Two hybrid tabu search-firefly algorithms for the capacitated job shop scheduling problem with sequence-dependent setup cost

This article considers a particular case of the capacitated job shop scheduling problem (CJSP) regarding sequence-dependent setup cost. At first, to formulate this problem a new mixed-integer programming (MIP) model is presented that minimises the sum of tardiness cost, overtime cost and setup cost. Then, due to the complexity of this problem, two novel hybrid approaches are developed to solve medium and large size problems. These proposed approaches are made based on two different combinations of tabu search and firefly algorithms: (i) integrated and (ii) hierarchical combination. Also, to improve the quality of solutions, in each step of the hybrid algorithms, an effective heuristic is proposed. This heuristic reduces the overtime costs of operations by efficient use of the operation's slack. Moreover, to obtain better and more robust solutions, the Taguchi method is used to calibrate the parameters of the hybrid algorithms. Finally, the computational results are provided for evaluating the performance and effectiveness of the proposed solution approaches.