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

TL;DR

This paper introduces a pre-processing technique called SPACES that optimizes machine state switching in energy-aware scheduling, significantly improving solution efficiency for large instances with variable energy costs and power-saving states.

Contribution

The paper presents SPACES, a novel pre-processing method that enhances integer and constraint programming models for energy-aware scheduling with variable pricing and machine states.

Findings

Outperforms existing methods on benchmark instances.

Finds optimal solutions for larger instances within an hour.

Efficiently models machine state transitions using shortest paths.

Abstract

This paper addresses a single machine scheduling problem with non-preemptive jobs to minimize the total electricity cost. Two latest trends in the area of the energy-aware scheduling are considered, namely the variable energy pricing and the power-saving states of a machine. Scheduling of the jobs and the machine states are considered jointly to achieve the highest possible savings. Although this problem has been previously addressed in the literature, the reported results of the state-of-the-art method show that the optimal solutions can be found only for instances with up to 35 jobs and 209 intervals within 3 hours of computation. We propose an elegant pre-processing technique called SPACES for computing the optimal switching of the machine states with respect to the energy costs. The optimal switchings are associated with the shortest paths in an interval-state graph that describes all possible transitions between the machine states in time. This idea allows us to implement efficient integer linear programming and constraint programming models of the problem while preserving the optimality. The efficiency of the models lies in the simplification of the optimal switching representation. The results of the experiments show that our approach outperforms the existing state-of-the-art exact method. On a set of benchmark instances with varying sizes and different state transition graphs, the proposed approach finds the optimal solutions even for the large instances with up to 190 jobs and 1277 intervals within an hour of computation.