Capacity Investment, Flexibility, and Product Substitution/Complementarity under Demand Uncertainty

We provide a comprehensive characterization of the relationship between optimal capacity and the degree of product substitution/complementarity under price/production postponement, considering different business practices (holdback versus clearance, negative price policies) and different demand models. Specifically, we consider a firm that produces two products, which can be substitutable or complementary. The demand of each product is a linear function of the prices of both products (with the relationship depending on the substitution/complementarity structure), and is subject to an additive stochastic shock. We consider two types of linear demand functions that are commonly used in the economics and operations management literature. The firm operates in a monopolistic setting and acts as a price-setter for both products. Overall the firm needs to make three sets of decisions: capacity, production quantities, and prices. While the capacity investment decision has to be made ex-ante observation of demand curves, price and/or quantity decisions can be postponed until after demand curves are observed. We consider two postponement strategies: price and quantity postponement, and price postponement only.We characterize the optimal pricing/production/investment decisions for each postponement strategy. Using these characterizations, we show that product substitution/complementarity is a key demand characteristic, which has a large impact on the optimal capacity. Our results show that how the optimal capacity behaves in substitution/complementarity parameter is quite similar under both postponement strategies, and under holdback and clearance. However, this behavior depends highly on other underlying assumptions (i.e., whether or not negative prices are allowed) and on the demand model used.