Lower and upper bounds on the probability that hazardous materials can be transported without incident from one point to another

Horváth, Alice (2008) Lower and upper bounds on the probability that hazardous materials can be transported without incident from one point to another. Pollack Periodica, 3 (3). pp. 113-120. ISSN 1788-1994

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Abstract

With the accelerating growth of traffic, the catastrophe avoidance models for hazardous material transport have become an important and exciting research field for engineers and scientists. In this paper propose the application of Boole-Bonferroni bounding technique introduced by Prékopa [1], in the framework of hazardous material transportation is proposed. In regard with road networks with one origin and destination node to transport hazardous material from origin to destination point paths from the origin to destination node without any cycle should be considered. If the incidents along the edges occur independently with probability p _ij on the edge connecting nodes i and j , then the probability of transporting hazardous material from origin to destination node without incident equals the product of (1 − p _ij ) probabilities along the edges of the actual path. The problem is that the number of paths from origin to destination is usually enormous, so it is not easy to choose one of them with high reliability. This is presented by the Boole-Bonferroni bounding technique whereas lower bound can be calculated on the probability that there exists at least one path from origin to destination node. Knowing this bound may help the decision maker in choosing a path with high reliability and low transportation cost.

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