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

Abstract

In 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.