The TOC-based algorithm for solving product mix problems

The five steps of the theory of constraints (TOC) emphasize exploiting constraints in order to increase the throughput of a system. The product mix decision is one application of the TOC five steps. However, these steps were considered to be implicit or incomplete, the criticism being that they result in deriving an infeasible solution when a plant has multiple resource constraints. This paper follows the essence of these five steps and presents an explicit algorithm to address the problem. When testing its effectiveness by using a dual-simplex method with bounded variables, this algorithm gives the same result in each iteration.