Department of Information Management
National Chi Nan University
470 University Rd., Puli Nantou 545, Taiwan
In this paper, we propose a simple linear multiple objective programming to deal with the fuzzy shortest path problem. The proposed approach does not need to declare 0-1 variables to solve the fuzzy shortest path problem because it meets the requirements of the network linear programming constraints. Therefore, the linear programming relaxation can be used to arrive at an integer solution without using the Branch and Bound technique, and the complexity of our proposed method can be reduced. A compromising non-dominated integer optimal solution, the fuzzy shortest path, can be obtained easily without adding extra constraints. This approach not only can obtain a fuzzy shortest path but also can reduce the complexity of solving the basic fuzzy shortest path problem without using 0-1 variables. Three examples with trapezoidal and triangular fuzzy numbers in arc length are used to demonstrate the proposed method in more details.
Keywords: shortest path, multiple objective programming, fuzzy number, network optimization
(*Contact: E-mail jennifer@ncnu.edu.tw )
Cite this article as: Jing-Rung Yu and Tzu-Hao Wei, "Solving the Fuzzy Shortest Path Problem by Using a Linear Multiple Objective Programming," Journal of the Chinese Institute of Industrial Engineers, 24, 360-365 (2007).