Optimization of a Multiple Minor Items Integrated EOQ With Correlated Demand By Cross-Selling

The correlated demand caused by cross-selling, Zhang et al (2011) proposed a two-item EOQ model, where the unmet demand for the major item can be partially backordered with lost sales that will reduce demand for the minor item. They developed an enumeration algorithm that can deal with only one minor associated item. Zhang et al (2011) proposed the partial backordering EOQ with correlated demand by cross selling where a portion of the sales of a minor item is associated with those of a major item. In this paper, we extend their model to make it more applicable to dealing with the inventory replenishment problem for multiple associated items. In this model we consider the fuzzy total cost under crisp order quantity or fuzzy order quantity in order to extend the traditional inventory model to the fuzzy environment. We use Function Principle as arithmetic operations of fuzzy total cost and use the Graded Mean Integration Representation Method to defuzzify the fuzzy total cost. Then we use the Kuhn-Tucker Method to find the optimal order quantity of the fuzzy order inventory model.