The Green Flexible Job-Shop Scheduling Problem Considering Cost, Carbon Emissions, and Customer Satisfaction under Time-of-Use Electricity Pricing
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3.3. Results and Discussions
The simplex grid method is an effective tool for multi-objective analysis. Its calculations are simple, allowing for a reasonable and uniform valuation of each weight. By defining the number of grids, it can meet the precision requirements for weights. In this study, a five-order simplex grid table with a weight precision of 0.2 was selected, as illustrated in Figure 9.
This study employs the improved genetic algorithm designed in Section 3 to solve the proposed model. The algorithm parameters are set as follows: the initial population size is 800, the crossover probability is 0.6, mutation probability is 0.02, and the maximum evolution iterations are set to 400. The improved algorithm is implemented using Python 3.7, and computations are performed on an Intel® Core (TM) i5_6300HQ CPU @ 2.80 GHz with 8 GB of random-access memory, running on the Windows 10 operating system. The computational results are presented in Table 8.
For the scheduling results in Table 8, we observe a cost range of CNY 1700.94 to 7433.04, a carbon emission range of 1194.39 to 1815.34 kg, and a customer satisfaction range of 5.64 to 13.30. The cost varies by CNY 5732.10, carbon emissions differ by 600.94 kg, and satisfaction varies by 7.66. This indicates significant fluctuations in cost, carbon emissions, and customer satisfaction with changing weights. The article defines four scheduling modes, Profit-oriented, Energy-saving, Customer-oriented, and Balanced, with weight configurations for minimizing cost, carbon emissions, and maximizing customer satisfaction of [1, 0, 0], [0, 1, 0], [0, 0, 1], and [1/3, 1/3, 1/3], respectively. Figure 10 illustrates the cost, carbon emissions, and customer satisfaction under different modes.
The balanced model emerges as a strategic compromise, aiming to harmonize the key objectives of cost minimization, carbon emission reduction, and customer satisfaction. This approach provides a nuanced and well-rounded solution compared to the singular objectives of the other three models. In terms of cost, the balanced model strikes a middle ground. While its cost is slightly higher than the profit-oriented model, it significantly outperforms the energy-saving model by saving approximately CNY 4863.92. This financial equilibrium positions the balanced model as a prudent choice for businesses seeking cost optimization without compromising excessively on other objectives. Carbon emissions present another pivotal dimension. The balanced model, with 1368.68 kg of emissions, achieves a delicate balance. It outperforms the energy-saving model by reducing emissions by 390.65 kg, showcasing a conscientious approach towards environmental sustainability. Simultaneously, it remains competitive when compared to the profit-oriented and customer-centric models, avoiding the excessive emissions seen in the profit-oriented model. Crucially, customer satisfaction under the balanced model experiences a remarkable improvement of 92.55% compared to the energy-saving model. This enhancement is substantial and positions the balanced model as an attractive choice for businesses aiming to enhance customer loyalty and repeat business without neglecting financial considerations and environmental responsibilities. When comparing the balanced model to the profit-oriented model, the slight increase in cost is justified by the notable improvements in both carbon emission reduction and customer satisfaction. The balanced model offers a superior alternative for businesses that seek a more holistic and sustainable approach to their operations. In contrast to the energy-saving model, the balanced model presents a more financially viable option while still making commendable strides in emission reduction and customer satisfaction. The balanced model, therefore, stands out as a pragmatic compromise, providing businesses with a versatile strategy that considers the triad of cost, environmental impact, and customer centricity. This strategic alignment positions the balanced model as a compelling choice for companies aiming to achieve comprehensive optimization across multiple objectives. Figure 11 shows the Gantt chart under this model, with the order priority allocation sequence H3J2 (the customer H3’s order for product J2), H5J2, H2J2, H2J1, H3J3, H1J1, H5J3, H1J4, H1J6, H2J5, H1J3, H4J5, H4J1, H5J6, and H4J4. Figure 12 illustrates the Gantt chart under this model, with the order priority allocation sequence H2J1, H3J2, H5J2, H2J2, H3J3, H1J4, H4J1, H1J6, H1J3, H4J5, H5J6, H1J1, H5J3, H2J5, and H4J4. Figure 13 illustrates the Gantt chart under this model, with the order priority allocation sequence H5J2, H3J2, H3J3, H2J1, H2J2, H1J4, H5J3, H1J3, H2J5, H1J6, H1J1, H4J1, H5J6, H4J5, and H4J4. Figure 14 illustrates the Gantt chart under this model, with the order priority allocation sequence H5J2, H3J2, H2J1, H1J4, H2J2, H3J3, H1J1, H5J3, H1J3, H2J5, H4J1, H5J6, H1J6, H4J5, and H4J4.
The profit-oriented model inadvertently leads to a surge in carbon emissions due to high-energy-consumption machines deployed to meet demanding production schedules. Conversely, the energy-saving model, despite showcasing a commendable commitment to lower carbon emissions, incurs higher costs. Similarly, the customer-centric model, prioritizing customer satisfaction, relies on high-energy-consumption machines operating at maximum capacity, contributing to heightened carbon emissions. The balanced model offers a comprehensive solution that addresses the inherent limitations of the above models. It provides a strategic advantage by coordinating the synergies between minimizing cost and carbon emissions and maximizing customer satisfaction to achieve sustainable growth. This innovative approach incorporates energy price fluctuations into scheduling strategies, enabling a multi-objective optimization model that considers cost, carbon emissions, and customer satisfaction. Companies can effectively control energy consumption, reduce operating cost, minimize environmental impacts, and improve customer satisfaction. At the societal level, this research contributes to sustainable development goals by promoting low-carbon production.
Contrasting with prior studies, such as those by Jiang et al. [39] and Zhang et al. [40] that prioritized minimizing completion times without regard for energy consumption implications, this approach falls short in fostering environmental sustainability. Although Jiang et al. [41] delved into energy-efficient scheduling to curtail energy expenditure, the omission of time-of-use electricity rates and customer satisfaction considerations from their analysis precludes a holistic embrace of enterprise sustainability. The GFJSP designed in this study contributes to the overall sustainability of the enterprise by harmonizing economic performance with ecological responsibility and consumer satisfaction. Of course, this study needs to be further extended in the future. Industry 4.0 (I4.0) technologies provide favorable conditions for sustainable development [42]. For example, dynamic layout planning based on I4.0 reduces costs, improves society, and protects the environment [43]. Consider the combination of collaborative robot allocation and job-shop scheduling to minimize cost and manufacturing spans [44]. Therefore, our work can be extended by I4.0 technologies, designing an adaptive, green, flexible job-shop scheduling system by combining I4.0 technologies such as Internet of Things, collaborative robots, and augmented reality [45]. This system enables collaborative multi-robot-machine scheduling, responding in real-time to market changes and energy price fluctuations. It automatically adjusts scheduling strategies to optimize energy efficiency and reduce carbon emissions.
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