Multi-Objective Human–Robot Collaborative Task Scheduling for Uncertain Execution Times

Human–robot collaboration (HRC) significantly enhances manufacturing flexibility and productivity, yet it faces persistent operational challenges stemming from the fundamental capability asymmetry between humans and robots. Task scheduling is a critical factor impacting the productivity of HRC systems, particularly when human worker fatigue is taken into account. Related task scheduling studies predominantly assume fixed subtask processing times, yet the inherent variability of human workers necessitates non-fixed durations. This paper addresses the HRC task scheduling problem with non-fixed human execution times, explicitly modelling workers’ temporal uncertainty using fuzzy triangular numbers. We proposed a new probability density function for fuzzy triangular numbers in Monte Carlo simulation, which is constructed based on a proportional-to-area principle. Through 5000 random simulations, the resulting distribution outperforms the existing method. Meanwhile, an improved decomposition-based multi-objective evolutionary algorithm is proposed to solve the multi-objective scheduling problem, simultaneously considering productivity and human fatigue. The numerical experiments indicate that the proposed algorithm outperforms the comparison methods.