چکیده:
In this paper we address the VRPCD, in which a set of homogeneous vehicles are used to transport products from the suppliers to customers via a cross-dock. The products can be consolidated at the cross-dock but cannot be stored for very long as the cross-dock does not have long-term inventory-holding capabilities. The objective of the VRPCD is to minimize the total traveled distance while respecting time window constraints of suppliers and customers and a time horizon for the whole transportation operation. Following the literature on vehicle routing problems with cross-docking, it seems that few studies consider that customer will receive its requests from several suppliers; therefore, the present study is an attempt to investigate this case. A heuristic and a memetic algorithm are used to solve the problem. The proposed algorithms are implemented and tested on data sets involving up to 200 nodes (customers and suppliers). The first results show that the memetic algorithm can produce high quality solutions. It is able to find the optimal solution for small instances, for the large ones, it is very powerful comparing with the best insertion heuristic, the gap achieved 30%.
خلاصه ماشینی:
"com A memetic algorithm forthe vehicle routing problema with cross docking Sanae Larioui a, Mohamed Reghioui a, Abdellah Elfallahi a and Kamal Eddine Elkadiri a a Ensate, University of Abdelmalek Essaadi, Mhannech II, Tetouan, Morocco Abstract In this paper we address the VRPCD, in which a set of homogeneous vehicles are used to transport products from the suppliers to customers via a cross-dock.
The objective is to determine the best pickup and delivery routes as well as the arrival times of pickup/delivery vehicles at the cross-dock so that all nodes are visited within their time windows at minimum total transportation cost, including variable and fixed costs.
The authors proposed a mixed integer programming formulation and a tabu search algorithm to assign tours to a set of vehicles at the cross dock so that suppliers and customers are visited within their time windows.
The VRPTW (vehicle routing problem with time windows) can be especially helpful in treating the VRPCD, since the pickup and delivery routes must be synchronized at the cross-dock and time windows of suppliers and customers should be respected.
They consist of arcs: {(i,j): i,j ∈ P U { o1; o2},i≠ j}and the arcs {(i,j): i,j ∈ D U { o3; o4}, i≠ j} K is the set of vehicles The parameters are: Cij = the travel time between node i and node j ((i, j) ∈ E); [ai, bi] = the time window of node i (i ∈ N); Dij = the amount of demand requested by the customer j to the supplier i (i ∈ P) (j ∈ D); Q = the vehicle capacity; A = the fixed time for unloading and reloading at the cross-dock; B = the handling time of one pallet."