A matheuristic for the two-stage fixed-charge transportation problem

This paper addresses the two-stage fixed-charge transportation problem which involves the distribution of a commodity from plants to customers through intermediate depots, while minimizing the overall costs incurred. There are two costs associated with each arc: a fixed cost for the use of the arc, and a variable cost proportional to the number of units sent along the arc. First, we prove some theoretical properties which extend well-known results of the fixed-charge transportation problem. Then, we present a matheuristic that uses an evolutionary algorithm and exploits these properties to guide the algorithm towards better solutions. The chromosome of the evolutionary algorithm controls the arcs that can be used in the delivery. Its fitness is computed as the objective function value of a feasible solution of the problem, which is obtained by applying optimization techniques. The computational results show the effectiveness of the algorithm.