Partial Backordering Inventory Model under Purchase Dependence

Abstract

Purchase dependence is a frequent phenomenon in retail shops and is characterized by the purchase of certain items together due to their unknown interior associations. Although this concept has been significantly examined in the marketing field (e.g. market basket analysis), it has largely remained unaddressed in operations management. Since purchase dependence is an important factor in designing inventory replenishment policies, this paper demonstrates the means of applying it to the partial backordering inventory model. Through computational analyses, this paper compares the performance of inventory models that either consider or ignore purchase dependence; the results demonstrate that inventory models that ignore purchase dependence incur more average cost per unit time than the model that considers purchase dependence, and the impact of purchase dependence can increase in significance as the item set becomes more closely correlated with regard to order demand.