On the unimodality of the price-setting newsvendor problem with additive demand under risk considerations

We present a mean-variance analysis of the single-product, single-period, price-setting newsvendor problem with additive, price-dependent demand. The main goal of this paper is to use a mean-variance framework to solve any risk-sensitive instance and find conditions under which the unimodality of the problem is guaranteed. We introduce such conditions via the lost sales rate elasticity, the elasticity of the optimal price, and the elasticity of the expected safety stock surplus to provide managerial insight in terms of the newsvendor's level of service. We also simplify the optimization problem in case that those conditions do not hold. The main contribution of this paper is that, by evaluating the unimodality of the problem for any possible risk attitude, it extends previously published results found for the concavity of the solution in risk-neutral and moderately risk-sensitive cases.