Institute of Food Science and Biotechnology, Department of Process Analytics and Cereal Science, University of Hohenheim, 70599, Stuttgart, Germany.
Institute of Food Science and Biotechnology, Department of Process Engineering and Food Powders, University of Hohenheim, 70599, Stuttgart, Germany.
Sci Rep. 2023 Jan 5;13(1):235. doi: 10.1038/s41598-022-26866-9.
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 CO 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.
生产周期主导面包生产的制造成本。烤箱的高能耗也有很大的影响，而面包师可能会忽略这一点。面包师让烤箱一直运行，直到最后一个产品烘焙完成，即使烤箱不在使用时也会消耗能源。这导致了能源浪费、制造成本增加和 CO 排放。本文研究了三条来自中小型面包店的生产线，以找到最优的生产周期和烤箱空闲时间（OIDT）。提出了一种混合无等待流水车间调度模型，考虑了在面包店中最常见的约束条件。为了找到最优解，使用了非支配排序遗传算法（NSGA-II）、强度 Pareto 进化算法（SPEA2）、广义差分进化（GDE3）、改进多目标粒子群优化算法（OMOPSO）和速度约束多目标粒子群优化算法（SMPSO）。实验结果表明，最短的生产周期并不总是意味着最低的 OIDT。即使是优化后的解决方案也有高达 231 分钟的过度 OIDT，而生产周期是最短的。Pareto 解提供了生产周期和 OIDT 之间有希望的权衡，在从最小可能的生产周期增加 61 分钟的情况下，将 OIDT 减少 1348 分钟。NSGA-II 在获得大量高质量解和少量低质量解方面优于所有其他算法，其次是 SPEA2 和 GDE3。相比之下，OMOPSO 和 SMPSO 提供了最差的解决方案，随着问题复杂性的增加，这些解决方案变得更加明显。
