an extended compact genetic algorithm for milk run problem with time windows and inventory uncertainty

in this paper, we introduce a model  to optimization of milk run system that is one of vrp problem with time window and uncertainty in inventory. this approach led to the routes with minimum cost of transportation while satisfying all inventory in a given bounded set of uncertainty .the problem is formulated as a robust optimization problem. since the resulted problem illustrates that grows up time in this method is progressive, and in order to solve the large-scale problems, ecga (extended compact genetic algorithm) has been proposed. the efficiency and effectiveness of the ecga to this optimization problem is tested and the results are presented. the results show the ability of the ecga to efficiently optimal solution for the cases considered. investigated example showed that this method has the ability to obtain a solution more accurate than other optimization methods.