Single-machine group scheduling with general linear deterioration and truncated learning effects

In this paper we consider single-machine scheduling problems with group technology, where the group setup times are general linear functions of their starting times and the jobs in the same group have general truncated learning effects. The objective is to minimize the makespan and total completion time, respectively. We show that the makespan minimization remains polynomially solvable. For the total completion time minimization, optimal properties are presented and then we introduce some heuristic algorithms and a branch-and-bound algorithm.