A Mathematical Model and a Firefly Algorithm for an Extended Flexible Job Shop Problem with Availability Constraints

Manufacturing scheduling strategies have historically ignored the availability of the machines. The more realistic the schedule, more accurate the calculations and predictions. Availability of machines will play a crucial role in the Industry 4.0 smart factories. In this paper, a mixed integer linear programming model (MILP) and a discrete firefly algorithm (DFA) are proposed for an extended multi-objective FJSP with availability constraints (FJSP-FCR). Several standard instances of FJSP have been used to evaluate the performance of the model and the algorithm. New FJSP-FCR instances are provided. Comparisons among the proposed methods and other state-of-the-art reported algorithms are also presented. Alongside the proposed MILP model, a Genetic Algorithm is implemented for the experiments with the DFA. Extensive investigations are conducted to test the performance of the proposed model and the DFA. The comparisons between DFA and other recently published algorithms shows that it is a feasible approach for the stated problem.