具有模糊成本的运输问题求解方法之研究.docVIP

具有模糊成本的運輸問題求解方法之研究 Studies on solution methods for the transportation problem with fuzzy cost 邱清爐1 張嘉華2 許惠馨3 1南台科技大學工業管理研究所副教授 2南台科技大學工業管理研究所助理教授 3南台科技大學工業管理研究所研究生 台南縣永康市南台街1號 TEL: 06-2533131 Ext.4122 E-mail：clchyu@mail.stut.edu.tw 摘要 運輸問題為供應鏈管理中不可或缺的角色，其為線性規劃的特例且可以利用運輸單體法加以有效求解。但在現實環境中，某些時候單位運輸成本因無法精確估計而具有模糊現象，致使傳統的求解方法難以使用。在Bellman與Zadeh提出模糊理論的概念後，許多學者便將線性規劃的問題擴展至模糊環境中，以做更廣泛的應用。但是，在現有模糊線性規劃模式中，許多研究求解得到的目標值為明確數值，以致於喪失了模糊資料的特性；有些模式的求解方法則是過於複雜，因而降低了模式的應用性。本研究則建構出一種具有通用性且易於執行的模糊運輸問題之求解方法，以求解企業運輸成本最小化的問題。當單位運輸成本為模糊數值時，廠商的總運輸成本亦為模糊數值，此時利用Yager的模糊數值排序法，先將成本係數的模糊數值轉換為明確數值，之後再利用傳統的運輸單體法進行求解。此種求解方法亦與在模糊決策中經常使用的重心法相互比較，透過其他三種常用的模糊數值排序法，以分析兩種求解方法的差異。結果顯示，Yager排序法所得到的總運輸成本會小於重心法所求解之結果；故Yager排序法的求解程序為此類問題的較佳求解方法。 關鍵字：模糊集合、運輸問題、模糊線性規劃、擴展法則、運輸單體法 Abstract The transportation problem plays an important role in the supply chain management which is a special type of linear programming and can be solved by the transportation simplex method effectively. In the real-life applications, sometimes the cost coefficients in the model are inherently fuzzy due to lack of historical data, making the classical analysis technique not applicable. Since Bellman and Zadeh proposed the concept of fuzzy set theory in 1970, many scholars have devised fuzzy linear programming models and the associated solution methods for wider applications. However, most of the existing studies on fuzzy linear programming problems only provide crisp solutions and some models are too complicated which are not suitable for the decision maker to use. In this research we develop a generalized method to construct the fuzzy transportation problem model to find the optimal total transportation cost for the firm. When the cost coefficients are fuzzy, the total transportation cost will be fuzzy as well. The Yager’s ranking method is utilized to transform the fuzzy cost coefficients into crisp value, then the firm’s optimal policy can be determined via the classical transportation simplex method. This method is compared with