Theory of constraints product mix optimisation based on immune algorithm

Product mix optimisation is one of the most fundamental problems in manufacturing enterprise. As an important component in theory of constraints (TOC), product mix optimisation is solved by the TOC heuristic (TOCh) and some intelligent search algorithms, even though these approaches often cannot effectively obtain a good solution in the previous attempts, especially for the large-scale product mix optimisation. Aiming at this problem, a contribution has been made to the following aspects in the present paper. Firstly, a model of TOC product mix optimisation, which identifies and exploits the capacity constrained resource (CCR) to maximise system throughput is put forward and simplified by cutting down some constraints of non-CCRs. Secondly, an intelligent optimisation approach based on immune algorithm (IA) and TOC for product mix optimisation is presented to search optimal solution(s), whether it is a small-scale or large-scale instance. Thirdly, the immune mechanisms, such as the immune response mechanism, immune self-adaptive regulation and vaccination, are studied in detail, which not only greatly improves the searching ability and adaptability, but also evidently increases the global convergence rate of immune evolution. Fourthly, the proposed approach is implemented and applied in both small-scale and large-scale product mix optimisation. Finally, a comparison between the proposed approach and existing approaches is made. Simulation results show that the proposed approach is superior to the existing approaches, such as the TOCh, revised TOCh, integer linear programming (ILP), tabu search (TS), and genetic algorithms (GA).