A systematic extreme point enumeration procedure for fixed charge problem

Abstract

In this paper the fixed charge problem viz: Min\(\sum\limits_{j = 1}^n {(c_j x_j + F_j \delta _j )} \) subject toAX=b, X>-0 $$\delta _j = \left\{ \begin{gathered} 0 if x_j = 0 \hfill \\ 1 if x_j > 0 \hfill \\ \end{gathered} \right.$$ is solved by systematically enumerating extreme points of a linear programming problem viz: $$Min \sum\limits_{j = 1}^n {(c_j x_j + F_j \delta _j )} $$ subject toAX= b, xj−dj °j≤0, X≥0 °≥0 where ° is an extreme point ofIn °≤1. The technique provides an exact solution of the problem. The theory is supported by a numerical example.