Solving a multimodal transport problem by DCA

The combined transport appears as a promising alternative to road transportation for containers allocation. It possesses a strong potential market, conditioned by the development of its quality of service (improvement of the system, terminals, and service performances in terminals). Multimodal transport of containers can be an alternative to the road transportation but it requires to be competitive in term of quality of service and price. We address specifically the problem of optimizing container loading on trains in rail-rail trans-shipment shunting yard to minimize the frequency of transfers within yards. In such yards, trains succeed one another upon arrival and departure. Based on their final destination, containers are unloaded from their initial original train by automated handling systems, to be reloaded on a departing train at a defined place. It is discussed how to determine the initial loading place of containers on arriving trains and their reloading place on departing trains. Our primary goal is to minimize the frequency of transfers within a particular yard, the secondary goal is to complete the use of handling equipments. The problem is characterized as problem of minimum cost multicommodity network flow with binary variables, which are often difficult to solve to optimality The problem statement and its mathematical formulation are developed. They can be reformulated, thanks to exact penalty techniques in DC Programming, as a polyhedral DC Program and globally solved by a combination of the local algorithm DCA and B&B. Numerical simulations that show the efficiency of DCA and the combined DCA - Branch and Bound algorithm are reported.