Target-based Inventory Pooling Problem

We study a stochastic inventory risk pooling problem, in which the objective is to minimize the risk that the remaining inventory and the unsatisfied demand exceed the pre-specified acceptable levels. We use the robustness optimization framework to model this problem, in which the decision maker does not need to determine the size of the ambiguity set. The model will then determine the most robust solution that satisfies the threshold levels. Moreover, we introduce a new utility-based probability distribution distance and formulate the problem as a convex optimization problem. A column and constraint generation (CCG) algorithm is derived to solve the model exactly. We conduct experiments to compare the performance of our model with two other benchmark models, and show that our model provides lower risk and more robustness to distribution ambiguity