This paper considers a group scheduling problem with shorten (i.e.,  a proportional linear shortening)  job processing times and ready times on a single machine. If the jobs are in the same group, they have independent and constant ready times. The setup time of a group is  independent constant setup time between each group. The goal is to determine the optimal group sequence and the job sequence within the groups such that the makespan (i.e., the maximum completion time) is minimized. For the general case of the problem, an initial heuristic algorithm (an upper bound) and some lower bounds are proposed, and  then a branch-and-bound algorithm can be developed to solve the problem.

This paper studies a single-machine problem with resource allocation (RA) and deteriorating effect (DE). Under group technology (GT) and limited resource availability, our goal is to determine the schedules of groups and jobs within each group such that the total completion time is minimized. For three special cases, polynomial time algorithms are given. For a general case, a heuristic, a tabu search algorithm, and an exact (i.e., branch-and-bound) algorithm are proposed to solve this problem.