A Max-Min Allocation Problem: Its Solutions and Applications

Abstract

This paper describes a max-min allocation problem that has M constraints and N nonnegative integer variables. By exploring the structure of the optimal solution to this max-min allocation problem, we develop a nonsimplex-based algorithm that finds an optimal solution within O(MN 2 ) operations. In addition, we show that a space allocation problem for a flexible component insertion machine can be formulated as a special case of this max-min allocation problem with one constraint. Furthermore, we present some manufacturing and production problems that can he formulated as max-min allocation problems, and hence, can be solved efficiently.