Designing Reliable Center Systems: A Vector Assignment Center Location Problem

Abstract

The p-center problem is one of the most important models in location theory. Its objective is to place a fixed number of facilities so that the maximum service distance for all customers is as small as possible. This article develops a reliable p-center problem that can account for system vulnerability and facility failure. A basic assumption is that located centers can fail with a given probability and a customer will fall back to the closest nonfailing center for service. The proposed model seeks to minimize the expected value of the maximum service distance for a service system. In addition, the proposed model is general and can be used to solve other fault-tolerant center location problems such as the (p, q)-center problem using appropriate assignment vectors. I present an integer programming formulation of the model and computational experiments, and then conclude with a summary of findings and point out possible future work.

Exploring Similarities in Discrete Facility Location Models with Equality Measures

“…The CEN appears very weakly correlated with all the other measures. This result seems to contradict the opinion of some researchers (e.g., Hodgart 1980;Lei 2016) which sustained that one method to assure equity is improving the condition of those who are worst-off. Among the selected measures, the coefficient of variation (VC) shows a very high correlation with all the other measures, apart from the CEN.…”

“…In any case, high correlations between these pairs of measures may suggest that a fundamental choice in the selection of the measure to be adopted lies in the distinction between not‐normalized and normalized measures. The CEN appears very weakly correlated with all the other measures. This result seems to contradict the opinion of some researchers (e.g., Hodgart ; Lei ) which sustained that one method to assure equity is improving the condition of those who are worst‐off. Among the selected measures, the coefficient of variation (VC) shows a very high correlation with all the other measures, apart from the CEN.…”