Anticipated Wait and Its Effects on Consumer Choice, Pricing, and Assortment Management

MSOM

34 Pages Posted: 12 May 2020 Last revised: 29 Feb 2024

See all articles by Ruxian Wang

Ruxian Wang

Johns Hopkins University - Carey Business School

Chenxu Ke

Shanghai University of Finance and Economics - College of Business

Zifeng Zhao

Mendoza College of Business, University of Notre Dame

Date Written: September 29, 2023

Abstract

Problem definition: We investigate the effects of waiting time, mainly due to production in a make-to-batch-order (MTBO) system, on consumer choice behavior, pricing, assortment, and model estimation. In an MTBO system, the seller/manufacturer first collects orders placed within a certain period of time into a batch and then starts the production process. After the production of all orders in a batch are complete, the products are then shipped and delivered to individual consumers. Due to batch production and shipping, the disutility of the waiting time exhibits negative externality. Methodology/results: We adopt the widely used multinomial logit (MNL) model as a starting point and incorporate the anticipated wait into consumers’ decision making. The derived model, referred to as the MNL with wait model, is a solution of the rational expectation equilibrium and is capable of capturing the effects of negative externality induced by anticipated wait that may change the substitution patterns dramatically. We characterize the multi-product price optimization problem under the MNL with wait model by establishing a one-to-one mapping between the price vector and the choice probability vector. We find that firms tend to charge higher prices for time-consuming items and charge lower prices for 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 mild conditions under which the optimality of revenue-ordered assortments still holds. However, the assortment problem under the MNL with wait model is generally NP-hard, so we develop approximation algorithms with performance guarantees and provide an easy-to-compute tight upper bound. Moreover, we develop an efficient maximum likelihood-based algorithm for model calibration and further conduct numerical studies to showcase the importance of incorporating disutility due to wait in estimation, pricing, and assortment planning problems. Managerial implications: The MNL with wait model can increase prediction accuracy for consumers’ choice behavior especially when they are aware of the potential wait. Failure to take into account the effects of anticipated wait in firms' decision making may lead to substantial losses.

Keywords: Negative Externality; Anticipated Wait; Multinomial Logit; Optimization; Estimation

Suggested Citation

Wang, Ruxian and Ke, Chenxu and Zhao, Zifeng, Anticipated Wait and Its Effects on Consumer Choice, Pricing, and Assortment Management (September 29, 2023). MSOM, Available at SSRN: https://ssrn.com/abstract=3579806 or http://dx.doi.org/10.2139/ssrn.3579806

Ruxian Wang (Contact Author)

Johns Hopkins University - Carey Business School ( email )

1625 Massachusetts Ave NW
Washington, DC 20036
United States

Chenxu Ke

Shanghai University of Finance and Economics - College of Business ( email )

777 Guoding Road
Shanghai, 200433
China

Zifeng Zhao

Mendoza College of Business, University of Notre Dame ( email )

Notre Dame, IN 46556
United States

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