The Multi-service Location Problems

In this paper, we aim to provide a general study on the framework of Multi-Service Location Problems from a broader perspective and provide systematic methodologies for this category of problems to obtain approximate solutions. In this category of problems, we are to decide the location of a fixed number of facilities providing different types of services, so as to optimize certain distance measures of interest regarding how well the clients are served. Specifically, we are to provide p types of services by locating k ≥ p facilities. Each client has a demanding list for the p types of services, and evaluates its service quality by its service distance, defined as its total transportation cost to those facilities offering the demanded services. Under this framework, we address two kinds of distance measures, the maximum service distance and the average service distance of all clients, and define the p-service k-center problem and the p-service k-median problem, according to the minimax and the minisum criteria, respectively. We develop a general approach for multi-service location problems, and propose a (2p)-approximation and a 4-approximation to the two problems, respectively.