The Application of Lagrange Relaxation on Taxi Dispatchments During Evening Rush Hours

Abstract

The city transportation status is directly related to the taxi supply arrangements during evening rush hours. The operation times, operation nature, operation requirements, vehicle resource types and quantities will have big influence on taxi drivers’ dispatchments, it is comparatively difficult to dispatch reasonably. This paper uses Lagrange Relaxation to solve the problem of taxi supply and demand during evening rush hours. NP-Hardness is the difficult point of dispatchments, thus Lagrange method is used to result an optimal solution on taxi dispatchments within reasonable calculating time, while the bottom limits of the approximate optimal solution and the approximate solution are resulted as well. This method can effectively solve the problem of the balance of taxi supply and demand during evening rush hours. Based on this, the dual problem is solved by using incremental subgradient method, while an improved strategy is proposed to rise the convergence rate.