A combined tramp ship routing, fleet deployment, and network design problem

In this paper, a tramp ship routing model of fleet deployment in a hub-and-spoke network is presented. This model simultaneously determines the selection of hubs, the assignment of spokes to hubs, the deployment of feeder-containerships as well as containership routing between spokes and spokes, hubs and spokes, and hubs and hubs. Even though some parts have been studied, this complex combination of shipping problems has never been addressed. Because the problem is NP-hard, a genetic algorithm (GA) with local search is proposed. In the algorithm, a cut-off procedure is applied to fleet deployment in a sub-route strategy. A number of randomly generated problem instances are solved by both a mathematical program and the GA with local search. A simple but realistic heuristic algorithm is also developed. Both the GA with local search and the heuristic algorithm are used to solve a number of real case instances. A comparison of the results shows the efficiency of the GA with local search. The developed model can be used as a route-decision support tool for shipping companies that provide long-haul shipping services in a hub-and-spoke network.