 2023. "Dynamic lot-sizing in a two-stage supply chain with liquidity constraints and financing options," International Journal of Production Economics, Elsevier, vol. 258(C).
    4. Jain, Richa & Reindorp, Matthew & Chockalingam, Arun, 2023. "Buyer-backed purchase-order financing for SME supplier with uncertain yield," European Journal of Operational Research, Elsevier, vol. 307(2), pages 758-772.
    5. Ke Fu & Xiting Gong & Vernon N. Hsu & Jiye Xue, 2021. "Dynamic Inventory Management with Inventory‐based Financing," Production and Operations Management, Production and Operations Management Society, vol. 30(5), pages 1313-1330, May.
    6. Shi, Jinzhao & Guo, Ju'e & Du, Qiang & Lin, Feng & Lai, Kin Keung & Cheng, T.C.E., 2020. "Optimal financing mode selection for a capital-constrained retailer under an implicit bankruptcy cost," International Journal of Production Economics, Elsevier, vol. 228(C).
    7. Yasin Alan & Vishal Gaur, 2018. "Operational Investment and Capital Structure Under Asset-Based Lending," Manufacturing & Service Operations Management, INFORMS, vol. 20(4), pages 637-654, October.
    8. Gökçe Esenduran & John V. Gray & Burcu Tan, 2022. "A Dynamic Analysis of Supply Chain Risk Management and Extended Payment Terms," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1394-1417, March.
    9. Jiao Wang & Lima Zhao & Arnd Huchzermeier, 2021. "Operations‐Finance Interface in Risk Management: Research Evolution and Opportunities," Production and Operations Management, Production and Operations Management Society, vol. 30(2), pages 355-389, February.
    10. Minjiao Zhang & Simge Küçükyavuz & Saumya Goel, 2014. "A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints," Management Science, INFORMS, vol. 60(5), pages 1317-1333, May.
    11. Gongbing Bi & Lei Song & Yalei Fei, 2020. "Dynamic mixed-item inventory control with limited capital and short-term financing," Annals of Operations Research, Springer, vol. 284(1), pages 99-130, January.
    12. Dan A. Iancu & Nikolaos Trichakis & Gerry Tsoukalas, 2017. "Is Operating Flexibility Harmful Under Debt?," Management Science, INFORMS, vol. 63(6), pages 1730-1761, June.
    13. Michel Minoux & Riadh Zorgati, 2019. "Sharp upper and lower bounds for maximum likelihood solutions to random Gaussian bilateral inequality systems," Journal of Global Optimization, Springer, vol. 75(3), pages 735-766, November.
    14. Xie, Xiaofeng & Chen, Xiangfeng & Xu, Xun & Gu, Jing, 2024. "Financing a dual capital-constrained supply chain: Profit enhancement and diffusion effect of default risk," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 181(C).
    15. Shiming Deng & Chaocheng Gu & Gangshu (George) Cai & Yanhai Li, 2018. "Financing Multiple Heterogeneous Suppliers in Assembly Systems: Buyer Finance vs. Bank Finance," Manufacturing & Service Operations Management, INFORMS, vol. 20(1), pages 53-69, February.
    16. Wang, Tingsong & Meng, Qiang & Wang, Shuaian & Tan, Zhijia, 2013. "Risk management in liner ship fleet deployment: A joint chance constrained programming model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 60(C), pages 1-12.
    17. Xiting Gong & Xiuli Chao & David Simchi‐Levi, 2014. "Dynamic inventory control with limited capital and short‐term financing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 184-201, April.
    18. Li, Hongping & Zha, Yong & Bi, Gongbing, 2023. "Agricultural insurance and power structure in a capital-constrained supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 171(C).
    19. Diglio, Antonio & Peiró, Juanjo & Piccolo, Carmela & Saldanha-da-Gama, Francisco, 2023. "Approximation schemes for districting problems with probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 307(1), pages 233-248.
    20. Quansheng Lei & Zhelian Xu & Siqi Yang, 2019. "Research on Trade Credit and Bank Credit Based on Dynamic Inventory," Sustainability, MDPI, vol. 11(13), pages 1-29, June.

    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:proeco:v:270:y:2024:i:c:s0925527324000483. 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/ijpe .

    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.