Optimizing (s, S) policies for multi-period inventory models with demand distribution uncertainty: Robust dynamic programing approaches

We consider a finite-horizon single-product periodic-review inventory management problem with demand distribution uncertainty. We formulate the problem as a dynamic program and prove the existence of an optimal (s, S) policy. The corresponding dynamic robust counterpart models are then developed for the box and the ellipsoid uncertainty sets. These counterpart models are transformed into tractable linear and second-order cone programs, respectively. We illustrate the e↵ectiveness and practicality of the proposed robust optimization approaches through a numerical study.