Preemptive just-in-time scheduling problem on uniform parallel machines with time-dependent learning effect and release dates

This paper considers uniform parallel machines scheduling problem with time-dependent learning effects, release dates, allowable preemption and machine idle time to minimise the total weighted earliness and tardiness penalties which is known to be strongly NP-hard. To solve this problem, this research proposes a mixed integer nonlinear programming (MINLP) model. Afterward, in order to find the best solution in an effective solution space, a dominant set is proposed for the length of the schedule experimentally. Also, based on the allowable idle time, a new time-dependent learning model on parallel machines is proposed. Furthermore, a genetic algorithm (GA) and a hybrid of genetic algorithm and particle swarm optimisation (HGA-PSO) are proposed. Taguchi method is applied to calibrate the parameters of the proposed algorithms. Finally, the computational results are provided to compare the results of the algorithms. Then, the efficiency of the proposed algorithms is discussed.