Multi-item inventory control with full truckloads: A comparison of aggregate and individual order triggering

In this paper, we consider the stochastic joint replenishment problem in an environment where transportation costs are dominant and full truckloads or full container loads are required. One replenishment policy, taking into account capacity restrictions of the total order volume, is the so-called QS policy, where replenishment orders are placed to raise the individual inventory positions of all items to their order-up-to levels, whenever the aggregate inventory position drops below the reorder level. We first provide a method to compute the policy parameters of a QS policy such that item target service levels can be met, under the assumption that demand can be modeled as a compound renewal process. The approximation formulas are based on renewal theory and are tested in a simulation study which reveals good performance. Second, we compare the QS policy with a simple allocation policy where replenishment orders are triggered by the individual inventory positions of the items. At the moment when an individual inventory position drops below its item reorder level, a replenishment order is triggered and the total vehicle capacity is allocated to all items such that the expected elapsed time before the next replenishment order is maximized. In an extensive simulation study it is illustrated that the QS policy outperforms this allocation policy since it results in lower inventory levels for the same service level. Although both policies lead to similar performance if items are identical, it can differ substantially if the item characteristics vary.