A new heuristic approach to solve product mix problems in a multi-bottleneck system

Product mix problem (PMP) is one of the most important and complicated problems in production systems. Different approaches have been applied to solve this problem, among them, theory of constraints (TOC) has been widely considered since 1990s. This paper develops a distinguished algorithm to solve product mix problems that is efficient both in single and multi-bottleneck problems. At first, the new algorithm uses a mathematical model to aggregate different priorities assigned to products by different bottlenecks and finds an initial solution. Then tries to improve the solution by solving a set of linear inequalities. It is shown that the new approach obtains better solutions than the previous algorithms.