Single machine group scheduling problems with deterioration and resource constrained setup times

In this paper, we consider the single-machine group scheduling problems with deterioration and resource constrains. In this model, the jobs in the same group shouldn´t be separated, the setup time of a group is a positive strictly decreasing function of the amount of resources consumed, and the processing time of a job is a linear function of its starting time. The linear increasing deterioration model is considered. Two versions of objectives, minimizing the total resource consumption under the makespan constrains and minimize the makespan under the total resource consumption constrains, are discussed. Based on the characterizations of optimal schedules that established for both models, the optimal allocation methods are presented, respectively.