Assortment and pricing in production/inventory systems

Abstract

For long, researchers and practitioners have been aware of the importance of aligning marketing decisions with the capabilities of the production system. Most of the existing models, however, make simplistic assumptions about the production capacity and thus do not capture the production lead time in a realistic manner. In this paper, we consider the impact of load-dependent lead times on the optimal assortment and pricing decisions of a make-to-stock manufacturer, who wishes to offer an assortment of vertically differentiated products (i.e., having different quality levels) to the market using a given (flexible) production capacity. Depending on the price and quality levels of the products offered, customers decide to either buy a given product, or not to buy at all. Inventories are reviewed periodically, and the goal of the manufacturer is to set the price, quality and inventory levels of the products to maximize long-run expected profit. For the sake of clarity, we limit the assortment to two products and fix the quality of one of the products. We first characterize the optimal decisions assuming no coordination between marketing and production departments: the marketing department is uninformed about the impact of its price and quality decisions on the production lead time so it assumes a fixed exogenous lead time (e.g., based on past experience; uncoordinated system). For normally distributed demands, the optimal decisions then have a simple structure. Next, we study the results of the coordinated system where the marketing department has perfect information about the impact of its decisions on the production lead time (i.e., lead time is endogenous and load-dependent). We assume that a single processor sequentially processes items one at a time on a FCFS basis and that the production time increases with the product quality level. To analyze the optimal decisions in this system, we build a queuing model and solve it using matrix analytic techniques. We show that lack of production-marketing coordination causes suboptimal assortment and pricing decisions, resulting in significantly lower profits for the firm. More specifically, the firm opts for excessively high quality levels and sets the price of the higher quality product too low. This will cause the utilization of the production system to soar and leads to high congestion levels and long production lead times.