A TABULAR SIMPLEX-TYPE ALGORITHM AS A TEACHING AID FOR GENERAL LP MODELS (original) (raw)

1989, Mathematical and Computer Modelling

The simplex algorithm requires additional variables (artificial variables) for solving linear programs which lack feasibility at the origin point. However, some students, particularly non-mathematics majors, have difficulty understanding the intuitive notion of artificial variables. A new general purpose solution algorithm obviates the use of artificial variables. The algorithm consists of two phases. Phase I searches for a feasible segment of the boundary hyper--plane (a face of feasible region or an intersection of several faces) by using rules similar to the ordinary simplex. Each successive iteration augments the BVS, by including another hyper-plane, until the BVS is full, which specifies a feasible vertex. In this phase movements are on faces of the feasible region rather than from a vertex to a vertex. This phase terminates successfully (or indicates infeasibility of the problem) with a finite number of iterations, which is the number of constraints. The second phase uses exactly the ordinary simplex rules, (if needed) to achieve optimality. This unification with the simplex method, is achieved by augmenting the feasible BVS which is always initially empty in phase 1. The algorithm working space is the space of the original (decision, slack, and surplus) variables with a geometric interpretation of its strategic process.