Scheduling Tasks towards Energy Autarky: Benefits and Computational Costs of Flexibility

2026-07-03

AI Summary

This study investigates the feasibility of achieving fully energy-autonomous task scheduling given energy forecasts, battery capacity constraints, and energy-consuming tasks with time windows. Focusing on task flexibility—defined as the number of time steps within which a task may be scheduled—the work combines computational complexity analysis, fixed-parameter algorithm design, and integer linear programming modeling. It establishes that the problem becomes NP-hard even when flexibility is as low as two, yet remains polynomial-time solvable under certain structural conditions despite high flexibility. Furthermore, the problem is shown to be fixed-parameter tractable with respect to parameters such as the number of tasks. Experimental results demonstrate that moderately increasing task flexibility substantially reduces reliance on external energy sources while maintaining manageable computational overhead.

Abstract

We study the autarky problem: given an energy forecast, a battery, and a set of energy-consuming jobs with time windows, decide whether all jobs can be scheduled without requiring external energy. We analyze the problem through the lens of job flexibility, defined as the number of time steps at which a job may be scheduled. We show that the problem is NP-hard already for flexibility two, even in restricted settings. On the positive side, we identify settings in which the problem is polynomial-time solvable, even for large flexibilities. Moreover, we obtain fixed-parameter tractability for combined parameters involving flexibility, such as the number of jobs. In contrast, we establish W-hardness when parameterized by maximum flexibility alone, even in a restricted setting. To complement our theoretical results, we formulate an integer linear program (ILP) that computes the minimum required external energy and evaluate it experimentally on instances derived from real-world energy-consumption and radiation data. The experiments indicate that increased job flexibility substantially reduces the need for external energy at moderate computational cost.

Problem

• energy autarky
• task scheduling
• job flexibility
• NP-hardness
• external energy

Innovation

• energy autarky
• job flexibility
• NP-hardness
• fixed-parameter tractability
• integer linear programming