Effects of production capacity and substitutability on optimal pricing and inventory policies

Manufacturers produce substitutable products to meet the different needs of consumers. Meanwhile, to formulate the optimal production strategy, manufacturers have to deal with demand uncertainty and capacity constraints. This study employs a stochastic model of a monopolistic manufacturer with limited capacity to sell two types of substitutable products: high- and low-end products. We then develop an expected profit function and solve for the optimal prices, safety stocks, and expected profit. Additionally, this study uses cost functions related to the substitutability (quality) to extend our basic model and investigate how the manufacturer makes decisions. The optimal results are derived under capacity constraints. The findings show that when the cost of low-end products is high, with an increasing substitutability, the manufacturer should reduce the price of high-end products and raise the price of low-end products. Otherwise, the manufacturer should conduct an opposite modification. In addition, different capacity constraints moderate the effects of demand uncertainty on the safety stocks, and the safety stock of high-end products may decrease in demand uncertainty. The results also reveal that, the manufacturer should raise the allocation ratio of high-end products if the capacity increases. With a higher substitutability, the manufacturer may allocate more capacity to high-end products. In the case of low-end products’ quality decision, a tighter capacity results in a higher optimal substitutability. Considering two products’ quality decisions, however, a moderately tight capacity leads to the highest quality level of low-end products, and the quality of high-end products always remains at a very high level.