Mean-variance analysis for the newsvendor problem

The newsvendor problem is a fundamental building block for inventory management with a stochastic demand. The classical newsvendor problem focuses on a sole objective of either minimizing the expected cost or maximizing the expected profit. However, the performance measure with expected value alone is insufficient, and it ignores the risk preferences of the decision makers. As a result, we carry out a mean-variance analysis of the newsvendor problem. We construct analytical models and reveal the problem's structural properties. We propose the solution schemes which help to identify the optimal solutions. Interesting findings regarding the efficient frontier, the case with a stockout penalty cost, and the safety-first objective are discussed.