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NTU Management Review
Vol. 33 No. 3 Dec. 2023, 1-34
https://doi.org/10.6226/NTUMR.202312_33(3).0001

Optimal Allocation of Capacitated Facilities Considering Time-
Dependent User Preference for User Number Maximization

最大化偏好因時而異之消費者服務人數的有限產能設施
選址模型

Ling-Chieh Kung, Department of Information Management, National Taiwan University
孔令傑 / 國立臺灣大學資訊管理學系
Jih-Sheng Chuang, Department of Information Management, National Taiwan University
莊日陞 / 國立臺灣大學資訊管理學系
Yun-Tung Kuo, Department of Information Management, National Taiwan University
郭芸彤 / 國立臺灣大學資訊管理學系
Received 2020/7, Final revision received 2022/9
Abstract
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.

【Keywords】facility location, preference, capacity, time dependency, maximum flow

摘 要
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。

【關鍵字】 設施選址、偏好、容量限制、因時而異、最大流

領域主編：蔡瑞煌教授

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