Heuristics for setting reorder levels in periodic review inventory systems with an aggregate service constraint

Inventory managers are responsible for the trade-off between inventory holding costs and customer service. In this paper we consider a periodic review multi-item inventory system with exogenous lot-sizes and backordering. The objective is to minimize the total inventory holding costs subject to the constraint that the aggregate fill rate should be at least equal to a target level. The aggregate fill rate is a weighted average of the fill rates of all items in the assortment. We consider three ways of defining this aggregate fill rate: using generic weights, weights based on the average demand (volume) or weights based on the average (monetary) turnover. We show that the definition of the aggregate service can have huge effects on the performance of the system. So, inventory managers should be very careful on which definition to apply. We also derive four heuristics to determine the reorder levels for all items. One heuristic is very generic and can be applied to many problems including multi- item multi-echelon inventory systems and systems with a constrained aggregate ready rate. Since multiple assumptions made to derive the heuristics are common assumptions made in the literature, we first test the accuracy of these approximations using simulation. Next, we evaluate the heuristics based on data from a large international reseller. The heuristic based on the most accurate approximation performs best, is close to optimal and very efficient. Savings compared to no service level differentiation are large (up to 28.7%) and depend on the definition of the aggregate service.