Technical Note—Stochastic Optimization with Decisions Truncated by Positively Dependent Random Variables

AbstractIn many operations management problems, the decisions are truncated by random variables. Take a dual sourcing inventory management problem as an example: the suppliers may have random capacities, and the actual received quantity from ordering is truncated by this random capacity. Often the random capacities of different suppliers may be dependent. An interesting challenge is that due to the truncation, the optimization problem may not be convex. In “Stochastic Optimization with Decisions Truncated by Positively Dependent Random Variables”, X. Chen and X. Gao propose a transformation technique to convert the original nonconvex minimization problem to an equivalent convex one. They demonstrate the application of their method using an inventory substitution problem with dependent random supply capacities and a two-part fee cost structure. In addition, their method can also incorporate the decision maker’s risk attitude.We study stochastic optimization problems with decisions truncated by random variables. This paper extends existing results in the literature by allowing positively dependent random variables and a two-part fee structure. We develop a transformation technique to convert the original nonconvex problems to equivalent convex ones. We apply our transformation technique to an inventory substitution model with random supply capacities and a two-part fee cost structure. In addition, we extend our results to incorporate the decision maker’s risk attitude.