Analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem

This paper studies the analytical and managerial implications of product substitutability on the joint pricing and procurement decisions. We consider a single-period model with two products: an existing product and an improved new product that can substitute the demand for the existing product in case of a shortage. Demand for each product follows a general distribution with an expected value that is a linear function of the price of the new product. While the price of the existing product is determined by the market, it is necessary to determine the new product’s price and the procurement quantities of both products so as to maximize the profits. We analytically show that the expected profit function is unimodal and in the existence of substitution: the expected total profit is higher; the optimal price and the safety stock of the new product are higher; and the optimal safety stock of the existing product is less. Using these properties an efficient algorithm is developed. We also provide a numerical analysis to demonstrate that considering substitution in advance could increase the profitability by 58% and the new product price by 5% while decreasing the total procurement quantity by 15%.