Technical Note—A Risk- and Ambiguity-Averse Extension of the Max-Min Newsvendor Order Formula

Abstract

Scarf's max-min order formula for the risk-neutral and ambiguity-averse newsvendor problem is a classical result in the field of inventory management. In this article, we extend Scarf's formula by deriving an analogous closed-form order formula for the risk- and ambiguity-averse newsvendor problem. Specifically, we provide and analyze the newsvendor order quantity that maximizes the worst-case expected profit versus risk trade-off (risk-averse) when only the mean and standard deviation of the product's demand distribution are known (ambiguity-averse), and the risk is measured by the standard deviation of the newsvendor's profit. We provide both analytical and numerical results to illustrate the combined effect of considering risk aversion and ambiguity aversion in computing the newsvendor order.

Joint Pricing and Purchasing Decisions for the Dual-Channel Newsvendor Model with Partial Information

“…Let * = ( * , * , * ) and Ψ * = Ψ( 1 , 1 ), respectively, denote maximum profit under demand uncertainty and certainty. The results of our experiments are shown in Figures 3,4,5,6,7,8,9,10,11,12,13,14,15,16,and 17. As shown in Figures 3 to 7, the results of the experiments are consistent with the theory analyzed in the previous section. The optimal riskless Internet price of 1 is never less than the robust optimal Internet price of * .…”

“…Liao et al [10] extend the model of Moon and Choi [4] to include the penalty for failing to make a sale. Han et al [11] derive an analogous closed-form order formula for the risk-and ambiguity-averse newsvendor problem to extend Scarf 's formula. The maximum approach has also been applied to multiperiod or multiproduct inventory models.…”

Quick Response in Supply Chains with Stochastically Risk Sensitive Retailers*

“…Other related studies include Buzacott et al. (), Choi (), Chow, Wang, Choi, and Shen (), Han, Du, and Zuluaga (), Leng and Parlar (), Wu, Zhu, and Teunter (), Wu, Zhu, and Teunter (), etc., which all focus on studying solely the (fixed) risk‐averse behavior in decision making concerning the inventory or supply chain coordination problem. It is obvious that risk preference has been well considered as an important topic in supply chain operations management.…”

Modern optimization theory and applications

“…Delage 和 Ye [470] 将上述已知需求分布部分信 息的鲁棒优化模型命名为分布鲁棒优化 (distributionally robust optimization) 模型, 并进一步在模型 中考虑需求分布矩信息的不确定性. Han 等 [471] 将文献 [467] 的模型推广到了风险规避下的报童模型.…”