On the Two-Stage Transportation Problem With Fixed Charge for Opening the Distribution Centers

In this paper, we are addressing the two-stage transportation problem with fixed charge for opening the distribution centers, which is an extension of the classical transportation problem. The problem models a distribution network in a two-stage supply chain which involves: manufacturers, distribution centers and customers, and its main characteristic is that a fixed charge for opening the distribution centers is associated, in addition to the variable transportation cost which is proportional to the amount of goods shipped. We describe a novel solution approach for the minimization of total distribution costs: a fast and efficient constructive heuristic algorithm that reduces the solution search space to a subspace with a reasonable size, without losing optimal or sub-optimal solutions by considering a perturbation mechanism that allows us to reconsider discarded feasible solutions that might lead to such solutions. Computational results are reported and discussed for the existing benchmark instances and on a set of instances that contains eight new randomly generated larger instances. The obtained results show that our solution approach is highly competitive as compared to the existing methods from the literature.