Medical facility network design: User-choice and system-optimal models

Abstract

Motivated by a real-life project, this paper presents several models for designing a network of “walk-in” medical facilities that provide a homogeneous service in competitive and centralized environments. The problem in a competitive environment is to optimize the location and capacity of each open facility for a focal firm so as to maximize its total demand volume, subject to a total capacity limit. We assume that travel time to a facility and expected waiting time at a facility are the two main determinants for clients to choose where to receive the service. We consider two alternative “user-choice” models, one “probabilistic-choice” and the other “deterministic-choice”. In a centralized environment, a central decision maker determines the optimal location and capacity of each open facility, to maximize overall social welfare. We consider a “system-optimal” model and two user-choice models. All the models follow a bilevel structure, i.e., the location-allocation framework. The user-choice models are formulated as mathematical programs with equilibrium constraints. To solve the problems efficiently, we propose a common solution methodology in line with the location-allocation framework. Through a real-life case study, we discuss several interesting managerial insights about model selection and facility network design strategies.