Petri Net Model and Mathematical Resolution for Cross Docking

In this paper, we consider a truck dock assignment problem. The constaints are: the number of trucks exceeds the number of docks available and we evaluate the time constaint in the cross docks with the use of resources. The goal is to minimize the penality cost, we are not able to unload all trucks for thre main reason:
• the number of trucks exceeds the number of docks available
• the time windows of trucks cannot permit the transhipment
• there are no sufficient resources or capacity in the cross dock to process the cargo.We will combine an existing model in Miao et al. [2009] to abstract the truck docks assignment and a model from a Petri net study of the internal cross dock with resources. The main idea is to integrate more details, like resource and operational time based on the number of pallets. And this is possible using a Petri net approach with a mathematical tool. Then the final IP model is solved with ILOG CPLEX Solver.