This paper, inspired by a real production process of steel hardening,
investigates a scheduling problem to minimize the idle energy consumption of
machines. The energy minimization is achieved by switching a machine to some
power-saving mode when it is idle. For the steel hardening process, the mode of
the machine (i.e., furnace) can be associated with its inner temperature.
Contrary to the recent methods, which consider only a small number of machine
modes, the temperature in the furnace can be changed continuously, and so an
infinite number of the power-saving modes must be considered to achieve the
highest possible savings. To model the machine modes efficiently, we use the
concept of the energy function, which was originally introduced in the domain
of embedded systems but has yet to take roots in the domain of production
research. The energy function is illustrated with several application examples
from the literature. Afterward, it is integrated into a mathematical model of a
scheduling problem with parallel identical machines and jobs characterized by
release times, deadlines, and processing times. Numerical experiments show that
the proposed model outperforms a reference model adapted from the literature.Comment: Accepted to 9th International Conference on Operations Research and
Enterprise Systems (ICORES 2020