The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. However, the K shortest hyperpaths problem has not yet been investigated. In this paper we present procedures for finding the K shortest hyperpaths in a directed hypergraph. This is done by extending existing algorithms for K shortest loopless paths. Computational experiments on the proposed procedures are performed, and applications in transportation, planning and combinatorial optimization are discussed.

We consider routing problems in dynamic networks where arc travel times are both random and time dependent. The problem of finding the best route to a fixed destination is formulated in terms of shortest hyperpaths on a suitable time-expanded directed hypergraph. The latter problem can be solved in linear time, with respect to the size of the hypergraph, for several definitions of hyperpath length. Different criteria for ranking routes can be modeled by suitable definitions of hyperpath length. We also show that the problem becomes intractable if a constraint on the route structure is imposed.

The risk associated with railroad transportation of hazardous materials is an ongoing subject of interest to the transportation industries, the government, and the public. A variety of approaches have been considered or adopted to manage and reduce risk. These include improving operating practices and personnel training, improving transportation packaging, maintaining and upgrading infrastructure, and rerouting hazardous materials traffic. Certain risk reduction options have received particular attention in recent years. Realizing the interest and the need for research in this area, this study focuses on consideration of routing, track infrastructure improvement and speed management as approaches to reducing the risk from railroad hazardous materials transportation. For each approach, potential benefits in terms of risk reduction are analyzed using operations research (OR) and quantitative risk assessment (QRA) methods. The goal is to facilitate the consideration of each approach and evaluate its potential application for a particular objective of interest. Furthermore, this study considers improvement of several parameters in the risk model to enhance the quality of risk estimates and to better understand their sensitivity to various assumptions. When resources are limited so that a complete analysis of the entire routes