Risk-Averse Selective Newsvendor Problems.

This dissertation examines a generalization of the selective newsvendor problem that accounts for risk-aversion. The selective newsvendor problem introduces demand shaping into the traditional newsvendor problem through selection decisions by considering a firm that procures and delivers a good within a single selling season in a number of different markets. Prior to the selling season, the firm determines how much to procure and also in which markets to operate. To measure risk-aversion we consider both Value-at-Risk and Conditional Value-at-Risk, common risk measures used in portfolio optimization. We first consider a decision maker who optimizes a weighted sum of expected profit and Conditional Value-at-Risk, a coherent risk measure. We summarize the results for the newsvendor problem without selection decisions and utilize these results to show that, similar to the risk-neutral selective newsvendor problem, the optimal solution to the weighted sum risk-averse selective newsvendor problem can be found among a small number of candidate solutions satisfying an intuitively appealing ranking structure. We then establish a branch and bound procedure to identify the Pareto efficient frontier for a bicriteria optimization problem maximizing both expected profit and Conditional Value-at-Risk. Finally, we study the risk-averse selective newsvendor considering Value-at-Risk, a non-coherent risk measure lacking subadditivity and convexity. We show that as in the Conditional Value-at-Risk case, we can use a branch and bound type procedure to identify the expected profit-Value-at-Risk Pareto efficient frontier for a selective newsvendor.