Energy consumption minimization for single machine scheduling with bounded maximum tardiness

This paper investigates a single machine scheduling problem to minimize energy consumption with bounded maximum tardiness. A set of jobs are to be processed on a single machine which is speed-scalable. Each job is characterized by its release time, deadline and processing time. The machine can process only one job with some speed at a time. No preemption is allowed. Since energy consumption is associated with the processing speed, both job sequencing and speed choosing decisions have to be made. Two MILP (mixed integer linear programming) models, which respectively use dichotomous constraints and assignment constraints to model the processing sequence of jobs, are built for this problem. The models are implemented in C++ and solved by CPLEX. Computational results with randomly generated instances demonstrate that the model using assignment constraints is much more efficient than that with dichotomous constraints.