- 學位論文
An Algorithm for 4-Median Problem with Obnoxious Facilities In Trees.
An Algorithm for 4-Median Problem with Obnoxious Facilities In Trees.
摘要
此篇文章中，我們研究有關區位選擇問題，此問題於1900年初由Weber學者開啟先驅，主要探討如何選擇一個倉庫，以盡量最小化倉庫和客戶之間的總距離。從1960年代中期開始，此區位選擇問題蓬勃發展。其中以p-中位和p-中心問題為最廣泛的研究範圍。近年來，對於鄰避設施選址問題發展愈來愈有興趣，其問題主要表示一個或多個設施被放置在距離顧客位置愈遠愈好。所以本研究將在樹枝圖上處理負權重的區位選址問題，並且透過模型二的目標函數：盡量將設施到需求點之最小距離加權後總和最小化，來探討此鄰避設施選址的問題。在本文中，我們將條件限制於 且擁有負權重的樹枝圖的情況下，求解出最佳的解決方案，並且最後透過例子來說明，以表明該模型的有效性。
並列摘要
We investigate the location problems which began in the early 1900 when Weber considered how to locate a single warehouse so as to minimize the total distance between it and customers. Since the mid-1960s, the study of location theory has flourished. The p-center and p-median problems are probably the most widely studied problems. In recent years, there has been an interest in obnoxious facility location problems where one or more facilities are to be placed as far away as possible from the customers. This paper deals with facility location problems with negative weights in trees, and we consider model which is one of objective functions to handle obnoxious facilities: minimize the sum of the weighted minimum distances of the vertices of the facilities to demand. In this paper we show that for the case an optimal solution for the second model in trees and an illustrative example is given to show the effectiveness of the model.