A lower bound generating procedure for a fixed charge capacitated multimodal transportation problem

We consider a fixed charge capacitated multimodal transportation problem which has wide application but not been extensively studied in the literature. The problem aims at determining the route for each demand, the transportation mode on the route and the number of containers for each transportation mode, such that all transportation requests are satisfied with the minimum logistic costs. We develop a column generation framework to provide a lower bound. In order to evaluate the quality of the lower bound generated, we compare the lower bound obtained with optimal objective function value. The average gap is 19.6%.