The rough interval shortest path problem

Abstract

The shortest path problem is one of the most popular network optimization problems and it is of great importance in areas such as transportation, network design or telecommunications. This model deals with determining a minimum weighted path between a pair of nodes of a given network. The deterministic version of the problem can be solved easily, in polynomial time, but sometimes uncertainty or vagueness is encountered. In this work we consider the rough interval shortest path problem, where each arc’s weight is represented by a lower approximation interval and an upper approximation interval, which surely contains the real weight value and that may possibly contain the real weight value, respectively. A labeling algorithm is developed to find the set of efficient solutions of the problem.