Traditional facility location models assume that the decision maker may assign a facility to serve a customer. While this assumption can be true in the case of assigning distribution centers to retail stores, it does not apply to the scenarios where end consumers choose serving facilities according to personal preferences. The problem becomes even more challenging when the facility is with limited capacity and the customer is 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.