The cost allocation issue in joint replenishment

Joint replenishment for several products to achieve a lower inventory logistics cost has been a topic of extensive studies. Less attention has been paid to the issue of deciding how the joint replenishment costs should be allocated across the individual products. Ideally, when items are ordered together one would require a stable cost allocation, such that no subset of products subsidizes another subset. When part of each products ordering cost is product specific and part can be shared with other products (like in a 3PL setting of Anily and Haviv), it has been shown that even when a stable allocation exists, such an allocation might be difficult to compute. In addition, usually the components of ordering costs are partially determined using estimates and accounting discretion. This paper provides two main insights for determining an appropriate cost allocation. It provides the means to test how sensitive a stable cost allocation is to a range of cost parameter values. Then, in a computational study, it is shown how to obtain a stable cost allocation without excessive computation.