Robust multi-echelon inventory management with multiple suppliers

We study a periodic-review multi-supplier series inventory system in which the demand is restricted to partial sum uncertainty sets. We present and solve a robust rolling-horizon model for the system. We propose an induction framework to characterize the closed-form robust optimal solution of the problem. We show that the robust optimal policy combines the echelon base-stock policy and a gap-of-echelon-base-stock policy for the uppermost stage and a modified echelon base-stock policy for the other downstream stages. The policy structure is easy for the manager to understand and implement in practice. The policy parameters are directly determined by a sequence of nominal partial-sum demands, and its computation is very effective. In addition, the policy does not rely on complete information about the demand distribution; its solution can be more robust than that of stochastic optimization methods, especially when demand is highly uncertain, and forecasting is difficult. Based on the structure of the robust optimal policy, we design two heuristic policies for the system and evaluate the policies' performance through an extensive numerical study using both synthetic and real data.