Inverse constrained bottleneck problems under weighted l∞ norm

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 bound constraint on w(2)-sum weight. In its inverse problem (ICBP), however, a candidate solution is given, and 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 weighted l infinity norm is minimum. When the modifications of the two weight vectors are proportional, we present a general method to solve the problem (ICBP) and give several examples to implement the method including the inverse constrained bottleneck spanning tree problem and the inverse constrained bottleneck assignment problem. (C) 2006 Elsevier Ltd. All rights reserved.