Sustainable scheduling for job shops with joint maintenance, machine speed scaling, and uncertain processing times

This paper addresses the job shop scheduling problem by integrating preventive and corrective maintenance, uncertain processing times, and machine speed scaling under an environmental constraint. A comprehensive mixed-integer nonlinear programming (MINLP) model is formulated to optimize job scheduling, considering machine reliability, energy consumption, and carbon emissions. The model captures uncertainty in processing times, influenced by variations in machine speed, and integrates machine degradation using a Weibull distribution. A global carbon footprint constraint ensures compliance with environmental targets. This study examines the trade-offs between minimizing makespan, scheduling maintenance, and achieving sustainability objectives. Given the NP-hard nature of the job shop scheduling problem, a two-fold approach is applied for efficient solving. First, the Relax-and-Fix heuristic generates a high-quality initial solution by iteratively relaxing and fixing subsets of variables, thereby significantly accelerating the optimization process. The second step employs a branch-and-bound algorithm, which systematically explores the solution space by solving relaxed subproblems and refining integer variables. Numerical experiments validate the model, offering insights into balancing maintenance strategies, speed scaling, and energy efficiency in complex manufacturing environments. For a maximum permissible carbon footprint of 550 kg CO2, the model achieves a makespan of 18.98 h with a total carbon footprint of 514.56 kg CO2 when processing time variability is set at 5%. Results show that preventive maintenance (PM) reduces repair times, mitigates the impact of failures on makespan, and enhances machine speed adjustments, thereby optimizing energy consumption to meet environmental constraints. Sensitivity analysis reveals that higher failure rates significantly increase repair times and overall makespan. The model dynamically adjusts machine speeds to balance environmental targets with operational reliability under varying conditions. This study also derives key managerial insights for a sustainable scheduling model for job shop operating environments, emphasizing the integration of maintenance, machine speed adjustments, and the effective handling of processing time variability.