A Generalized Minimum Cost Flow Model for Multiple Emergency Flow Routing

Abstract

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.

Optimization of a Traffic Control Scheme for a Post-Disaster Urban Road Network

“…Faturechi and Miller-Hooks [7] elaborated upon the performance of transportation infrastructure during a disaster, including the risk, vulnerability, reliability and flexibility. Cui et al [8] studied the conflict of two traffic flows caused by simultaneous rescues and evacuations in an emergency, and they introduced the concept of conflict cost and redistributed two types of traffic flows. These studies mainly focused on the change characteristics of traffic flows in emergencies, and they built the foundation of subsequent traffic-control-scheme optimizations.…”

A Bilevel Multiobjective Optimisation Approach for Solving the Evacuation Location Assignment Problem

“…In terms of mass transport to shelters, some of the common models proposed include linear programs [16], mixed-integer programs [17,18], cell transmission models [19,20], location routing [17], classical vehicle routing [21], and dynamic network flows [22]. Objectives that are optimised in these models include total travel time [18,19], total evacuation time [21], total travel distance [23], waiting time of evacuees [24], and cost of travel flow [25,26].…”

Disaster relief routing in limited capacity road networks with heterogeneous flows

“…Lim et al [26] propose the capacitated maximum flow model and Campos et al [12] minimize intersection delays and traffic congestion. Among traffic flow management articles, Cui et al [16] are the only authors so far to consider evacuation flows and the counterflows of rescuers over a capacitated road network, but they do not consider relief distribution or routing.…”