我們提出了著名的工廠選址問題的衍生，稱為多重服務之工廠選址問題。在此問題中，每個工廠能夠提供多種不同的服務，而每個客戶對不同的服務有不同的需求，此問題的目標是找到一個開啟工廠的位置集合，決定其中提供的服務給相對應的客戶，使得所有客戶的需求皆被滿足，並且最小化總成本，包括開啟工廠的成本、提供服務的成本及運輸成本。為了解決此問題，我們修改了區域搜尋啟發式演算法，並且提出了一個近似演算法和理論分析，在本研究中，證明了我們提出的演算法所得到的結果最差不會大於三倍的最佳解，並且將演算法實作，透過實驗結果驗證了我們的演算法的效率和有效性。

We propose a generalization of the well-known facility location problem, called the multi-service facility location problem. In this problem, each facility has the ability to provide at most p kinds of distinct services, and each client has different requirements from the p kinds of services. The objective is to select a subset of facilities and to identify its corresponding service assignment to clients such that the requirements of each client can be satisfied, and the total cost, including the facility setup cost, service cost and connection cost is minimized. To solve this problem, we modify a local search heuristic algorithm, and present an approximation algorithm with theoretical analysis. In this study, we prove that our algorithm has a locality gap of 3 for this problem. We also implement the algorithm and the experimental result demonstrates its efficiency and effectiveness.

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