Optimal policy for inventory systems with capacity commitment and fixed ordering costs

This paper investigates a single-product, periodic-review, non-stationary inventory system with total maximum capacity commitment and fixed ordering costs over a finite planning horizon. We characterize the optimal ordering policy as a state-dependent ($s,S$) policy whose parameters only depend on the sum of the net inventory and the remaining capacity. We show that such policy can degenerate into two simple policies in two special cases respectively. We also derive bounds on parameters of the optimal ordering policy.