弹性需求下网络设计问题和电子路票问题研究

The combined model and relaxation algorithm for continuous network design problem with the second-best credits charging under elastic demand

应用双(二)层规划模型研究弹性需求下网络设计问题与电子路票收取问题,其中只考虑在部分路段进行路段能力扩充和收取电子路票.上层决策者(网络规划者)选择路段能力增加和收取电子路票的数量来获得最优的社会总福利.下层决策者(网络用户)选择路径来最小化他们的出行成本(路径出行时间与所付出电子路票的价值的和).应用下层规划问题的Karush-Kuhn-Tucker(KKT)条件,将双层规划模型转化为单层规划模型.为了解决互补条件所造成的求解困难,本文构造了松弛算法进行求解,并用数值试验研究了模型和算法的可行性.数值结果表明,本文的模型在缓解交通拥挤方面可以得到更好的效果,而且只在部分路段进行路段能力扩充和收取电子路票更加方便实用.在可交易电子路票方案中,更多出行的用户需要购买电子路票来为他们的额外出行付费,而减少出行的用户则可以卖出多余电子路票得到补偿,同时电子路票的交易价格是在完全竞争的市场上形成的,因此本文中的可交易电子路票机制是收入中性的.

In this paper,the bi-levl programming model is proposed to study the continuous network design problem with the second-best credits charging under elastic demand. The upper level decision maker maximizes the total social benefits by choosing the link enhancement and link credit charging. The lower level decision makers（ the users） choose their optimal paths to minimize their generalized travel costs including the travel time and the value of credit for using the credit-charging link. By replacing the lower level programming problem with its Karush-Kuhn-Tucker（ KKT） conditions,the bi-level programming model can be transformed into a single level problem. To deal with the difficult slackness conditions in the above single level problem,we propose a relaxation algorithm to solve it. Numerical experiments demonstrate the feasibility of the proposed model and algorithm. The numerical results show that this proposed model can obtain better effects to alleviate the congestion. It will be convenient and feasible to implement if we improve the link enhancement and charge the credit only in the subset of the network. In this proposed model,the users who travel more should buy the credits from the market and pay money for those additional travel need. While the users who reduce their travel can sell their extra credits to compensate their inconvenience for reducing travel. Thus,this tradable credit scheme is revenue neutral.