Multiple objective linear programming over the probability simplex

TL;DR

This paper addresses the problem of optimizing multiple linear functions over the probability simplex, providing a classification of feasible points, a characterization of efficiency, and a computational method that does not rely on extreme points.

Contribution

It introduces a new characterization and computational procedure for efficiency in multiple objective linear programming over the probability simplex.

Findings

Provides a necessary and sufficient condition for efficiency.

Develops a computational procedure that does not require extreme points.

Includes an illustrative example of the procedure.

Abstract

This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient solution is stated. This characterization yields a computational procedure for ascertaining whether a feasible point is efficient. The procedure does not require that candidates for efficiency be extreme points. An illustration of the procedure is offered.