Replenishment decisions for complementary components with supply capacity uncertainty under the CVaR criterion

In this paper we consider a risk-averse newsvendor to assemble a final product that is made up of multiple complementary components, where both the product demand and the supply capacity of each component are random. A novel approach is proposed to derive the first-order condition for the optimal order quantity under the Conditional Value-at-Risk (CVaR) criterion. A comprehensive comparative statics analysis is conducted. The basic model is also extended to allow dependence among the random demand and supply capacities. We show that the objective function remains to be quasi-concave if those random variables are negatively dependent, and that the positive (negative) dependence of those random variables increases (decreases) the optimal order quantity and objective value. Numerical examples are provided to illustrate some of the main results.