An energy-efficient single machine scheduling with release dates and sequence-dependent setup times

This study considers single machine scheduling with the machine operating at varying speed levels for different jobs with release dates and sequence-dependent setup times, in order to examine the trade-off between makespan and total energy consumption. A bi-objective mixed integer linear programming model is developed employing this speed scaling scheme. The augmented ε-constraint method with a time limit is used to obtain a set of non-dominated solutions for each instance of the problem. An energy-efficient multi-objective variable block insertion heuristic is also proposed. The computational results on a benchmark suite consisting of 260 instances with 25 jobs from the literature reveal that the proposed algorithm is very competitive in terms of providing tight Pareto front approximations for the problem.