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

48 Pages Posted: 12 May 2020 Last revised: 25 Aug 2022

See all articles by Ruxian Wang

Ruxian Wang

Johns Hopkins University - Carey Business School

Chenxu Ke

Nanjing University - School of Business

Date Written: June 26, 2019


Problem definition: 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 into customers’ choice behavior. The resulting choice model shares the same spirit of the rational expectation equilibrium, and captures the effects of negative externality induced by the anticipated wait on choice behavior. Methodology/results: We adopt the widely used multinomial logit (MNL) model as a starting point, and show that the newly derived model is still well-defined but the anticipated wait may change the substitution patterns dramatically. We characterize the multi-product price optimization problem under the MNL with wait by establishing the one-to-one mapping between the price vector and the choice probability vector. Firms tend to charge higher prices for the time-consuming items, but charge lower prices for the time-saving items compared with the optimal prices under the standard MNL model. In addition to price competition, we also study the Cournot-type competition, in which the decision is the choice probability for each firm, and
establish the existence of a Nash equilibrium. For assortment optimization, we identify the conditions under which the optimality of revenue-ordered assortments still holds. In particular, revenue-ordered assortments return an optimal or near-optimal solution if the disutility due to wait increases at a relatively slow rate. However, the assortment problem under the MNL with wait is generally NP-hard, so we develop efficient approximations with performance guarantee and provide an easy-to-compute tight upper bound, which can be used to gauge the performance of heuristic policies. Managerial implications: The proposed model has the potential to increase prediction accuracy for customers’ choice behavior especially when customers faced with multiple choices are aware of the possible wait for their purchased products. Failure to take into account the effects of the anticipated wait in customers’ purchase behavior may result in substantial losses.

Keywords: Negative Externality, Waiting Time, Queueing Model, Multinomial Logit Model, Price Optimization and Competition, Assortment Planing

Suggested Citation

Wang, Ruxian and Ke, Chenxu, Capacity, Pricing and Assortment Management under Discrete Choice Model with Anticipated Wait (June 26, 2019). Available at SSRN: or

Ruxian Wang (Contact Author)

Johns Hopkins University - Carey Business School ( email )

1625 Massachusetts Ave NW
Washington, DC 20036
United States

Chenxu Ke

Nanjing University - School of Business ( email )

22 Hankou Road
Nanjing, Jiangsu 210093 210093

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