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This paper addresses a single machine scheduling problem with non-preemptivejobs to minimize the total electricity cost. Two latest trends in the area ofthe energy-aware scheduling are considered, namely the variable energy pricingand the power-saving states of a machine. Scheduling of the jobs and themachine states are considered jointly to achieve the highest possible savings.Although this problem has been previously addressed in the literature, thereported results of the state-of-the-art method show that the optimal solutionscan be found only for instances with up to 35 jobs and 209 intervals within 3hours of computation. We propose an elegant pre-processing technique calledSPACES for computing the optimal switching of the machine states with respectto the energy costs. The optimal switchings are associated with the shortestpaths in an interval-state graph that describes all possible transitionsbetween the machine states in time. This idea allows us to implement efficientinteger linear programming and constraint programming models of the problemwhile preserving the optimality. The efficiency of the models lies in thesimplification of the optimal switching representation. The results of theexperiments show that our approach outperforms the existing state-of-the-artexact method. On a set of benchmark instances with varying sizes and differentstate transition graphs, the proposed approach finds the optimal solutions evenfor the large instances with up to 190 jobs and 1277 intervals within an hourof computation.

Power of Pre-Processing: Production Scheduling with Variable Energy Pricing and Power-Saving States