Mathematical models and an elephant herding optimization for multiprocessor-task flexible flow shop scheduling problems in the Manufacturing Resource Planning (MRPII) system

Shop floor control (SFC) is one of the main concepts in manufacturing resource planning (MRPII) and production scheduling is a key element in SFC. This paper studies the hybrid flow shop scheduling problem where jobs are multiprocessor. The objective is to minimize total completion time. Although there are several papers considering hybrid flow-shop scheduling problem with multiprocessor tasks, but none propose a mathematical model for this problem. At first, the two problems (fixed and selective cases) are mathematically formulated by mixed integer linear programming models. Using commercial software, the model is used to solve the small instances of the problems. Moreover, an elephant herding optimization is developed to solve large instances of the problems. To numerically evaluate the proposed algorithm, it is compared with two available algorithms in the literature, simulated annealing and shuffled frog-leaping algorithm in the literature.