A green model for identical parallel machines scheduling problem considering tardy jobs and job splitting property

In most organizations, especially order-oriented ones meeting deadlines are crucial. Job shop environments could be mentioned as an example where decision makers are try to schedule all jobs in such a way that tardy jobs (TJ) are minimized. Indeed, manufacturers are received customers’ orders and required to deliver them no later than the determined due dates. Otherwise, penalties should be paid to customers and it can lead to a huge amount of financial loss. Also, regarding global warming and climate changes manufacturers should redesign their processes from an eco-friendly perspective. Motivated by these issues, in this paper, a green bi-objective model has been formulated to solve the problem of scheduling parallel machines considering TJ and job splitting property (JSP). In the proposed model, the first objective function minimizes the total number of TJ while the second objective function is minimization of total energy consumption. An augmented ε-constraint method has been deployed for solving small-scale problems. However, to solve large-scale problems, an efficient Simulated Annealing (SA) algorithm has been developed while a Harmony Search (HS) algorithm has also been applied to examine the quality of the proposed SA algorithm. Random generated problems have been used to compare the results of three deployed algorithms. Results approved that the proposed SA algorithm outperforms others significantly. In particular, SA solved the problems sooner than others while its solutions were closer to solutions of the augmented ε-constraint method.