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On the Properties of Yield Distributions in Random Yield Problems: Conditions, Class of Distributions and Relevant Applications

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  • Panos Kouvelis
  • Guang Xiao
  • Nan Yang

Abstract

In this study, we propose two technical assumptions to ensure the unimodality of the objective functions in two classes of price and quantity decision problems with one procurement opportunity under supply random yield and deterministic demand in a price‐setting environment. The first class of problems involves a decentralized supply chain/assembly system under different configurations, and the second class focuses on a single firm's price and quantity decisions under different contracts, payment schemes and supplier portfolios. We provide appealing economic interpretations and easy‐to‐verify sufficient conditions for our proposed technical assumptions. We show that both assumptions are preserved under truncation and positive scale, and satisfied by most commonly used continuous yield distributions. Moreover, similar to the role that the increasing generalized failure rate (IGFR) property plays in analyzing operations problems with demand uncertainty, our Assumption 1 plays a fundamental role in regulating the behaviors of the objective functions for both classes of random yield problems. Assumption 2 is more general than both Assumption 1 and the IGFR property and is used to analyze the second class of problems. Finally, we discuss the difference between random yield and random demand problems, and explain the rationale for the need of different technical assumptions.

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  • Panos Kouvelis & Guang Xiao & Nan Yang, 2018. "On the Properties of Yield Distributions in Random Yield Problems: Conditions, Class of Distributions and Relevant Applications," Production and Operations Management, Production and Operations Management Society, vol. 27(7), pages 1291-1302, July.
    • Handle: RePEc:bla:popmgt:v:27:y:2018:i:7:p:1291-1302
    DOI: 10.1111/poms.12869
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    Cited by:

    1. Niu, Baozhuang & Bao, Jinxiao & Cao, Bin, 2022. "Retailer's make-or-buy decision for remanufactured products under in-house yield uncertainty," Omega, Elsevier, vol. 110(C).
    2. 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.
    3. Anh Ninh & Zuo‐Jun Max Shen & Martin A. Lariviere, 2020. "Concavity and Unimodality of Expected Revenue Under Discrete Willingness to Pay Distributions," Production and Operations Management, Production and Operations Management Society, vol. 29(3), pages 788-796, March.
    4. Zhi Chen & Weijun Xie, 2021. "Regret in the Newsvendor Model with Demand and Yield Randomness," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4176-4197, November.
    5. Ding, Wen & Wan, Guohua, 2020. "Financing and coordinating the supply chain with a capital-constrained supplier under yield uncertainty," International Journal of Production Economics, Elsevier, vol. 230(C).
    6. 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.
    7. Stefanos Leonardos & Costis Melolidakis & Constandina Koki, 2022. "Monopoly pricing in vertical markets with demand uncertainty," Annals of Operations Research, Springer, vol. 315(2), pages 1291-1318, August.
    8. 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.

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