Supply rationing in multi-echelon divergent systems

In this paper we determine a simple inventory control rule for multi-echelon distribution systems under periodic review without lot sizing. The primary focus is the two-echelon model with a stockless central depot, but several extensions (> 2 echelons, central stock allowed) are discussed as well. The control rule consists of two parameter sets: a set of rationing fractions at the central depot with the purpose to minimize inventory imbalance, and a set of order-up-to levels for the local stockpoints with the purpose to achieve a target service level (fill rate) per local stockpoint. The problem to calculate these control parameters is solved by decomposition in two subproblems. First the rationing fractions are determined such that the (approximate) expected system imbalance is minimized. Next the order-up-to levels are calculated such that the target fill rates are achieved. Numerical results show that this control rule, called Balanced Stock (BS) rationing, is accurate and more robust than the Consistent Appropriate Share (CAS) rationing policy.