In this paper, we present a genetic algorithm embedded with mathematical optimization to solve a green inventory routing problem with interval fuel consumption. Using the idea of column generation in which only attractive routes are generated to the mathematical problem, we develop a genetic algorithm that allow us to determine speedily attractive routes that are connected to a mathematical model. We code our genetic algorithm using the idea of a integer number that represents all the feasible set of routes in which the maximum number allowed is the binary number that represents if a customer is visited or not. We approximate the fuel consumption as an interval number in which we want to minimize the overall fuel consumption of distribution. This is the first approximation made in the literature using this type of methodology so we cannot compare our approach with those used in the literature.
