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论文范文
1. Introduction The vehicle scheduling problems arise when owners and operators of transportation systems must manage a fleet of vehicles over space and time to serve current and forecasted demands. The capacity of a transportation system is directly related to the number of available vehicles. Determining the optimal number of vehicles for a transportation system requires a tradeoff among the benefits for meeting demands, the ownership costs of the vehicles, and the penalty costs associated with not meeting some demands. Serving demand results in the relocation of vehicles. Each vehicle is in a particular location, and each task demand requires a vehicle in a particular location. The assignment of a vehicle to a task demand generates revenue. Thus, we consider the problem of vehicles assignment strategy. The interaction between fleet sizing decisions and vehicle assignment decisions is the focus of this paper. There is a substantial history of research on vehicle assignment problems with fixed vehicle fleet. But the research described in this paper attempts to integrate vehicle fleet sizing decisions with vehicle assignment decisions. In this paper, we consider the dynamic vehicle scheduling for working service network with dual demands by applying an optimization modeling approach, in which the service demand in each terminal includes two type, that is, minimum demands and maximum demands. We name this type of problem as the dynamic working vehicle scheduling with dual demands (DWVS-DD). The objective is to optimize the performance of the transportation system over the entire planning horizon. The model of problem starts with the classical mixed integer programming formulation and is then reformulated as a piecewise form. We develop two types of reformulated models for the issue and present a piecewise method by updating preset control parameters. In addition to the integration of the vehicle fleet sizing and the vehicle assignment problem, two other factors, such as the working service network and working vehicle, increase significantly the complexity of the research in this paper. First, we must recognize one crucial characteristic of working service network: at any location of working service network in space and time, the demands include two types, that is, minimum demands and maximum demands. The minimum demands must be met, but maximum demands are not. If insufficient vehicles are available to meet maximum demand, the penalty cost for unmet demand will generate. This characteristic is the cornerstones of the model developed in this paper. Second, vehicles usually provide pickup or delivery services between various locations in previous studies. However, in reality, vehicles themselves can sometimes act like a facility to provide real-time services when they are stationary at one location. The vehicles cannot provide services when they are in motion, and the service begins when a vehicle arrives at a location and ends when it departs. For instance, medical treatment vehicles provide first aid services to areas where the established medical facility is temporarily insufficient. Also, food trucks provide fast food services in different regions in different time periods of the day. Note that when these vehicles are in service, they behave like traditional facilities. The term working vehicle (WV) will be used in this paper to denote this vehicle. Applications of problems arise in many settings, ranging from managing emergency vehicles, medical testing vehicles, traveling salesman, and military force deployment. 
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