IDEAS home Printed from https://ideas.repec.org/a/bla/popmgt/v31y2022i4p1433-1453.html
   My bibliography  Save this article

Applications of Stochastic Orders and Stochastic Functions in Inventory and Pricing Problems

Author

Listed:
  • Qi Feng
  • J. George Shanthikumar

Abstract

Uncertainties involved in decision making often impose challenges to our ability of modeling and analyzing the reality. The purpose of this study is to demonstrate how one can go beyond the conventional optimization thinking, via taking a stochastic viewpoint, to push the boundaries of the analysis. We review the basic notions of stochastic orders and stochastic functions, with which the conventional (deterministic) way of modeling can be generalized. Based on the orders among distribution functions associated with random variables, we can treat the input–output relationship as stochastic functions in our models. This viewpoint, leads to extended functional properties in the stochastic sense. Taking the existing models involving inventory and pricing decisions, we show how the stochastic notions are powerful in simplifying and generalizing the analysis, as well as generating new insights.

Suggested Citation

  • Qi Feng & J. George Shanthikumar, 2022. "Applications of Stochastic Orders and Stochastic Functions in Inventory and Pricing Problems," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1433-1453, April.
    • Handle: RePEc:bla:popmgt:v:31:y:2022:i:4:p:1433-1453
    DOI: 10.1111/poms.13629
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/poms.13629
    Download Restriction: no
    File URL: https://libkey.io/10.1111/poms.13629?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. Z. Jemai & F. Karaesmen, 2005. "The influence of demand variability on the performance of a make-to-stock queue," Post-Print hal-00126137, HAL.
    2. Qi Feng & J. George Shanthikumar, 2018. "Supply and Demand Functions in Inventory Models," Operations Research, INFORMS, vol. 66(1), pages 77-91, 1-2.
    3. Ad Ridder & Erwin van der Laan & Marc Salomon, 1998. "How Larger Demand Variability May Lead to Lower Costs in the Newsvendor Problem," Operations Research, INFORMS, vol. 46(6), pages 934-936, December.
    4. Jing-Sheng Song, 1994. "The Effect of Leadtime Uncertainty in a Simple Stochastic Inventory Model," Management Science, INFORMS, vol. 40(5), pages 603-613, May.
    5. Jing-Sheng Song & Hanqin Zhang & Yumei Hou & Mingzheng Wang, 2010. "The Effect of Lead Time and Demand Uncertainties in ( r, q ) Inventory Systems," Operations Research, INFORMS, vol. 58(1), pages 68-80, February.
    6. Jemai, Zied & Karaesmen, Fikri, 2005. "The influence of demand variability on the performance of a make-to-stock queue," European Journal of Operational Research, Elsevier, vol. 164(1), pages 195-205, July.
    7. Alain Bensoussan & Yangyang Xie & Houmin Yan, 2019. "Joint Inventory‐Pricing Optimization with General Demands: An Alternative Approach for Concavity Preservation," Production and Operations Management, Production and Operations Management Society, vol. 28(9), pages 2390-2404, September.
    8. Jing-Sheng Song & Paul H. Zipkin, 1996. "The Joint Effect of Leadtime Variance and Lot Size in a Parallel Processing Environment," Management Science, INFORMS, vol. 42(9), pages 1352-1363, September.
    9. Qi Feng & Sirong Luo & Dan Zhang, 2014. "Dynamic Inventory–Pricing Control Under Backorder: Demand Estimation and Policy Optimization," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 149-160, February.
    10. Qi Feng & Sirong Luo & J. George Shanthikumar, 2020. "Integrating Dynamic Pricing with Inventory Decisions Under Lost Sales," Management Science, INFORMS, vol. 66(5), pages 2232-2247, May.
    11. Brian Tomlin, 2009. "Impact of Supply Learning When Suppliers Are Unreliable," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 192-209, August.
    12. Juzhi Zhang & Tsan‐Ming Choi & T. C. E. Cheng, 2020. "Stochastic production capacity: A bane or a boon for quick response supply chains?," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(2), pages 126-146, March.
    13. Wang, Yunzeng & Hu, Xiangpei, 2016. "Optimal production planning for assembly systems with uncertain capacities and random demandAuthor-Name: Ji, Qingkai," European Journal of Operational Research, Elsevier, vol. 253(2), pages 383-391.
    14. Larry Y. Tzeng & Rachel J. Huang & Pai-Ta Shih, 2013. "Revisiting Almost Second-Degree Stochastic Dominance," Management Science, INFORMS, vol. 59(5), pages 1250-1254, May.
    15. Goker Aydin & Serhan Ziya, 2009. "Technical Note---Personalized Dynamic Pricing of Limited Inventories," Operations Research, INFORMS, vol. 57(6), pages 1523-1531, December.
    16. Ilia Tsetlin & Robert L. Winkler & Rachel J. Huang & Larry Y. Tzeng, 2015. "Generalized Almost Stochastic Dominance," Operations Research, INFORMS, vol. 63(2), pages 363-377, April.
    17. Diwakar Gupta & William L. Cooper, 2005. "Stochastic Comparisons in Production Yield Management," Operations Research, INFORMS, vol. 53(2), pages 377-384, April.
    18. Jian Yang & Xiangtong Qi & Yusen Xia, 2005. "A Production-Inventory System with Markovian Capacity and Outsourcing Option," Operations Research, INFORMS, vol. 53(2), pages 328-349, April.
    19. Frank W. Ciarallo & Ramakrishna Akella & Thomas E. Morton, 1994. "A Periodic Review, Production Planning Model with Uncertain Capacity and Uncertain Demand---Optimality of Extended Myopic Policies," Management Science, INFORMS, vol. 40(3), pages 320-332, March.
    20. 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.
    21. Maqbool Dada & Nicholas C. Petruzzi & Leroy B. Schwarz, 2007. "A Newsvendor's Procurement Problem when Suppliers Are Unreliable," Manufacturing & Service Operations Management, INFORMS, vol. 9(1), pages 9-32, August.
    22. Yigal Gerchak & David Mossman, 1992. "On the Effect of Demand Randomness on Inventories and Costs," Operations Research, INFORMS, vol. 40(4), pages 804-807, August.
    23. Liao Wang & David D. Yao, 2017. "Production with Risk Hedging—Optimal Policy and Efficient Frontier," Operations Research, INFORMS, vol. 65(4), pages 1095-1113, August.
    24. Awi Federgruen & Nan Yang, 2011. "TECHNICAL NOTE---Procurement Strategies with Unreliable Suppliers," Operations Research, INFORMS, vol. 59(4), pages 1033-1039, August.
    25. Qi Feng & Justin Jia & J. George Shanthikumar, 2019. "Dynamic Multisourcing with Dependent Supplies," Management Science, INFORMS, vol. 67(6), pages 2770-2786, June.
    26. Maggi G. & Rodriguez-Clare A., 1995. "On Countervailing Incentives," Journal of Economic Theory, Elsevier, vol. 66(1), pages 238-263, June.
    27. Burcu Tan & Qi Feng & Wen Chen, 2016. "Dual Sourcing Under Random Supply Capacities: The Role of the Slow Supplier," Production and Operations Management, Production and Operations Management Society, vol. 25(7), pages 1232-1244, July.
    28. Qing Li & Derek Atkins, 2002. "Coordinating Replenishment and Pricing in a Firm," Manufacturing & Service Operations Management, INFORMS, vol. 4(4), pages 241-257, May.
    29. Qi Feng, 2010. "Integrating Dynamic Pricing and Replenishment Decisions Under Supply Capacity Uncertainty," Management Science, INFORMS, vol. 56(12), pages 2154-2172, December.
    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. Ba, Luyao & Xie, Yangyang & Ma, Lijun, 2023. "Finite-horizon joint inventory-pricing optimization with non-concave demand and lost sales," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 172(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. Qi Feng & J. George Shanthikumar, 2018. "Supply and Demand Functions in Inventory Models," Operations Research, INFORMS, vol. 66(1), pages 77-91, 1-2.
    2. Wen Chen & Burcu Tan, 2022. "Dynamic procurement from multiple suppliers with random capacities," Annals of Operations Research, Springer, vol. 317(2), pages 509-536, October.
    3. Jing-Sheng Song & Hanqin Zhang & Yumei Hou & Mingzheng Wang, 2010. "The Effect of Lead Time and Demand Uncertainties in ( r, q ) Inventory Systems," Operations Research, INFORMS, vol. 58(1), pages 68-80, February.
    4. Panos Kouvelis & Guang Xiao & Nan Yang, 2021. "Role of Risk Aversion in Price Postponement Under Supply Random Yield," Management Science, INFORMS, vol. 67(8), pages 4826-4844, August.
    5. Awi Federgruen & Min Wang, 2013. "Monotonicity properties of a class of stochastic inventory systems," Annals of Operations Research, Springer, vol. 208(1), pages 155-186, September.
    6. Qi Feng & Zhongjie Ma & Zhaofang Mao & J. George Shanthikumar, 2021. "Multi‐Stage Supply Chain with Production Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(4), pages 921-940, April.
    7. Fleischhacker, Adam J. & Fok, Pak-Wing, 2015. "On the relationship between entropy, demand uncertainty, and expected loss," European Journal of Operational Research, Elsevier, vol. 245(2), pages 623-628.
    8. Xu, Minghui & Lu, Ye, 2013. "The effect of supply uncertainty in price-setting newsvendor models," European Journal of Operational Research, Elsevier, vol. 227(3), pages 423-433.
    9. Li, Yanhai & Ou, Jinwen, 2022. "Replenishment decisions for complementary components with supply capacity uncertainty under the CVaR criterion," European Journal of Operational Research, Elsevier, vol. 297(3), pages 904-916.
    10. Cheung, Ki Ling & Song, Jing-Sheng & Zhang, Yue, 2017. "Cost reduction through operations reversal," European Journal of Operational Research, Elsevier, vol. 259(1), pages 100-112.
    11. Xiting Gong & Youhua (Frank) Chen & Quan Yuan, 2022. "Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 511-528, February.
    12. Lingxiu Dong & Guang Xiao & Nan Yang, 2023. "Supply diversification under random yield: The impact of price postponement," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1112-1132, April.
    13. Long He & Ying Rong & Zuo‐Jun Max Shen, 2020. "Product Sourcing and Distribution Strategies under Supply Disruption and Recall Risks," Production and Operations Management, Production and Operations Management Society, vol. 29(1), pages 9-23, January.
    14. Serel, Doğan A., 2017. "A single-period stocking and pricing problem involving stochastic emergency supply," International Journal of Production Economics, Elsevier, vol. 185(C), pages 180-195.
    15. Svoboda, Josef & Minner, Stefan & Yao, Man, 2021. "Typology and literature review on multiple supplier inventory control models," European Journal of Operational Research, Elsevier, vol. 293(1), pages 1-23.
    16. Xu, Minghui & Chen, Youhua (Frank) & Xu, Xiaolin, 2010. "The effect of demand uncertainty in a price-setting newsvendor model," European Journal of Operational Research, Elsevier, vol. 207(2), pages 946-957, December.
    17. Weidong Chen & Cong Shi & Izak Duenyas, 2020. "Optimal Learning Algorithms for Stochastic Inventory Systems with Random Capacities," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1624-1649, July.
    18. Wen Chen & Ying He, 2022. "Dynamic pricing and inventory control with delivery flexibility," Annals of Operations Research, Springer, vol. 317(2), pages 481-508, October.
    19. Luo, Sha & Ahiska, S. Sebnem & Fang, Shu-Cherng & King, Russell E. & Warsing, Donald P. & Wu, Shuohao, 2021. "An analysis of optimal ordering policies for a two-supplier system with disruption risk," Omega, Elsevier, vol. 105(C).
    20. Xiuli Chao & Xiting Gong & Shaohui Zheng, 2016. "Optimal pricing and inventory policies with reliable and random-yield suppliers: characterization and comparison," Annals of Operations Research, Springer, vol. 241(1), pages 35-51, 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:bla:popmgt:v:31:y:2022:i:4:p:1433-1453. 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: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1937-5956 .

    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.