Optimal Obnoxious Paths on a Network: Transportation of Hazardous Materials

This paper considers the problem of determining optimal paths for routing an undesirable vehicle on a network embedded on an Euclidean plane. A typical application is the transporting of hazardous materials. Demand points, or population centers, are discretely distributed at nodes and continuously distributed on straight-line links of the network. The objective is to find, without incorporating the probability of accidental leakage of hazardous material, a path that minimizes the weighted sum of lengths over which this vehicle is within a threshold distance λ of population centers. By appropriately redefining link lengths, we can use a shortest-path algorithm to solve the problem. Special properties of the objective function allow us to efficiently calculate the modified link lengths. We discuss the properties of the optimal routing strategy and the objective value, and offer an economic interpretation of the case when λ varies. Operating within the framework of risk analysis, we integrate the probability of accidental release of hazardous material into our basic model. The routing objective becomes the minimization of expected damage, where accidental leakage of hazardous materials can inflict damage within a neighborhood λ of the accident site. We also discuss our computational experience in using the model.