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基于最优控制理论和人工蜂鸟算法研究具有非线性需求的产品保修与绿色水平的影响

Impact of warranty and green level of the product with nonlinear demand via optimal control theory and Artificial Hummingbird Algorithm.

作者信息

Ali Hachen, Akhtar Fleming, Manna Amalesh Kumar, Alrasheedi Adel Fahad, Shaikh Ali Akbar

机构信息

Department of Mathematics, The University of Burdwan, Burdwan, 713104, India.

Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology (KIIT), Deemed to be University, Bhubaneswar, 751024, India.

出版信息

Sci Rep. 2024 May 11;14(1):10809. doi: 10.1038/s41598-024-61453-0.

DOI:10.1038/s41598-024-61453-0
PMID:38734734
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11088665/
Abstract

Due to the current environmental situation and human health, a green manufacturing system is very essential in the manufacturing world. Several researchers have developed various types of green manufacturing models by considering green products, green investments, carbon emission taxes, etc. Motivated by this topic, a green production model is formulated by considering selling price, time, warranty period and green level dependent demand with a carbon emission tax policy. Also, the production rate of the system is an unknown function of time. Per unit production cost of the products is taken as increasing function of production rate and green level of the products. In our proposed model, carbon emission rate is taken as linear function of time. Then, an optimization problem of the production model is constructed. To validate of our proposed model, a numerical example is considered and solved it by AHA. Further, other five metaheuristics algorithms (AEFA, FA, GWOA, WOA and EOA) are taken to compare the results obtained from AHA. Also, concavity of the average profit function and convergence graph of different metaheuristics algorithms are presented. Finally, a sensitivity analysis is carried out to investigate the impact of different system parameters on our optimal policy and reach a fruitful conclusion from this study.

摘要

由于当前的环境状况和人类健康问题，绿色制造系统在制造业中非常重要。一些研究人员通过考虑绿色产品、绿色投资、碳排放税等因素，开发了各种类型的绿色制造模型。受此主题的启发，通过考虑销售价格、时间、保修期以及与碳排放税政策相关的绿色水平需求，制定了一种绿色生产模型。此外，系统的生产率是时间的未知函数。产品的单位生产成本被视为生产率和产品绿色水平的增函数。在我们提出的模型中，碳排放率被视为时间的线性函数。然后，构建了生产模型的优化问题。为了验证我们提出的模型，考虑了一个数值示例并通过AHA求解。此外，采用其他五种元启发式算法（AEFA、FA、GWOA、WOA和EOA）来比较从AHA获得的结果。还给出了平均利润函数的凹性和不同元启发式算法的收敛图。最后，进行了敏感性分析，以研究不同系统参数对我们最优策略的影响，并从本研究中得出富有成效的结论。

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