Routing and location on a network with hazardous threats
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Routing and location on a network with hazardous threats O Berman1, Z Drezner2* and GO Wesolowsky3 1
University of Toronto, Canada, 2California State University, USA and 3McMaster University, Canada
The aim of this paper is to minimise the impact of hazards located on or near a network. Two situations are considered: (1) where a hazard is located on a network and affects off network sites and (2) an off-network hazard which can affect traf®c on the network. Eight models aimed at optimising different objectives are developed and solved, including ®nding a route between two nodes on a network which minimises the hazard along it and ®nding a location on a network where the hazard is minimised. Keywords: routing hazardous materials; location; obnoxious facilities
Introduction Routing of hazardous materials has received a lot of attention recently, and extensive reviews have been reported by Boffey and Karkazis,1 and Erkut and Verter.2 The normal modelling of such issues involve the probability that a truck carrying hazardous materials will be involved in an accident and will release hazardous materials into the environment. In this paper we formulate and solve two mirror-image problems which lead to the exact same formulation. In one formulation a hazard may be generated at off-road point and the possible victims of the hazard are traveling on the network. The intensity of the hazard decreases inversely to the square of the Euclidean distance from the source. The second model assumes that a hazard may happen on a network, and its damages at a point off the road is inversely proportional to the squared Euclidean distance from the accident. In this formulation, the off-road points are the location of the possible victims of the hazard. These two models lead to the following formulation. Consider a network of roads in the plane with a set of offroad points, which we term hazardous points. Each of the hazardous points emanates a hazard which is de®ned by a weight. The hazard decreases inversely proportional to the square of the Euclidean distance from the point. The risk can be de®ned either as the `maximum risk' generated by any hazardous point (assuming that only one hazard may occur at any time), or as `total risk' which is the sum of all hazards generated at the hazardous points (assuming a continuous on-going hazard or nuisance). The network is to be utilised with an objective of risk avoidance. *Correspondence: Dr Z Drezner, Department of Management Science= Information Systems, California State University, Fullerton, CA 92834, USA. E-mail: [email protected]
For example, a hazardous material needs to be transported along a network with minimal risk to the population along the way. The objective is to minimise the impact of a freak accident on these population centers. Another example is pollution, such as noise pollution, which is generated at points off the network. We wish to ®nd a route which avo
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