Modeling and optimization of bakery production scheduling to minimize makespan and oven idle time

Makespan dominates the manufacturing expenses in bakery production. The high energy consumption of ovens also has a substantial impact, which bakers may overlook. Bakers leave ovens running until the final product is baked, allowing them to consume energy even when not in use. It results in energy waste, increased manufacturing costs, and CO₂ emissions. This paper investigates three manufacturing lines from small and medium-sized bakeries to find optimum makespan and ovens' idle time (OIDT). A hybrid no-wait flow shop scheduling model considering the constraints that are most common in bakeries is proposed. To find optimal solutions, non-dominated sorting genetic algorithm (NSGA-II), strength Pareto evolutionary algorithm (SPEA2), generalized differential evolution (GDE3), improved multi-objective particle swarm optimization (OMOPSO), and speed-constrained multi-objective particle swarm optimization (SMPSO) were used. The experimental results show that the shortest makespan does not always imply the lowest OIDT. Even the optimized solutions have up to 231 min of excess OIDT, while the makespan is the shortest. Pareto solutions provide promising trade-offs between makespan and OIDT, with the best-case scenario reducing OIDT by 1348 min while increasing makespan only by 61 min from the minimum possible makespan. NSGA-II outperforms all other algorithms in obtaining a high number of good-quality solutions and a small number of poor-quality solutions, followed by SPEA2 and GDE3. In contrast, OMOPSO and SMPSO deliver the worst solutions, which become pronounced as the problem complexity grows.