A multiple server location–allocation model for service system design

Service systems are endemic in a service economy, and effective system design is fundamental to the competitiveness of service organizations such as retailers, distributors, and healthcare providers. This is because system design may significantly facilitate (or hinder) the attainment of important organizational objectives such as minimizing system cost and maximizing service level. This paper develops and solves a comprehensive nonlinear location–allocation model for service system design that incorporates several relevant costs and considerations. These include, for instance, transportation, facility, and waiting costs, queuing considerations, multiple servers, multiple order priority levels, multiple service sites, and service distance limits. The model is first converted to an equivalent linear form and then solved using Lagrangian relaxation. A computational study shows problems with 250 service districts, 60 service sites, and 250 candidate locations are solved in about two and a half minutes. An extensive managerial experiment is conducted that evaluates alternative system designs from a number of important perspectives including centralization versus decentralization, system configuration, and service distance limit. Each scenario is evaluated with respect to two fundamental criteria, namely, total cost and service level. The analysis provides insights into important tradeoffs that must be taken into consideration in designing an effective service system.