A logic-based Benders decomposition algorithm for a repair crew routing and drone scheduling problem after a natural disaster

Abstract

Natural disasters may lead to the isolation of rural areas due to the destruction of roads. Therefore, as a direct consequence of the impossibility of distribution of relief goods, more damages are expected in the aftermath of disasters in these areas. In this situation, we assume that damaged roads must be repaired immediately by a single repair crew and based on a specific route to prevent further damages and facilitate access to ground relief. There exists usually some stored medical equipment in isolated areas so that it can be consumed until destroyed roads become accessible again. In order to reflect this issue in this research, deadlines are considered for making isolated areas accessible. These deadlines are flexible and can be updated whenever a drone visits an isolated area and provide the area with limited amounts of air relief items. An integer linear programming is developed to formulate the repair crew routing problem and drone scheduling in an integrative manner. The developed model is complex and fails to provide the optimal solution even for instances including more than six demand areas and six damaged roads within one hour when the deadline is tight. Therefore, we developed a logic-based Benders decomposition algorithm that is able to find the optimal solution of instances including sixteen nodes in less than three quarters. Using a set of randomly generated instances, we compare the performance of the proposed solution approaches and provide a set of sensitivity analyses based on significant parameters of the problem.