Capacity, Pricing and Assortment Management under Discrete Choice Model with Anticipated Wait

Customers often face multiple choices when purchasing a product or service. After making a choice, they sometimes have to wait for a while before receiving their purchased item due to the firm’s limited capacity
to process orders. This paper incorporates the anticipated wait for receiving purchased products or services into customers’ choice behavior. The resulting choice model shares the same spirit of the rational expectation equilibrium, and captures the effects of negative externality caused by the anticipated wait, because all orders may be processed by a common facility. Our analysis shows that the anticipated wait may change the substitution patterns dramatically. We further investigate the effects of the anticipated wait on the decisions of capacity investment, product pricing and assortment planning. We establish the one-to-one mapping between the price vector and the choice probability vector, and show that the equivalent profit function of the choice probabilities is explicitly defined and more tractable. We characterize the multi-product price optimization problem under the MNL model with waiting. In addition to price competition, we also study the Cournot competition, in which the decision is the choice probability for each firm, and show that there exists a Nash equilibrium. For the assortment optimization, we identify the conditions under which the optimality of the revenue-ordered assortment still holds. Because the assortment problem with waiting is generally NP-hard, we develop efficient approximations with performance guarantee and also provide an easy-to-compute tight upper bound. The new model has the potential to increase prediction accuracy for customers’ choice behavior especially when customers faced with multiple choices are aware of the possible waiting for their purchased products. Failure to take into account the effects of the anticipated wait in customers’ purchase behavior may result in substantial losses to firms.