A shortest path problem with random and interval variables for arcs based on conditional Value at Risk

This paper considers a shortest path problem with both random and interval variables for arcs and proposes a new risk measure to synthesize both stochastic conditional Value at Risk and order relation of interval values. 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 to the shortest path problem is equivalently performed. The numerical example is provided to compare the proposed model with the other standard models.