Optimal Recovery Plan after Disaster: Continuum Modeling Approach

Abstract

This paper presents an application of continuum traffic equilibrium model for the design of optimal recovery plan after a disaster. The continuum traffic equilibrium model is adopted for its strength in defining: (1) alternative routes after disaster; (2) spatially varied impacts of the disaster; and (3) continuously distributed demand. In this study, demands for emergency services, reconstruction activities, and normal-travel activities are separately modeled throughout the recovery period. A bilevel model is set up for designing the optimal recovery plan in the modeled region. At the lower-level model, sets of differential equations are constructed to describe the traffic equilibrium problems at different times of the recovery period. In the upper-level model, a constrained minimization problem is set up to find the optimal recovery plan such that the total travel cost is minimized and the demand of normal/reconstruction traffic is maximized throughout the recovery period. A sensitivity-based solution algorithm that adopts the finite element method (FEM) is proposed to solve the bilevel model, and a numerical example is completed to demonstrate the characteristics of the proposed model.