Stochastic p-hub center covering problem with delivery time constraint

In this paper, stochastic version of p-hub covering center problem (we call it Sp-HCCP) has been presented that optimizes the location of the hubs and allocation of non-hub nodes to hub nodes. The goal of our model is to maximize the minimum service-level that can achieved for a given maximum path length (delivery time on the path). We have formulated this problem using the chance constraints with a linear structure and a Genetic Algorithm (GA) has been developed to solve large scale problems. Numerical examples are solved by GA and the results are compared with exact solutions to prove the efficiency and robustness of the proposed GA. The results show that the optimal solutions are sensitive to the amount of stochastic demands also they show the precision of proposed GA method.