A Mathematical Programming with Equilibrium Constraints for Managing Traffic after a Major Earthquake: a Merit-function Based Approach

This paper proposes the methodology to evaluate the road network anti-hazardous ability by the concept of network capacity reliability. The methodology proposed here considers the area-traffic regulation, which may be implemented when a large disaster occurs in Japan. The model to calculate entry permission rates is formulated as MPEC (Mathematical Programming with Equilibrium Constraints) in which the travellers are assumed to rationally respond to the imposed permission rate according to the Wardrop’s equilibrium. Also in this paper, an efficient algorithm to find a solution of MPEC problem is proposed. The proposed method transforms the original bi-level optimisation problem into a smooth single level optimisation problem by utilising the idea of merit function. The efficiencies of proposed network reliability index together with calculation methodology are discussed by the numerical experiment.