Single-machine ready times scheduling with group technology and proportional linear deterioration

Scheduling research has increasingly taken the concept of deterioration into consideration. In this paper, we study a single machine group scheduling problem with deterioration effect, where the jobs are already put into groups, before any optimization. We assume that the actual processing times of jobs are increasing functions of their starting times, i.e., the job processing times are described by a function which is proportional to a linear function of time. The setup times of groups are assumed to be fixed and known. For some special cases of minimizing the makespan with ready times of the jobs, we show that the problem can be solved in polynomial time for the proposed model. For the general case, a heuristic algorithm is proposed, and the computational experiments show that the performance of the heuristic is fairly accurately in obtaining near-optimal solutions. The results imply that the average percentage error of the proposed heuristic algorithm from optimal solutions is less than 3%.