A column generation-based algorithm for solving combined inventory and routing problems

This paper presents a column generation algorithm for solving combined vehicle and inventory problems. This problem is based on the idea of coordinating customer inventory levels through a minimum routing cost. This is a combinatory decision problem since vehicle routing and inventory problems, are combined. Using the column generation method, we can iteratively generate interesting routes to the system, based on their dual costs, this is routes that will improve the quality of the objective function because its reduced costs are negatives. The initial mixed integer problem has to be relaxed for getting its reduced costs. The sub problem is defined as the shortest pathproblem that returns a set of desirable routes. Finally, when the set of desirable routes is obtained, the mixed integer model should select a set of routes that fulfill bothminimum shipping costs and the constraints of the system.