A joint decision model of product variety and inventory control under fuzzy substitution rate

The problem of jointly determining the product variety decision with inventory control decision for the different brand of a certain product under fuzzy substitution rate and fuzzy inventory holding cost is studied in this paper. The fuzzy total profit and possible service level at the retailer are both given. Based on it, a nonlinear integer programming model to maximize total multi-period profits subject to given stocking space, budgetary and service level constraints is established. Finally, numerical results and conclusions are presented. Computation results show that it may be more profitable to adopt narrower assortment policy versus complete assortment policy for the retailer and the net profit criterion is prior to the conventional gross profit criterion in our scenario.