Optimal Allocation of Capacitated Facilities considering Time-dependent User Preference for User Number Maximization

Traditional facility location models assume that the decision maker may assign a facility to serve a customer. While this can be true between distribution centers and retail stores, this does not work for facilities serving end consumers who choose facilities to visit according to their own preference. The problem is challenging as in practice facilities are capacitated and preferences are time-dependent. In this study, we consider a decision maker who builds facilities of various scale levels to maximize the number of customers served. We propose a mixed integer programming formulation to describe the problem. As the problem is NP-hard, we develop a heuristic algorithm by reducing part of the problem to the maximum flow problem. Through numerical studies we demonstrate the effectiveness of our proposed algorithm