A heuristic algorithm for an integrated routing and scheduling problem with stops en-route

Abstract

In this study, we examine an integrated routing and scheduling problem that arises in the context of transportation of hazardous materials. The purpose of the problem is to find a minimum risk route between an origin and a destination point on a given network and to build a schedule on this route that determines where and how long to stop for a truck carrying hazardous materials. The objective is to minimize the risk imposed to the society while completing the path within a given time limit. The risk is defined as the expected population exposure in the presence of an accident which varies different times in a day. There are exact algorithms available in the literature that solve the problem. However, these algorithms are not capable of solving large sized networks due to memory constraints. Our aim is to develop a heuristic procedure that can handle larger networks. We separate the problem into two independent components, routing and scheduling, and propose solution algorithms which would communicate each other when running the algorithm. For the routing component we define a neighborhood structure that can be used to generate several paths around a given path on a network. The search procedure takes an initial path and improves it by generating different paths in the defined neighborhood. For the scheduling component, we discuss mixed integer programming, dynamic programming and heuristic approaches. We run the proposed heuristic algorithm on several test networks and compare its performance with the optimal solutions. We also present the application of the heuristic procedure on a large sized Turkey Road Network.