Assortment and pricing decisions in production/inventory systems

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 and quality levels of the products to maximize long-run expected profit. We characterize the optimal decisions for the infinite capacity system (where replenishment is instantaneous), and compare these to the optimal decisions in the finite capacity system (which implies load-dependent replenishment lead times). We show that, for normally distributed demands, the optimal solution of the infinite capacity system has a simple structure. This solution, however, will typically be suboptimal in the finite capacity case, as it tends to cause high utilization, implying excessive replenishment lead times and high inventory-related costs.