Modified critical fractile approach for a class of partial postponement problems

This paper studies a single period partial postponement problem, which is motivated by an inventory planning problem encountered in Reebok NFL replica jersey supply chain. We consider a group of regular products each facing a random demand. There are two stocking options. One is to procure the regular products. The other is to stock a common component which can be customized later to any one of the regular products, after demand realization.We obtain an insightful interpretation of the optimality conditions for this class of problems, and use it to obtain rules of thumb that practitioners can incorporate into their inventory models to determine the stocking levels to minimize the supply chain cost. Instead of proposing a numerical procedure to obtain the optimal solution, we propose an adaptation of the classical critical fractile approach for this class of partial postponement problem. The closed-form formula obtained are surprisingly effective. Our numerical results suggest that this simple approach to inventory planning often comes close to the performance of the optimal solution obtained from numerical method.