Deterministic EOQ with partial backordering and correlated demand caused by cross-selling

There has been much work regarding the deterministic EOQ with partial backordering. The majority of these studies assume no correlation in sales, so independent demands across items is applied in the models. However, it is generally recognized that cross-selling effects between items often appear in real contexts. Thus, incorporating such effects in the inventory model in the form of correlated demands makes it of more practical relevance. In this paper, the authors address a two-item inventory system where the demand of a minor item is correlated to that of a major item because of cross-selling. We firstly present a two-item EOQ model with identical order cycles, where the unmet demand of the major item can be partially backordered with lost sales whereas the demand of the minor item must be met without stockouts. This model is further extended to fit a more practical case where the order cycle of the major item is an integer multiple of that of the minor item. The optimal solutions of the two models, as well as the inventory decision procedures, are also developed. Comparative analysis on these two EOQ models has been drawn in the computational study which presents some insights into the parameter effect on the optimal inventory policy.