IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v31y2023i3d10.1007_s11750-022-00650-4.html
   My bibliography  Save this article

Optimizing a single-product production-inventory system under constant absolute risk aversion

Author

Listed:
  • Sen Lin

    (Ningbo China Institute for Supply Chain Innovation)

  • Bo Li

    (Ningbo China Institute for Supply Chain Innovation
    Ningbo University)

  • Antonio Arreola-Risa

    (Texas A&M University)

  • Yiwei Huang

    (Penn State Shenango)

Abstract

This paper considers a single-product production-inventory system managed by a base-stock policy where the factory inventory manager with cost concerns over a short time horizon can be modeled with the constant absolute risk aversion (CARA) utility function. We consider both backordering cost and stockout cost scenarios and investigate the roles of capacity utilization level and CARA coefficient on the optimal base-stock level. We derive closed-form solutions for the optimal inventory decisions, present related numerical experiments, and discuss their managerial implications. It is discovered that both scenarios share certain common structure in their optimal inventory decisions. Specifically, in the backordering cost scenario, if the backordering cost is high or the holding cost is low, the optimal base-stock level is high. In the stockout cost scenario, if the stockout cost is high or the holding cost is low, the optimal base-stock level is high. For both scenarios, inventory levels are high with tight capacity, and optimal base-stock level generally increases if the manager becomes more risk averse.

Suggested Citation

  • Sen Lin & Bo Li & Antonio Arreola-Risa & Yiwei Huang, 2023. "Optimizing a single-product production-inventory system under constant absolute risk aversion," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 510-537, October.
  • Handle: RePEc:spr:topjnl:v:31:y:2023:i:3:d:10.1007_s11750-022-00650-4
    DOI: 10.1007/s11750-022-00650-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11750-022-00650-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11750-022-00650-4?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. Kan Huang & David Simchi-Levi & Miao Song, 2012. "Optimal Market-Making with Risk Aversion," Operations Research, INFORMS, vol. 60(3), pages 541-565, June.
    2. Uday S. Karmarkar, 1987. "Lot Sizes, Lead Times and In-Process Inventories," Management Science, INFORMS, vol. 33(3), pages 409-418, March.
    3. Babcock, Bruce A. & Choi, E. Kwan & Feinerman, Eli, 1993. "Risk And Probability Premiums For Cara Utility Functions," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 18(1), pages 1-8, July.
    4. S. Otten & R. Krenzler & H. Daduna, 2016. "Models for integrated production-inventory systems: steady state and cost analysis," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6174-6191, October.
    5. Stratton C. Jaquette, 1976. "A Utility Criterion for Markov Decision Processes," Management Science, INFORMS, vol. 23(1), pages 43-49, September.
    6. Robert S. Kaplan, 1970. "A Dynamic Inventory Model with Stochastic Lead Times," Management Science, INFORMS, vol. 16(7), pages 491-507, March.
    7. Andrew E. B. Lim & J. George Shanthikumar, 2007. "Relative Entropy, Exponential Utility, and Robust Dynamic Pricing," Operations Research, INFORMS, vol. 55(2), pages 198-214, April.
    8. Louis Eeckhoudt & Christian Gollier & Harris Schlesinger, 1995. "The Risk-Averse (and Prudent) Newsboy," Management Science, INFORMS, vol. 41(5), pages 786-794, May.
    9. Yong-Joo Lee & Paul Zipkin, 1992. "Tandem Queues with Planned Inventories," Operations Research, INFORMS, vol. 40(5), pages 936-947, October.
    10. Richard Ehrhardt, 1984. "( s , S ) Policies for a Dynamic Inventory Model with Stochastic Lead Times," Operations Research, INFORMS, vol. 32(1), pages 121-132, February.
    11. King, Robert P. & Lybecker, Donald W., 1983. "Flexible, Risk-Oriented Marketing Strategies For Pinto Bean Producers," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 8(2), pages 1-10, December.
    12. Evan L. Porteus, 1975. "On the Optimality of Structured Policies in Countable Stage Decision Processes," Management Science, INFORMS, vol. 22(2), pages 148-157, October.
    13. Yong-Joo Lee & Paul Zipkin, 1995. "Processing Networks with Inventories: Sequential Refinement Systems," Operations Research, INFORMS, vol. 43(6), pages 1025-1036, December.
    14. Ted O'Donoghue & Jason Somerville, 2018. "Modeling Risk Aversion in Economics," Journal of Economic Perspectives, American Economic Association, vol. 32(2), pages 91-114, Spring.
    15. Mokrane Bouakiz & Matthew J. Sobel, 1992. "Inventory Control with an Exponential Utility Criterion," Operations Research, INFORMS, vol. 40(3), pages 603-608, June.
    16. Janssen, Fred & Heuts, Ruud & de Kok, Ton, 1998. "On the (R, s, Q) inventory model when demand is modelled as a compound Bernoulli process," European Journal of Operational Research, Elsevier, vol. 104(3), pages 423-436, February.
    17. Saif Benjaafar & Mohsen ElHafsi & Tingliang Huang, 2010. "Optimal control of a production‐inventory system with both backorders and lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(3), pages 252-265, April.
    18. Tapiero, Charles S. & Kogan, Konstantin, 2009. "Risk-averse order policies with random prices in complete market and retailers' private information," European Journal of Operational Research, Elsevier, vol. 196(2), pages 594-599, July.
    19. Arreola-Risa, Antonio, 1996. "Integrated multi-item production-inventory systems," European Journal of Operational Research, Elsevier, vol. 89(2), pages 326-340, March.
    20. Maria Albareda-Sambola & Elena Fernández & Francisco Saldanha-da-Gama, 2017. "Heuristic Solutions to the Facility Location Problem with General Bernoulli Demands," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 737-753, November.
    21. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    22. Yuri Levin & Jeff McGill & Mikhail Nediak, 2008. "Risk in Revenue Management and Dynamic Pricing," Operations Research, INFORMS, vol. 56(2), pages 326-343, April.
    23. Michael K. Lim & Ho-Yin Mak & Zuo-Jun Max Shen, 2017. "Agility and Proximity Considerations in Supply Chain Design," Management Science, INFORMS, vol. 63(4), pages 1026-1041, April.
    24. Xiaomin Wang & Yifan Xu, 2009. "Multi-period multi-product inventory control with substitution and an exponential criterion," International Journal of Revenue Management, Inderscience Enterprises Ltd, vol. 3(4), pages 333-353.
    25. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2007. "Choosing Among Living-Donor and Cadaveric Livers," Management Science, INFORMS, vol. 53(11), pages 1702-1715, November.
    26. Giri, B.C., 2011. "Managing inventory with two suppliers under yield uncertainty and risk aversion," International Journal of Production Economics, Elsevier, vol. 133(1), pages 80-85, September.
    27. Burak Kazaz & Scott Webster, 2015. "Technical Note—Price-Setting Newsvendor Problems with Uncertain Supply and Risk Aversion," Operations Research, INFORMS, vol. 63(4), pages 807-811, August.
    28. Randall A. Kramer & Rulon D. Pope, 1986. "Participation in Farm Commodity Programs: A Stochastic Dominance Analysis: Reply," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 68(1), pages 189-190.
    29. Yun Fong Lim & Chen Wang, 2017. "Inventory Management Based on Target-Oriented Robust Optimization," Management Science, INFORMS, vol. 63(12), pages 4409-4427, December.
    30. Seçil Savaşaneril & Paul M. Griffin & Pınar Keskinocak, 2010. "Dynamic Lead-Time Quotation for an M/M/1 Base-Stock Inventory Queue," Operations Research, INFORMS, vol. 58(2), pages 383-395, April.
    31. René Caldentey & Lawrence M. Wein, 2003. "Analysis of a Decentralized Production-Inventory System," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 1-17, November.
    32. Morris A. Cohen & Hau L. Lee, 2020. "Designing the Right Global Supply Chain Network," Manufacturing & Service Operations Management, INFORMS, vol. 22(1), pages 15-24, January.
    33. C. Barz & K. Waldmann, 2007. "Risk-sensitive capacity control in revenue management," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 565-579, June.
    34. Cochran, Mark C. & Raskin, Rob, 1987. "Interpretations And Transformations Of Scale For The Pratt-Arrow Absolute Risk Aversion Coefficient: Implications For Generalized Stochastic Dominance: Reply," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 12(2), pages 1-2, December.
    35. Vipul Agrawal & Sridhar Seshadri, 2000. "Impact of Uncertainty and Risk Aversion on Price and Order Quantity in the Newsvendor Problem," Manufacturing & Service Operations Management, INFORMS, vol. 2(4), pages 410-423, July.
    36. Wilson, Paul N. & Eidman, Vernon R., 1983. "An Empirical Test Of The Interval Approach For Estimating Risk Preferences," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 8(2), pages 1-13, December.
    37. Bo Li & Subodha Kumar, 2018. "Should You Kill or Embrace Your Competitor: Cloud Service and Competition Strategy," Production and Operations Management, Production and Operations Management Society, vol. 27(5), pages 822-838, May.
    38. Alavi Fard, Farzad & He, Jian & Ivanov, Dmitry & Jie, Ferry, 2019. "A utility adjusted newsvendor model with stochastic demand," International Journal of Production Economics, Elsevier, vol. 211(C), pages 154-165.
    39. Rainer Schlosser, 2016. "Stochastic dynamic multi-product pricing with dynamic advertising and adoption effects," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 15(2), pages 153-169, April.
    40. Xin Chen & Melvyn Sim & David Simchi-Levi & Peng Sun, 2007. "Risk Aversion in Inventory Management," Operations Research, INFORMS, vol. 55(5), pages 828-842, October.
    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. H Xiong & J Xie & X Deng, 2011. "Risk-averse decision making in overbooking problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1655-1665, September.
    2. Li, Xiang & Qi, Xiangtong & Li, Yongjian, 2021. "On sales effort and pricing decisions under alternative risk criteria," European Journal of Operational Research, Elsevier, vol. 293(2), pages 603-614.
    3. Gönsch, Jochen, 2017. "A survey on risk-averse and robust revenue management," European Journal of Operational Research, Elsevier, vol. 263(2), pages 337-348.
    4. Kim, Kyoung-Kuk & Park, Kun Soo, 2014. "Transferring and sharing exchange-rate risk in a risk-averse supply chain of a multinational firm," European Journal of Operational Research, Elsevier, vol. 237(2), pages 634-648.
    5. Schlosser, Rainer & Gönsch, Jochen, 2023. "Risk-averse dynamic pricing using mean-semivariance optimization," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1151-1163.
    6. Monahan, George E. & Sobel, Matthew J., 1997. "Risk-Sensitive Dynamic Market Share Attraction Games," Games and Economic Behavior, Elsevier, vol. 20(2), pages 149-160, August.
    7. Chun-Hung Chiu & Tsan-Ming Choi, 2016. "Supply chain risk analysis with mean-variance models: a technical review," Annals of Operations Research, Springer, vol. 240(2), pages 489-507, May.
    8. Bo Li & Antonio Arreola‐Risa, 2022. "Minimizing conditional value‐at‐risk under a modified basestock policy," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1822-1838, April.
    9. Li, Xiang & Qi, Xiangtong, 2021. "On pricing and quality decisions with risk aversion," Omega, Elsevier, vol. 98(C).
    10. Jochen Gönsch & Michael Hassler & Rouven Schur, 2018. "Optimizing conditional value-at-risk in dynamic pricing," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 711-750, July.
    11. Sayın, F. & Karaesmen, F. & Özekici, S., 2014. "Newsvendor model with random supply and financial hedging: Utility-based approach," International Journal of Production Economics, Elsevier, vol. 154(C), pages 178-189.
    12. Jiri Chod & Nils Rudi & Jan A. Van Mieghem, 2010. "Operational Flexibility and Financial Hedging: Complements or Substitutes?," Management Science, INFORMS, vol. 56(6), pages 1030-1045, June.
    13. Bo Li & Antonio Arreola‐Risa, 2021. "On minimizing downside risk in make‐to‐stock, risk‐averse firms," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(2), pages 199-213, March.
    14. Sungyong Choi & Andrzej Ruszczyński & Yao Zhao, 2011. "A Multiproduct Risk-Averse Newsvendor with Law-Invariant Coherent Measures of Risk," Operations Research, INFORMS, vol. 59(2), pages 346-364, April.
    15. Poormoaied, Saeed & Atan, Zümbül, 2020. "A multi-attribute utility theory approach to ordering policy for perishable items," International Journal of Production Economics, Elsevier, vol. 225(C).
    16. Yuri Levin & Jeff McGill & Mikhail Nediak, 2008. "Risk in Revenue Management and Dynamic Pricing," Operations Research, INFORMS, vol. 56(2), pages 326-343, April.
    17. Vaagen, Hajnalka & Wallace, Stein W., 2008. "Product variety arising from hedging in the fashion supply chains," International Journal of Production Economics, Elsevier, vol. 114(2), pages 431-455, August.
    18. Koenig, Matthias & Meissner, Joern, 2010. "List pricing versus dynamic pricing: Impact on the revenue risk," European Journal of Operational Research, Elsevier, vol. 204(3), pages 505-512, August.
    19. Wu, Meng & Zhu, Stuart X. & Teunter, Ruud H., 2013. "Newsvendor problem with random shortage cost under a risk criterion," International Journal of Production Economics, Elsevier, vol. 145(2), pages 790-798.
    20. Youhua (Frank) Chen & Minghui Xu & Zhe George Zhang, 2009. "Technical Note---A Risk-Averse Newsvendor Model Under the CVaR Criterion," Operations Research, INFORMS, vol. 57(4), pages 1040-1044, August.

    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:spr:topjnl:v:31:y:2023:i:3:d:10.1007_s11750-022-00650-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.