Abstract
In this chapter, we carry out mean-risk analysis for the single-period inventory problems. We first construct the basic inventory control model under the mean-risk framework. We then present two kinds of mean-risk objective functions and analytically prove the existence of an efficient region for either mean-risk model. After that, we explore the construction of the efficient frontier in the mean-risk domain. Before we conclude, numerical analysis is presented to illustrate the mean-risk trade-off in the single-period inventory decision making problems.
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- 1.
To avoid confusion, we use exp( ) to represent exponent in this chapter.
- 2.
Notice that the concavity of expected profit function is a standard result in the literature. The result on variance of profit is first proven by Chen and Federgruen (2000). Notice that when we incorporate the loss of goodwill opportunity cost of stockout, the variance of profit is no longer monotone (see Choi et al. 2008; Wu et al. 2009).
- 3.
References
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Choi, TM., Chiu, CH. (2012). Mean-Risk Analysis of Single-Period Inventory Problems. In: Risk Analysis in Stochastic Supply Chains. International Series in Operations Research & Management Science, vol 178. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3869-4_2
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DOI: https://doi.org/10.1007/978-1-4614-3869-4_2
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