The Compact Simplex Method

The vast majority of Operational Research OR textbooks describe the simplex method of solving small LP problems. In many elementary quantitative methods courses, thousands of students at least pretend to understand the rationale for the mechanics of the simplex tableau. Some students are exposed to the ‘Big M’ method of dealing with artificial variables, but the authors suspect that this exposure is demotivating rather than enlightening. In this note they describe the Compact Simplex Method and provide an APL2 implementation thereof which neatly handles problems with less than, greater than and equality constraints by executing-in a very compact manner-the essential steps of the conventional dual and primal simplex algorithms. The authors have extended the algorithms, using Bland’s Rules, to eliminate the possibility of cycling.