The maximum capacity shortest path problem: generation of efficient solution sets

Individual items of flow in a telecommunications or a transportation network may need to be separated by a minimum distance or time, called a ‘headway’. If link dependent, such restrictions in general have the effect that the minimum time path for a ‘convoy’ of items to travel from a given origin to a given destination will depend on the size of the convoy. The Quickest Path problem seeks a path to minimise this convoy travel time. A closely related bicriterion problem is the Maximum Capacity Shortest Path problem. For this latter problem, an effective implementation is devised for an algorithm to determine desired sets of efficient solutions which in turn facilitates the search for a ‘best’ compromise solution. Numerical experience with the algorithm is reported.