Optimizing Service Operations with Price- and Density-Dependent Demand: A Copula-Based Approach

67 Pages Posted: 16 May 2023 Last revised: 5 May 2024

See all articles by Andrew Frazelle

Andrew Frazelle

University of Texas at Dallas - Naveen Jindal School of Management

Toghrul Rasulov

University of Texas at Dallas - Naveen Jindal School of Management

Shouqiang Wang

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: May 4, 2024

Abstract

Exclusivity is a key component of certain service offerings such as elite members-only social or country clubs. Indeed, such services may only appeal to customers if they limit the crowd density, i.e., the maximal number of customers granted access to the service. We consider a service provider, who sets its crowd density cap in addition to its price. Customers are heterogenous in both their willingness to pay (WTP) for the service and their density tolerance. Each customer purchases the service only if the price is below her WTP and the density is below her tolerance. Importantly, customers’ WTP and density tolerance may be statistically dependent, and we develop a novel, copula-based framework to model the dependence structure of these two dimensions of heterogeneity. We analytically characterize the provider’s optimal price and density decisions. As long as the customer population is not too severely sensitive to density, (i) the provider optimally serves all segments of the market and activates the price (rather than the density) to regulate the demand and (ii) as customers’ valuations and density tolerances become more positively dependent, the provider earns higher revenue and optimally increases its service density. By contrast, the optimal price may be decreasing, increasing, or decreasing followed by increasing. On the other hand, with severely density-sensitive customers, it may be optimal to partially cover the market and to activate density to regulate the demand.
Our findings offer prescriptive guidelines for service operations in the presence of density-sensitive demand, and also provide an explanation for the failed versus successful practices of prominent private clubs.

Keywords: service operations, revenue management, copulas, exclusivity/privacy

Suggested Citation

Frazelle, Andrew and Rasulov, Toghrul and Wang, Shouqiang, Optimizing Service Operations with Price- and Density-Dependent Demand: A Copula-Based Approach (May 4, 2024). Available at SSRN: https://ssrn.com/abstract=4449155 or http://dx.doi.org/10.2139/ssrn.4449155

Andrew Frazelle (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

HOME PAGE: http://andrewfrazelle.com

Toghrul Rasulov

University of Texas at Dallas - Naveen Jindal School of Management ( email )

Shouqiang Wang

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

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