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On lot-sizing problem in a random yield production system under loss aversion

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Abstract

Based on the framework of prospect theory, this paper studies the optimization problem for a random yield production system under loss aversion preference. The objective is to determine production quantity to maximize the expected utility considering loss aversion. We formulate the problem under the scenarios of multiplicative and additive random yield risks, respectively, and prove the uniqueness of the optimal production quantity under each scenario. This optimal production quantity is compared with the one in risk-neutral case, and its relationship on the loss-aversion degree is analyzed. We also explore the sensitivities of the production quantity to the system parameters. It is shown that the optimal production quantity is increasing with shortage penalty and decreasing with holding cost, whereas the sensitivities to market price and production costs are conditional.

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Notes

  1. We define that \((a,b)=\emptyset \) if \(a\ge b\), and \([a,b]=\emptyset \) if \(a>b\). Also, we define \(\frac{(p-c_2)d}{c_1}=+\infty \) if \(c_1=0\).

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Acknowledgments

We gratefully acknowledge the support of grants from (i) Fundamental Research Funds for the Central Universities (No.NKZXB1228) and National Natural Science Foundation of China (NSFC), Research Fund Nos. 71002077 and 71372002, for X. Li; and (i) National Natural Science Foundation of China (NSFC), Research Fund Nos. 70971069 and 71372100, for Y. J. Li.

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Authors and Affiliations

  1. College of Economic and Social Development, Nankai University, Tianjin, 300071, People’s Republic of China

    Xiang Li

  2. Business School, Nankai University, Tianjin, 300071, People’s Republic of China

    Yongjian Li

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  1. Xiang Li
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  2. Yongjian Li
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Correspondence to Yongjian Li.

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Li, X., Li, Y. On lot-sizing problem in a random yield production system under loss aversion. Ann Oper Res 240, 415–434 (2016). https://doi.org/10.1007/s10479-014-1715-2

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