在傳統的設施選址問題中，決策者可以指定由哪個設施去服務哪個顧客。雖然這可能適用於配送中心與零售店之間；但對於根據自身偏好決定要前往哪個設施的終端消費者而言，這個設定便顯得不夠實際。當要設置的設施有容量限制，而消費者的偏好又會因時而異時，這樣的問題將變得更具挑戰性。在這個研究中，我們考慮如何建造不同規模的設施以吸引盡量多的使用者，並為此建立了一個混合整數規劃模型；又由於此問題是NP-hard，本研究開發了一個將一部份問題轉換為最大流問題的啟發性演算法，並利用數值實驗來檢驗此演算法的成效。

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.