Research on Group Scheduling with General Logarithmic Deterioration Subject to Maximal Completion Time Cost

Single-machine group scheduling with general logarithmic deterioration is investigated, where the actual job processing (resp. group setup) time is a non-decreasing function of the sum of the logarithmic job processing (resp. group setup) times of the jobs (resp. groups) already processed. Under some optimal properties, it is shown that the maximal completion time (i.e., makespan) cost is solved in polynomial time and the optimal algorithm is presented. In addition, an extension of the general weighted deterioration model is given.