【正文】
vehicles by integer programming. The improving procedure is based on the deterministic threshold accepting heuristic method with integrated core methods. We test the new heurist method with a set of 9 test problems taken from the literature. Our new method can solve some problems feasibly, and for infeasible problems, the new method can solve them with penalties. Although some putational results by our new heuristic are not so good as those by previous researches, we do develop a new heuristic method to solve the VRPM. Keywords VRP, multiple use of vehicles, heuristic, threshold accepting Transportation lies at the heart of human effort for a long time. The transportation of resources and goods advances the human economy because transportation supports most of the social and economic activity in the world. Manufacturing needs transportation to obtain materials and transport their products to customers or downriver manufacturer. Other industries such as hypermarket or store need support of transportation, too. Therefore, transportation bees a necessary activity of industries. From the view point of logistics, transportation plays an important role in distribution management. Because the plan of transportation has great influence on cost such as the fixed cost of vehicles and depots, the variable cost of gas, overtime pay of driver and the penalty cost of delay. On the other hand as the establishing of the world trade organization, industries all over the world pete bitterer and bitterer. Besides nowadays the market of product changes more rapidly and the life cycle of product bees much shorter. As the rising of home delivery and global shipping recent year, a thorough and reliable plan of transportation has bee a necessary condition of high petitiveness. The well known Vehicle Routing Problem (VRP) is one of the core problems of transportation. The goal of VRP is to establish a distribution plan which has the minimum total cost (distance) with a number of customers (nodes), vehicles and a single depot. The vehicles’ capacity and sometimes the distance limit of vehicles are concerned, too. In the planning period each vehicle can only assign one planning route. However, the VRP is a hard binatorial optimization problem