Staggering periodic replenishment in multivendor just in time environments

The delivery scheduling problem studied in this paper was motivated by the operation in a large personal computer assembly plant, which was using multisourcing for some of its materials. The company's objective was to design a delivery schedule so that the average inventory level in the factory was minimized. We show that the problem is intimately related to a classical inventory staggering problem, where the focus is on the computation of the peak inventory level associated with the replenishment policy. This connection allows us to show that the delivery scheduling problem is NP-hard. For the two-vendor case with integral replenishment intervals, we propose a generalized form of Homer's scheduling heuristic and obtain performance bounds for the classical inventory staggering problem. Our analysis uses the Chinese remainder theorem in an interesting way. The approach can be generalized to the case with more than two vendors, leading to a strong linear-programming-based lower bound for the inventory staggering problem. We illustrate this technique for the case in which all the replenishment intervals are relatively prime, establishing a bound that is not greater than 140% of the optimal. We examine the implications of these results to the delivery scheduling problem.