A Note on Nadir Values in Bicriteria Programming Problems

In multiple criteria programming, a decision maker has to choose a point from the set of efficient solutions. This is usually done by some interactive procedure, where he or she moves from one efficient point to the next until an acceptable solution has been reached. It is therefore important to provide some information about the "size" of the efficient set, i.e. to know the minimum (and maximum) criterion values over the efficient set. This is a difficult problem in general. In this paper, we show that for the bicriteria problem, the problem is easy. This does not only hold for the linear bicriteria problem, but also for more general problems. (author's abstract)