Outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem

This article presents a finite, outcome-based algorithm for optimizing a lower semicontinuous function over the efficient set of a bicriteria linear programming problem. The algorithm searches the efficient faces of the outcome set of the bicriteria linear programming problem. It exploits the fact that the dimension of the outcome set of the bicriteria problem is at most two. As a result, in comparison to decision-based approaches, the number of efficient faces that need to be found is markedly reduced. Furthermore, the dimensions of the efficient faces found are always at most one. The algorithm can be implemented for a wide variety of lower semicontinuous objective functions.