A joint optimization of product variety and ordering approach

The OPROVAR model is a non-linear optimization model that determines the optimal product line that would maximize profits while considering costs of ordering and carrying inventory, subject to given system constraints. The model has been formulated with the assumption that consumer preferences for products are known and are ordinally scaled for the subset of products in the product line. Further, products can be added and deleted according to the profitability criterion. The problem of jointly determining the product variety decision with the ordering decision for the different variations of a brand of a certain product that comprises a product line is considered. We determine optimal solutions to the OPROVAR model that not only considers the order quantity decision of a product but also makes stocking decision of a product line to maximize total profits. It has been generally recognized that the product variety or product line decision is one of critical importance to marketing and product managers. Product line composition is one of the most pervasive problems that includes analysis of product additions as well deletions and the degree of complementarity and substitutability among the different items within the product line. Equally important is the ordering decision which determines the order size and timing of the order for replenishing the stock of each of the products that constitute the given product line. We develop a model, OPROVAR (optimization of product variety and ordering strategy) that considers simultaneously the order quantity decision of a product and the stocking decision of a product line to maximize total profits.