A customer-item decomposition approach to stochastic inventory systems with correlation

We consider an inventory system with a single stage, periodic review, correlated, non-stationary stochastic demand and correlated, non-stationary stochastic and sequential leadtimes. We use the customer-item decomposition approach to decompose the problem into sub-problems, each involving a single customer-item pair. We then formulate each sub-problem as an optimal stopping problem. We use properties that arise from this formulation to show that the optimal policy is a state-dependent base-stock policy and to show, for several cases, that the optimal policy can be obtained via a polynomial time algorithm. We also use the formulation to construct a myopic heuristic which leads to an explicit solution for the optimal policy in the form of a critical fractile. We characterize conditions under which the myopic heuristic is optimal.