A model and imperialist competitive algorithm for hybrid flow shops with sublots and setup times

•This paper extends flowshop scheduling with parallel machines, divisible jobs and setup times.•A mixed integer linear programming model is presented.•An imperialist competitive algorithm is proposed.•The algorithm is compared with optimal solution of the model and two available algorithms.

This paper considers the problem of hybrid flow shops with sublots and sequence dependent setup times to minimize the total tardiness. A mixed integer linear programming model is presented for the problem. The paper also proposes an imperialist competitive algorithm. This algorithm utilizes three effective features of imperialist behavior, imperialist competition and colony improving mechanisms. To evaluate the algorithm, it is compared with optimal solution of the model and adaptations of two available algorithms. The results show that the effectiveness of the proposed model and algorithm.