Diversification strategy with random yield suppliers for a mean-variance risk-sensitive manufacturer

We consider the diversification strategy for a mean-variance risk-sensitive manufacturer with unreliable suppliers. We first analyze the linear model and find that the suppliers are selected according to the descending order of their contributed marginal expected profit, and increasing the manufacturer's risk-averseness leads to a more even allocation of demand across the suppliers. Then, we study the general newsvendor model. By approximating the leftover inventory with a normal distribution, we establish the general properties of the active supplier set and show that the supplier selection rule is similar to that under the risk-neutral setting when the demand uncertainty is large. Moreover, we conjecture that the selection rule also applies when the demand uncertainty is low, which we verify with an extensive numerical study. Our paper makes two contributions: First, we establish the properties of the optimal diversification strategy and develop corresponding insights into the trade off between cost and reliability under the mean-variance framework. Second, we perform comparative statics on the optimal solution, with a particular emphasis on investigating how changes in the supplier's cost or reliability affect the risk-averse manufacturer's ordering decisions and customer service level.