A polynomial-time scheduling approach to minimise idle energy consumption: an application to an industrial furnace

TL;DR

This paper introduces a polynomial-time scheduling method that minimizes idle energy consumption by incorporating full machine dynamics, demonstrated on a heat-intensive furnace, leading to significant energy savings.

Contribution

It proposes a novel scheduling approach that integrates complete machine dynamics into energy minimization, applicable to systems with concave idle energy functions, validated on industrial furnace data.

Findings

The scheduling problem can be solved in polynomial time for concave idle energy functions.

The approach achieves higher energy savings compared to existing methods.

The idle energy function for the furnace model is proven to be concave.

Abstract

This article presents a novel scheduling approach to minimise the energy consumption of a machine during its idle periods. In the scheduling domain, it is common to model the behaviour of the machine by defining a small set of machine modes, e.g. "on", "off" and "stand-by". Then the transitions between the modes are represented by a static transition graph. In this paper, we argue that this type of model might be too restrictive for some types of machines (e.g. the furnaces). For such machines, we propose to employ the complete time-domain dynamics and integrate it into an idle energy function. This way, the scheduling algorithm can exploit the full knowledge about the machine dynamics with minimised energy consumption encapsulated in this function. In this paper, we study a scheduling problem, where the tasks characterised by release times and deadlines are scheduled in the given order such that the idle energy consumption of the machine is minimised. We show that this problem can be solved in polynomial time whenever the idle energy function is concave. To highlight the practical applicability, we analyse a heat-intensive system employing a steel-hardening furnace. We derive an energy optimal control law, and the corresponding idle energy function, for the bilinear system model approximating the dynamics of the furnace (and possibly other heat-intensive systems). Further, we prove that the idle energy function is, indeed, concave in this case. Therefore, the proposed scheduling algorithm can be used. Numerical experiments show that by using our approach, combining both the optimal control and optimal scheduling, higher energy savings can be achieved, compared to the state-of-the-art scheduling approaches.