Fuzzy random shortest path problem using conditional Value at Risk

This paper considers a fuzzy random shortest path problem and proposes a new risk measure to synthesize both stochastic conditional Value at Risk and credibility measure for fuzziness. The proposed model defined by the hybrid conditional Value at Risk is equivalently transformed into a 0-1 mixed integer programming problem. In order to this problem analytically and efficiently, the Lagrange 0-1 relaxation problem using the property of totally unimodular and proposed the efficient solution algorithm based on the hybrid algorithm of standard Dijkstra algorithm and subgradient method.