During real-life disasters, that is, earthquakes, floods, terrorist attacks, and other unexpected events, emergency evacuation and rescue are two primary operations that can save the lives and property of the affected population. It is unavoidable that evacuation flow and rescue flow will conflict with each other on the same spatial road network and within the same time window. Therefore, we propose a novel generalized minimum cost flow model to optimize the distribution pattern of these two types of flow on the same network by introducing the conflict cost. The travel time on each link is assumed to be subject to a bureau of public road (BPR) function rather than a fixed cost. Additionally, we integrate contraflow operations into this model to redesign the network shared by those two types of flow. A nonconvex mixed-integer nonlinear programming model with bilinear, fractional, and power components is constructed, and GAMS/BARON is used to solve this programming model. A case study is conducted in the downtown area of Harbin city in China to verify the efficiency of proposed model, and several helpful findings and managerial insights are also presented.
2Mathematical Problems in Engineering as lane reversal operations) during emergency response to fully explore the capacity of the current network. Contraflow design commonly refers to the shift of the normal driving directions of a subset or all danger-bound lanes for use by safety-bound evacuation traffic. Such control is based on the observation that danger-bound traffic is usually light, whereas evacuation traffic always oversaturates the safetybound capacity. In nature, contraflow design constitutes a network redesign problem. If evacuation flow and rescue flow exist together in the same network, we can reshape the network to better serve these two flows.Based on the previous discussion, this paper aims to present a generalized minimum cost flow model for collaboration between evacuation flow and rescue flow that also accounts for optimal contraflow design in a complex road network.The paper is organized as follows. We first review related prior work, and the subsequent section presents the model formulation. The Baron solver is used to solve the nonconvex mixed-integer nonlinear programming model, and a local network in downtown Harbin City, Heilongjiang, China, is adopted to implement the case study. The paper concludes with a discussion of the results and areas for further research.