Note--A Comment on the Use of Simplex Method for Absolute Value Problems

The linear programming approach to the absolute value problem is to transform the unrestricted variable by the difference of two nonnegative variables. This transformation creates an unbounded feasible region which may lead to erroneous solution. To avoid this, Kaplan [Kaplan, Seymour. 1971. Comment on a précis by Shanno and Weil. Management Sci. 17 (11, July) 778-780.] introduced a new constraint to bound the feasible region and suggested a solution scheme using the simplex method. We shall give two counter examples to the proposed scheme and discuss the difficulties involved with this particular class of problem.