Group scheduling problems with simultaneous considerations of learning and deterioration effects on a single-machine

Group technology is important to manufacturing as it helps increase the efficiency of production and decrease the requirement of facilities. In this paper we investigate group scheduling problems with simultaneous considerations of learning and deterioration effects on a single-machine setting. The learning phenomenon is implemented to model the setup time of groups. Three models of deteriorating for the job processing time within a group are examined. We show that all the problems studied are polynomially solvable with or without the presence of certain conditions where the objective is to find an optimal schedule for minimizing the makespan. We also investigate the minimization of the total completion time. We proved that one of the deterioration models examined in this study can also be solved in a polynomial time algorithm under certain conditions.