Optimization models for shortest path problem with stochastic arc lengths taking fuzzy information

Abstract

Shortest path problem is a fundamental problem in network optimization and combinational optimization. The existing literature mainly concerned with the problem in deterministic, stochastic or fuzzy environments by using different tools. Different from the existing works, we investigate shortest path problem by regarding arc lengths as uncertain variables which are employed to describe the behavior of uncertain phenomena. According to different decision criteria, three concepts of path are proposed in uncertain environment, and three types of uncertain programming models are formulated. Furthermore, these models are concerted into deterministic optimization models in several special cases. © 2013 Springer-Verlag.