Uncertainty Analysis And Optimization Strategy Of Remanufacturing System From The Perspective Of Low-carbon Economy

After forty years(1978-2018)of great development,as the “engine of the world economy”,China has completed the feat from the backward economy to the prosperity of civilization.However,the impact of disruptive economic development is of the profound,long-term and irreversible impacts on the environment.The rapid development of industry has led to a large amount of energy consumption and eventually is converted into greenhouse gases into the environment.The emission of greenhouse gases(GHGs)directly leads to global climate warming.Numerous studies show that most of the greenhouse gases come from the consumption of materials and energy in the industrial productive process.Serves as an advanced form of circular economy,remanufacturing is much less dependent on raw materials comparing with manufacturing.It provides an excellent solution to the problems of environmental degradation and global warming.In recent years,with the rapid development of manufacturing and equipment upgrading,the number of scrapped products has increased significantly.Many industries begin to integrate remanufacturing into the original strategic planning.To carry out better practice guidance for remanufacturing and give full play to the advantages of economic benefits,many researchers have carried out necessary research on the optimization and application of remanufacturing system.Although in the long run,the development of remanufacturing system is beneficial to the economy and the environment,it is worth note that there is unpredictability in the time,place and quality of returned end-of-life(EOL)products,which leads to uncertainties in all aspects of the remanufacturing system.These uncertainties have greatly increased the complexity of the remanufacturing management and the difficulty of research on model optimization.The existing related literature mostly analyzes the uncertainty from a single stage of the remanufacturing system,or studies the single uncertain factor in different stages.As the remanufacturing system has a complex structure,and when a variety of uncertainties are coupled together,the factors interfere with each other,whose impacts on the economy and the environment cannot be regarded as the simple accumulation of each factor.Therefore,how to apply appropriate analysis methods to quantifying the impacts of uncertainties and establish a reasonable mathematical model to optimize economic and environmental indicators of remanufacturing system comprehensively,thus it can highlight the characteristics of low-carbon and cyclic production.To explore the potential advantages of the economic benefits and environmental protection of remanufacturing projects,this paper studies the economic and environmental benefits in the remanufacturing system from different stages and under the influence of various uncertainties.In general,this article mainly carried out some useful work and exploration in the following aspects:The classical EOQ model is a simple but effective optimal order model that can optimize the total cost of transportation and warehousing without significantly increasing other inputs.It assumes that the market demand is a constant amount.But the reality is that the market demand in the remanufacturing system is full of unpredictability,so the classic EOQ model cannot continue to apply.Although some literatures deduced the corresponding optimal order quantity according to the stochastic distribution of the specific market demand,which makes a necessary contribution to the development of the classical EOQ model.However,little literatures explore the extended application of the EOQ model when the demand is randomly distributed and deduce the analytical formulas for the corresponding optimal order quantity and storage costs and penalty costs for different order quantities.This paper derives the optimal strategy for cost or profit of remanufacturing system under uncertain demand derived from both environmental and economic levels.Through the mathematical proof,the optimal solution of the order quantity under any demand distribution and the analytical expression of the expected logistics,storage and penalty costs corresponding to different order quantities are given.Some sound exploration was conducted on the innovation of application methods for remanufacturing environmental benefits.For example,for a typical 3R remanufacturing system(reuse,remanufacturing,and recycling),the recycled products are divided into multiple grades by quality,and the products of different quality grades adopt different reprocessing procedures.The traditional algebraic methods are complicated and logically uneasy to understand.This paper innovatively designed an algorithm for comprehensive recycle of quality coefficients,and used matrix operations to derive quantitative relationships between comprehensive quality coefficients of recovered products and environmental indicators under conditions of uncertain quality.The deduced result contains only one variable —the remanufacturing probability matrix.It provides a simple calculation tool and an easy-tounderstand method for the study of the 3R remanufacturing system.(3)In addition to passively calculating and evaluating the environmental benefits of3 R remanufacturing,a stochastic analysis of the uncertainty in the quality of recycled scrap products was adopted to make active predictions of environmental benefits in the recovery and productive process.By studying the influence of quality uncertainty on remanufacturing probability and carbon footprint under the typical distribution type,the optimal solution of the recycling quality comprehensive coefficient corresponding to the best environment benefit in the recycling and productive process is deduced in the 3R remanufacturing system.The close-form expressions of the optimal solution existence interval and the optimal environmental benefit analytical solution are given.This allows the remanufacturing system not only to use matrix operations to conveniently evaluate the environmental benefits and carbon footprint,but also to analyze and predict different environmental indicators in advance and formulate an optimal recycling strategy.(4)Taking into account the uncertainties in returns and demand of remanufacturing systems,based on the previous analysis,we further relaxed the assumptions of unlimited supply in the classical EOQ model,making it suitable for remanufacturing systems in which both the recycling quantity and the market demand are indeterminate,the extended model of the optimal order quantity under the dual uncertainties of demand and supply and the corresponding optimal remanufacturing rate is deduced,optimizing the remanufacturing system environmental cost or the total environment benefits.Through rigorous mathematical argumentation,the existence and uniqueness of the optimal solution for remanufacturing rate in the recycle and productive process are proved.Due to the complexity of the uncertainty analysis of the remanufacturing system,as far as the authors know,there is currently no literature on the extension and application of the EOQ model of the remanufacturing system under double uncertainties.The model provides theoretical basis and optimization results for optimal production and returning strategies in remanufacturing systems.(5)Finally,considering the discreteness of the quality grade variables in the recycled products,the traditional analysis methods tend to treat the remanufacturing cost related to the quality level as a series,and isolate it from other quantitative analysis.However,the real situation is of various uncertainties and mutual interference factors.In order to solve the problem of disconnection between the theoretical analysis and the actual situation,based on the limit theory,the paper fits the continuous function of unit remanufacturing cost based on the discrete data and substitute it into the profit equation for further optimization analysis.The advantage of this novel method is significant over the traditional discrete cost series in optimization analysis,from which we can quantify the impacts of different uncertainties on the production indexes and then derive the optimal production strategies by eliminating the negative effects of them.This optimal solution of remanufacturing rate under different strategies provides a reference and idea for the mathematical modeling and optimization analysis of multiple uncertainties in the remanufacturing system.