A game theory approach for optimizing job shop scheduling problems with transportation in common shared human–robot environments

The Job Shop Scheduling Problem with Transportation (JSSPT) is a critical challenge in modern industrial systems, particularly in environments where human operators and Autonomous Intelligent Vehicles (AIVs) interact. Traditional scheduling approaches often fail to address the dynamic and unpredictable nature of these shared human–robot environments. In response, this paper introduces a game theory-based scheduling algorithm that optimizes transportation tasks in Industry 5.0 settings, where human–robot collaboration is essential. By modeling AIVs as rational agents within a potential game framework, we reformulate JSSPT as a Multi-robot task allocation problem (MRTA), applying iterative best-response strategies to reach a Nash equilibrium that minimizes the overall makespan. Our approach uniquely integrates human movements into the scheduling process, enabling real-time adaptation to fluctuating production environments. Experimental results demonstrate that the proposed algorithm outperforms state-of-the-art methods, namely the VNS and entropybased approaches, particularly in settings where human unpredictability significantly impacts performance. On average, the game-theory-based algorithm reduces the makespan by 7 s compared to the entropy-based algorithm and by 17 s compared to the VNS algorithm. Despite the restrictive assumptions regarding human movement, this study underscores the significance of dynamic scheduling approaches in highly variable settings, contributing to more resilient and efficient production systems in line with Industry 5.0’s vision.