Inverse constrained bottleneck problems on networks

In this paper, we consider a class of Inverse Constrained Bottleneck Problems (ICBP). Given two weight vectors w(1) and w(2), the constrained bottleneck problem is to find a solution that minimizes w(1)-bottleneck weight subject to a budget constraint on w(2)-sum weight. Whereas, in the inverse problem (ICBP), a candidate solution is given, we wish to modify the two weight vectors under bound restrictions so that the given solution becomes an optimal one to the constrained bottleneck problem and the deviation of the weights under some norm is minimum. When the modifications of two weight vectors are proportioned, we present a general method to solve the problem (ICBP) under weighted h norm and give two examples of the method including the inverse constrained bottleneck spanning tree problem and the inverse constrained bottleneck assignment problem.