A Game Theoretical Pricing Scheme to Allocate the Cost of Empty Railcars to Participating Rail Companies

铁路工业在世纪的工业化进程中发挥了重要作用。该行业的特点是固定成本高，但可变成本相对较低。今天，随着国家高速公路拥堵程度的增加以及自动化和计算机化的迅速发展，铁路业在美国经济服务部门的潜力再次增长。 虽然对铁路车辆管理的研究，如最小化总空车里程，是非常广泛的，从空英里的成本分配到一个加载的行程，这是一个重要的定价问题，在货物运输，没有得到足够的重视。 现有的成本分配方案分配空英里装载行程似乎没有明确考虑到合作中产生的收益和损失，因此，不能确保在所有情况下的公平性。近年来，随着信息技术的迅速发展，各个层次的合作已经成为许多服务行业成功的关键因素。本研究的目的是发展一个大规模的网络与许多参与者的空车运动的成本分配方案。 具体而言，拟制定的费用分摊办法将反映参与合作的程度、合作前后产生的费用以及每个参与方因合作而获得的收益。本研究所采用的具体研究方法是基于博弈论。 我们还将把车辆交通的网络流理论纳入研究中，以描述参与者子集参与的各种级别的合作所产生的成本。将在不同的运营环境、策略和目标下研究所提出的定价方案的优点和缺点。 虽然所提出的研究是在铁路行业的背景下进行的，本研究中开发的成本分配方案可以应用于其他服务部门，如商业车队管理，供应链和公共交通系统与不同模式之间的定时转移，一些修改。

The railroad industry played an important role in industrialization in the nineteenth century. The industry is characterized by high fixed costs but relatively low variable costs. Today, with the increased level of congestion on national highways and the rapid development in automation and computerization, the potential of the railroad industry is growing again in the service sector of the United States economy. While research on railcar management, such as minimization of the total empty car miles, is very extensive, allocation of the cost incurred from empty miles to a loaded trip, which is an important pricing problem in freight transportation, has not received adequate attention. The existing cost distribution schemes to allocate empty miles to loaded trips do not seem to explicitly take into account the gain and loss incurred in cooperation and, as a result, do not ensure the fairness in all situations. With the rapid development in information technologies in recent years, cooperation at various levels has already become a key factor to success for many service sectors. The objective of this research is to develop a cost-allocation scheme of empty car movements for a large-scale network with many participants. In specific, the cost-allocation scheme to be developed will reflect the level of participation in cooperation, the costs generated before and after cooperation, and the benefits obtained by each participant due to cooperation. The specific research approach adopted in this study is based on game theory. We will also incorporate the network flow theory of vehicular traffic into the study to characterize the costs incurred at various level of cooperation participated by a subset of participants. The advantage and disadvantage of the proposed pricing scheme will be studied under different operation settings, strategies and objectives. Though the proposed research is conducted in the context of the railroad industry, the cost-allocation scheme developed in this study can be applied, with some modifications, to other service sectors such as commercial fleet management, supply chains, and public transportation systems with timed-transfer between different modes.