A two-stage Data Envelopment Analysis Approach Incorporating Global Bounded Adjustment Measure to evaluate the e�ciency of medical waste recycling systems with undesirable inputs and outputs

With the ever-increasing focus on sustainable development, recycling waste and renewable use of waste products has earned immense consideration from academics and policy-makers. The serious pollution, complex types, and strong infectivity of medical waste (MW) have brought serious challenges to management. Although several researchers have addressed the issue of the MW by optimizing MW management networks and systems, there is still a significant gap in systematically evaluating the efficiency of MW recycling systems. Therefore, this paper proposes a two-stage data envelopment analysis (DEA) approach that combines the virtual frontier and the global bounded adjustment measure (BAM-VF-G), considering both undesirable inputs and outputs. In the first stage, the BAM-G model is used to evaluate the efficiency of MW recycling systems, and the BAM-VF-G model is used to further rank super-efficient MW recycling systems. In the second stage, two types of efficiency decomposition models are proposed. The first type of models decomposes unified efficiency into production efficiency (PE) and environment efficiency (EE). Depending upon the systems structure, the second type of models decomposes unified efficiency into the efficiency of the MW collection and transport subsystem (MWCS) and the efficiency of the MW treatment subsystem (MWTS). The novel approach is used to measure the efficiency of the MW recycling systems in China's new first-tier cities (CNFCs), and we find that: (1) Foshan ranks the highest in efficiency, followed by Qingdao and Dongguan, with efficiency values of 0.3593, 0.1765, and 0.1530, respectively. (2) EE has always been lower than PE and is a critical factor influencing the overall efficiency of MW recycling systems in CNFCs. (3) The MWCS lacks resilience, with an efficiency 0.042 lower than that of the MWTC. Following the outbreak of COVID-19, the efficiency of the MWCS has been decreasing year by year, reaching only 0.762 in 2021, which is a decline of 0.111 compared to 2017.


Introduction
Waste, as the byproduct of human activities, is characterized by diverse types, uncertain origins, vague quantities, and high pollution levels, presenting significant risks and challenges to social development.
In the face of the dual constraints of resource scarcity and environmental concerns, there is considerable attention from decision-makers, companies, and academic researchers worldwide on recovering value through waste recycling and the renewable use of waste products.
Medical waste (MW), as a distinct waste category, possesses characteristics such as high infectivity, substantial contamination, and diverse categories.Notably, hazardous wastes account for approximately 41% of the total waste volume, a proportion eight times higher than that of ordinary waste.(Rani et al.,2022).With the advancement of China's socio-economic status, improved medical insurance services, and the arrival of an aging population era.There is a gradual increase in medical demands, leading to a rise in the generation and disposal of MW.Over the past five years, the average annual increase in MW volume has been 6.2% (Hashemi, 2021).National health, environment quality, and economic well-being are crucial considerations in any society (Yang and Chen,2021).The continual growth in MW production poses significant challenges to the effective management of environmental quality and sustainable resource utilization.Consequently, in-depth studies of the efficiency of MW recycling systems are essential to enhance MW management.
Numerous prior studies have concentrated on assessing the efficiency of a specific part of the MW recycling process.Despite this, as evidenced by the literature review in Section 2, a glaring deficiency persists in research on the evaluation of the efficiency of MW recycling systems.This paper endeavors to bridge this knowledge gap by utilizing a two-stage Bounded Adjustment Measure-Data Envelopment Analysis (BAM-DEA) approach.
The characteristics of this study are as follows: (1) We propose a two-stage BAM-DEA model that combines the virtual frontier and the global bounded adjustment measure (BAM-VF-G) to rank the super-efficient decision units.It is the first time that a two-stage problem has been solved using the BAM-VF-G model, considering both undesirable inputs and outputs.
(2) This paper adopts a new two-stage structure considering the internal network structure: the MW collection and transport subsystem (MWCS) and the efficiency of the MW treatment subsystem (MWTS), which is helpful for distinguishing the effectiveness during different processes and can comprehensively evaluate efficiency in combination with MWCS efficiency and MWTS efficiency.
(3) The efficiency of the MW recycling systems in China's new first-tier cities (CNFCs) from 2017 to 2021 is revealed, which can support relevant departments to make scientific decisions in the future.
The technical framework is illustrated in Fig. 1.The framework contains three steps.The first step is preliminary preparation, which includes classical approaches, problem analysis, and data acquisition and processing.In the second step, the BAM-G model is used to calculate the efficiency of the MW recycling systems and further rank the super-efficient DMUs using the virtual frontier.Two types of efficiency decomposition models are proposed, which decompose the unified efficiency into PE and EE and then divide recycling systems into two stages: the MWCS and the MWTS.Finally, a discussion is conducted based on the results.

Fig.1 Technical framework of this study
The remainder of this paper is structured as follows: Section 2 reviews the literature.In Section 3, we develop a two-stage BAM-VF-G model for analyzing the super-efficient MW recycling systems, and subsequently two types of efficiency decomposition models are proposed.Section 4 evaluates the recycling efficiency of MW in CNFCs from 2017 to 2021 used the proposed models.Conclusions and future research directions are provided in Section 5.

BAM
DEA, a nonparametric frontier efficiency analysis method, uses linear (and non-linear) programming techniques to assess the relative efficiency of homogeneous decision-making units ( DMUs ).DEA models are highly versatile, as they do not require a specific known production frontier and are wellsuited for handling situations involving multiple inputs and outputs.In 1978, Chams et al. (1978) introduced the first DEA model, known as the CCR model, which remains a classic in the field.
DEA models can be categorized into two groups: radial DEA and non-radial DEA.Radial DEA models, including input-oriented, output-oriented, and non-oriented models, assume that inputs and/or outputs change proportionally.However, in many real-world scenarios, inputs like labor, energy, and capital cannot change proportionally (Tone and Tsutsui,2009).This is where non-radial DEA comes into play, as it relaxes the assumptions of proportionality and direction, allowing for non-proportional changes in inputs and outputs, making it particularly suitable for handling undesirable outputs.Classical non-radial DEA models include the additive DEA (Charnes et al., 1985), the slacks-based measure (SBM) (Tone, 2001), and the range-adjusted measure (RAM) (Cooper et al., 1999).While the additive DEA cannot directly generate efficiency scores, the SBM approach overcomes this limitation.However, efficiency scores calculated by SBM models may vary depending on the orientation (input-oriented or outputoriented).Non-oriented SBM models address this issue but require nonlinear programming and often need to be transformed using the Charnes-Cooper transformation (Li et al., 2016).The RAM approach, being a non-oriented linear programming model, can directly generate efficiency scores.However, it still has some limitations.As its parameters are composed of the extremes of inputs and outputs and frequently results in efficiency scores ranging between 0.9 and 1, making it difficult to discriminate highly efficient DMUs .
To address the above issues, the Bounded Adjusted Measure (BAM), which considered lower bounds for inputs and upper bounds for outputs, was introduced by Cooper et al. (2011).The BAM model is a linear programming model, which makes it easy to obtain the global optimal solution.The BAM model also possesses a strong ability to differentiate DMUs and is suitable for production situations with any scale economies (Chen, et al., 2022).Qin et al. (2018) proposed radial and non-radial BAM-G models based on a virtual efficient frontier to investigate a specific evaluation of the energy efficiency in China's coastal areas.In this study, we extend the BAM-VF-G model proposed by incorporating a two-stage model to evaluate the efficiency of MW recycling systems while considering both undesirable inputs and outputs.

MW efficiency evaluation
MW recycling is crucial for ensuring public health and environmental sustainability.Both practitioners and researchers have long recognized the complexity and challenges involved in assessing the efficiency of MW recycling.To the best of our knowledge, research on the evaluation of MW recycling systems has primarily focused on specific aspects, such as the professionalism of recyclers during the classification and collection stages, the MW treatment equipment and disposal technology in the disposal stage, as well as the risk assessment of MW throughout the transportation and disposal stages.Deress et al. (2018) conducted a survey of 296 healthcare workers in 12 healthcare facilities located in a town in the Amhara Prefecture of northwestern Ethiopia.The survey utilized questionnaires and observation checklists to assess the education, attitudes, and experience of the healthcare workers.
Bivariate and multivariate logistic regression analyses were performed.The findings revealed that the medical staff in the town had a low level of education, unfavorable attitudes, and limited experience.Furthermore, they lacked training in MW management, which presented a significant barrier to the effective recycling of MW.Taghipour et al. (2016) conducted a six-month mechanical, chemical, and biological monitoring of MW disinfection equipment in 10 hospitals in Iran.Chemical monitoring results showed that 38.9% of the autoclaves examined had operational problems with pre-vacuum, air leakage, insufficient steam penetration into the waste, and/or vacuum pumps.Biological indicators showed that about 55.55% of the samples were positive.Most applications are equipped with equipment that is not suitable for handling anatomical, pharmaceutical, cytotoxic, and chemical wastes.
Tang et al. ( 2023) developed an integrated model to evaluate COVID-19 MW transportation risk by integrating an extended type-2 fuzzy total interpretive structural model (TISM) with a Bayesian network (BN).Taking the transportation process of MW in Nanjing as an example, the results show that insufficient personal protection of employees is a crucial risk factor for controlling the transportation of MW.Wang (2020) used the groundwater flow model software Visual Modflow to construct a numerical simulation model of groundwater flow.The study aimed to determine the diffusion of leachate pollutants by analyzing their migration in different spatial locations and at various time intervals.This analysis allowed for an accurate assessment of the pollutants' impact on the groundwater environment.Liu et al.
(2022) used life cycle assessment to determine the economic, environmental, health and safety benefits of medical plastic waste recycling in China.A logistics model for medical plastic waste recycling in China was established, the output range of medical plastic waste by 2050 was predicted, and the benefits and costs of the medical plastic waste recycling system were evaluated under three scenarios: low, medium and high.Through the analysis of sensitive factors, it is found that the recycling method of medical plastics is an important factor restricting their recycling.Al-Sulbi et al. (2023) proposed a method based on the fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to rank MW management, and proved the effectiveness of the method by comparing it with the analytic hierarchy process (AHP).The results showed that recycling was the most advantageous option.
Chemical treatment, incineration, and landfills rank low due to their higher environmental and financial costs.Dwivedi et al. (2022) analyzed the factors influencing third-party MW management and revealed the salient factors that led to the failure of the MW management system in India.Firstly, the causal relationship between factors was described by the unique Interval-Valued Intuitionistic Fuzzy Set (IVIFS) of the Decision Experiment and Evaluation Laboratory (DEMATEL).Then the analytic network process (ANP) was used to estimate the impact ranking of each factor.The results show that transportation and disposal are important factors restricting the third-party logistics management of MW. Ho (2011) employed the fuzzy analytic hierarchy process to set the objective weights of the evaluation criteria and select the optimal infectious MW disposal firm through calculation and sorting.
There are few studies on evaluating the efficiency of MW recycling systems from a system perspective, and there are no relevant studies based on the DEA method.Only some scholars have applied the DEA efficiency evaluation method to hospital efficiency evaluation (Cantor and Poh,2018;Samut, Pınar Kaya PhD,2023).DEA can systematically evaluate the efficiency of MW recycling through multiple inputs and multiple outputs, but there is no research on the efficiency evaluation of MW recycling systems using the DEA method.In light of this, we propose the BAM-VF-G model, a DEA method known for its computational convenience, resilience to outliers, and capacity to yield more objective and accurate results, for evaluating the efficiency of MW recycling systems.

Problem description
The MW recycling process includes waste segregation and collection, primary harmless treatment, transportation, and systematic treatment (Committee Red Cross, 2011).Therefore, this paper adopts a new two-stage structure as shown in Fig. 2, which is helpful for distinguishing the effectiveness during different processes and can comprehensively evaluate efficiency in combination with MWCS efficiency and MWTS efficiency.The MWCS includes segregation and collection, preliminary harmless handling, storage, and transportation of MW.The MWTS includes the harmless disposal of waste, landfilling, and recovery of available resources.The concrete network structure is depicted in Fig. 3.
In the MWCS, inputs include two desirable inputs and two undesirable inputs, and outputs consist of one desirable output and one undesirable output.The desirable inputs are labor and transportation cost.
The undesirable inputs are the MW generated volume and annual precipitation (Rashid and Saen,2015).
The desirable output is MW collected volume, and the undesirable output is CO2 emissions.In the MWTS, inputs include two desirable inputs and two undesirable inputs, and outputs consist of one desirable output and one undesirable output.Desirable inputs include energy and operating costs.The undesirable inputs are the MW collected volume and annual precipitation.In addition, government support is also considered as an undesirable input.The desirable output and undesirable output are MW disposal volume and waste gas, respectively.The MW collected volume, serving as an intermediate variable commonly referred to as a dual-role variable, can play roles either as a desirable output in MWCS or as an undesirable input in MWTS.Annual precipitation is considered as an undesirable input in both the MWCS and the MWTS.

BAM model
A classical BAM model can be written as the model (1) (Cooper et al., 2011).Suppose that there are ) indicate inputs and outputs, respectively.

BAM-G model
To make the distance function in different periods comparable (Feng et al.,2020), based on previous studies (Rashidi and Saen, 2015;Qin. et al.,2018), we extended the BAM model considering undesirable inputs and outputs using the global benchmark technology (GBT), and each DMU uses , , , : , can produce , This novel DEA model is constructed as follows: i and 2 i stand for undesirable and desirable inputs, respectively; 1 r , 2 r represent the desirable and undesirable outputs, respectively.The total inputs: i=i1 ∪ i2, and the total outputs: there is no desirable input excesses.For example, the corresponding slack is zero ( B will be zero.These discussions have been proved by Cooper et al. (2011).In this model, )

Virtual frontier data envelopment analysis
When the efficiency scores of several DMUs are all equal to 1, the BAM-G model cannot distinguish between these DMUs .To address this issue, Andersen and Petersen (1993) proposed the Super DEA method.The principle behind it is to exclude the evaluated 0 DMU in which the efficient DMUs have scores greater than 1, thus enabling a more refined ranking.For illustration, let's consider four DMUs , as shown in Table 1.When Super DEA model evaluates B DMU , the inputs of the reference DMUs are {2,7,4} and the outputs are {7,5,3}, resulting in a reference frontier of ACD.However, when the Super DEA model evaluates D DMU , the inputs of reference set are {2,9,7}, and the outputs are {7,4,5}, which leads to a reference frontier of ACB.The issue here is that the reference sets and reference frontiers vary for different units being evaluated, which can result in less consistent or reasonable results.The reference DMU set and the evaluated DMU set are two different sets in this method and the reference DMU set remains unchanged so that its results may be more reasonable than existing models (Barrosa et al.,2017).Qin et al. ( 2018) combined the virtual frontier with BAM to further sequence the evaluation units.In this paper, we propose a two-stage DEA approach that combines the virtual frontier and the BAM-G, considering both undesirable inputs and outputs.The proposed model is as follows:  .

Efficiency decomposition models
To study technological level and environmental emission capacity, it is necessary to calculate PE and EE.PE focuses on inputs utilization and desirable outputs, while it does not consider desirable outputs such as carbon dioxide and waste gas.EE only considers environmental impacts, measuring inputs and undesired outputs.PE and EE can be defined as follows:

General two-stage BAM-G models
The MW recycling systems are complex, encompassing various stages such as segregation and collection, preliminary harmless treatment, storage, transportation, harmless disposal of waste, landfill, and recovery of available resources.It is important to note that the 'black box' DEA method does not account for the internal network structure of systems, and as a result, it cannot accurately reflect the internal efficiency of these systems (Wang et al., 2021).To address this limitation, our paper adopts a new two-stage structure, as illustrated in Fig. 2, to calculate the MWCS and the MWTS efficiency.This approach allows us to analyze the specific factors that impact the efficiency of MW recycling systems (Shao et al., 2019).The MWCS efficiency of j DMU can be evaluated by the model ( 8).
In the MWTS, annual precipitation needs to be invested again.The MWTS efficiency can be evaluated by the model ( 9). )

Data
The diversity in MW recycling patterns and MW treatment technology levels across China can be attributed to variations in geographical environment, socioeconomic factors, and demographic variables (Yuan et al., 2019).The China New First-tier Cities (CNFCs) are identified by the China First Financial and Economics New First-tier City Research Institute, using data from 170 prominent businesses, user behavior data from 19 internet companies, and urban big data from data agencies.These cities exhibit comprehensive capabilities that are second only to first-tier cities, and their disparities in overall development levels are relatively minor.Therefore, evaluating the efficiency of MW recycling systems in these cities holds significant reference value.For the year 2022, the CNFCs list includes Chengdu, Chongqing, Hangzhou, Xi'an, Wuhan, Suzhou, Zhengzhou, Nanjing, Tianjin, Changsha, Dongguan, Ningbo, Foshan, Hefei, and Qingdao.Consequently, these 15 cities have been selected as the focal points of this study.
The amount of MW generated in the CNFCs from 2017 to 2021 is shown in Fig. 5.The MW generated volume in these cities showed an increasing trend from 2017 to 2019, followed by a decreasing trend from 2019 to 2021.This phenomenon can be primarily attributed to the coronavirus disease (COVID-19).Fig. 6 displays the heat map of MW generated volume in these cities from 2017 to 2021.According to recent research, the variables of inputs and outputs are defined as follows.Table 2 summarizes the descriptive statistics of the inputs and outputs of MW recycling systems.(2) EE remain a significant factor contributing to the inefficiency of the MW recycling systems in CNFCs.Fig. 9 indicates that EE has consistently been lower than the overall efficiency and PE.With the advancement of science and technology, the MW generated volume can now be fully managed by existing MW disposal centers.However, addressing the pollution from exhaust gases and waste residues produced during the disposal process remains a formidable challenge.Therefore, the government should intensify its research and development investment in MW disposal to reduce the environmental pollution caused by MW during the MWTS.
(3) Due to the impact of the COVID-19, the efficiency of MW recycling in CNFCs has decreased.In CNFCs, the unified efficiency of MW recycling decreased by 2.52% in 2019 and further declined by 12.18% in 2020.With the relaxation of the pandemic, the CNFCs MW recycling systems are gradually recovering.To adhere to and implement the "Green Development of China in the New Era," strengthen environmental protection, and resolutely fight the critical battle against pollution, the government and relevant entities must continue to focus on the MW recycling.
(4) There are still numerous issues in CNFCs regarding the MWCS.On one hand, the MW collection process is not standardized, and there is a lack of professional recycling personnel.On the other hand, the MW recycling system network is irrational, leading to high transportation costs and posing challenges to transportation safety.Especially after the outbreak of the COVID-19 pandemic, with the surge in the generation of MW, the MW recycling efficiency has significantly declined, highlighting the poor resilience of the MWCS.

Conclusion
Resource utilization and environmental governance have become hot topics of current research.Waste recycling is a key measure to respond to this slogan, receiving widespread attention and call from all sectors of society.As a special waste, scientific recycling and proper treatment of the MW can avoid secondary pollution and promote resource reuse.The MW recycling system encompasses two stages: MWCS and MWTC.Unlike other inputs where the expectation is to achieve the maximum output with the minimum input, the MW collected volume, precipitation levels, and the degree of government support are considered input indicators (harmful inputs or naturally occurring conditions that are non-cost inputs), and it is desired to have as much of these inputs as possible, hence they are referred to as undesirable inputs.To evaluate the efficiency of the MW recycling systems, this paper proposes a two-stage G-BAM model that considers both non-desired inputs and outputs.To address the situation where multiple DMUs have an efficiency value of 1, we extend a virtual frontier to rank efficient DMUs and proposes the BAM-VF-G model.Secondly, by calculating PE and EE, the production and environmental efficiencies of CNFCs are explored.Finally, the efficiency of the MW recycling system is decomposed into MWCS and MWTS to further understand the internal operations of the MW recycling system.The conclusions are as follows.
(1) From 2017 to 2019, the efficiency of the medical waste recycling systems in new first-tier cities, as well as all subsystems, saw significant improvements.Although the overall efficiency declined in 2020 due to the impact of the COVID-19 pandemic, it gradually increased after 2021.In recent years, in accordance with the "Comprehensive Management Plan for Medical Institution Waste," local authorities have strengthened the comprehensive management of medical institution waste, achieving waste reduction, resource utilization, and harmless treatment, resulting in fruitful outcomes in the governance of medical waste and environmental protection.
(2) The PE is higher than the EE.With the continuous development and application of MW disposal technologies, the disposal efficiency is sufficient to meet the growing demand for the MW generated volume.However, due to the complexity and polluting nature of MW types, it poses a risk of environmental pollution.On the other hand, existing technologies still face insurmountable challenges, and the treatment of MW generates a significant number of emissions such as smoke and gases, which may contain harmful substances, causing pollution to the environment and air quality.
(3) The MWCS exhibits a lower level of efficiency.On one hand, the MWCS involves multiple stages and requires collaboration and coordination with various stakeholders, including medical institutions, government departments, and waste management enterprises.Its management encompasses several aspects, including regulation, operation, and technical support.If the management system is not robust, with inadequate supervision and unclear responsibilities, it can lead to operational inefficiencies and impact the effectiveness of the MWCS.On the other hand, MW originates from a wide range of sources, including hospitals, clinics, and pharmacies.However, during the initial stages of waste management and recycling system construction, there may not have been sufficient consideration for the MW generated volume and characteristics of each stage, leading to an irrational layout and incomplete coverage, which affects the overall efficiency of the MWCS.

Policy recommendations
Building upon the aforementioned conclusions, policy recommendations have been proposed to enhance the efficiency of the medical waste recycling systems.
(1) Improve the efficiency of the MWCS.On one hand, it is essential to promote the scientific construction of the MW recycling network, which includes optimizing the recycling process, selecting facilities for recycling nodes, and planning routes for MW transportation vehicles, thereby improving the efficiency and quality of recycling.On the other hand, the government should formulate and refine relevant regulations and standards for MW recycling, clarifying the management requirements and division of responsibilities for MW recycling.
(2) Reduce environmental pollution.On one hand, optimize the MW recycling network to minimize the exhaust pollution generated during the transportation of MW.On the other hand, MW disposal enterprises should introduce new technologies to maximize the reduction of MW generation and the release of emissions.At the same time, the government should implement incentive mechanisms, encouraging continuous innovation and application of relevant technologies through R&D subsidies and tax incentives, to achieve waste reuse and resource utilization.

Fig. 2
Fig. 2 General two-stage network structure

B
will be zero.Similarly, if desirable output r for 0 output shortfalls.For instance, the corresponding slack is zero ( established by adjusting inputs and outputs in a specific proportion, ensuring that the efficiency values fall between 0 and 1, unlike the traditional DEA model.As shown in Fig. 4, the efficiency values of entities A, B, C, and D are all 1 in the traditional DEA model, making it unable to distinguish between them.Virtual frontier DEA, on the other hand, constructs virtual frontiers F, G, H, and I as the optimal reference frontiers for entities A, B, C, D, and E. This allows for differentiation of the efficiencies of A, B, C, D, and E, all of which are considered DEA inefficient.

Fig. 4
Fig. 4 The principle of virtual frontier DEA

Fig. 7
Fig. 7 Trends efficiency in the top three and bottom three cities Production efficiency (PE) and Environment efficiency (EE) obtained from BAM-G The average PE and EE scores are shown in Fig. 8 Zhengzhou, Qingdao, Dongguan, Nanjing, Suzhou, Foshan, Tianjin all have PE and EE scores of 1, indicating a high technological level and environmental emission capacity.It is worth noting that Hangzhou is still maintains low PE and EE scores, with the lowest scores at 0.3335 and 0.2806, respectively.PE and EE in CNFCs are closely correlated.This phenomenon can be attributed to two factors.First, cities with higher levels of waste disposal technology have stricter environmental requirements for waste management, leading to a strong correlation between production and environmental emission capacity.Second, environmentally friendly companies have a higher appeal to customers, contributing to the close relationship between production and environmental emission capacity.As shown in Fig. 9, CNFCs' MW recycling systems has low scores (the highest is only 0.9416) over the entire sample period.Unified efficiency, PE, and EE show an increasing trend from 2017 to 2018, followed by a slight decline in 2019.They reach their lowest point in 2020 and gradually recover in 2021.These phenomena are all influenced by the impact of COVID-19, with EE being the most significantly affected, reaching only 0.7980 in 2020.In general, PE slightly exceed EE, suggesting the need for additional attention to environmental protection in the MW recycling systems.

Fig. 10 Fig. 11
Fig. 10 Comparisons the efficiency of MWCS and MWTS from 2017 to 2021 the undesirable and desirable outputs of the MWCS; 1 denote the minimum among the ith desirable input and the rth undesirable output, denotes the maximum among the ith undesirable input and the rth desirable outputs.It is important to note that the lower-sided range for each desirable input and undesirable output depend only on the lower bound of the desirable input, undesirable output and 0 DMU .In contrast, the upper-sided range for each undesirable input and desirable output depend only on the upper bound of the undesirable input, desirable output and

Table 2
Statistical description of input and output indicators from 2017 to 2021

Table 5
The efficiency of MW recycling systems in CNFCs from 2017 to 2021 obtained from the BAM-VF-G model

Table 6
The efficiency of MW recycling systems in CNFCs obtained from the BAM-G model and the BAM-VF-G Table7illustrates the efficiency of MWCS and MWTS in CNFCs from 2017 to 2021.Suzhou, Tianjin, Dongguan, Foshan, and Qingdao have higher efficiency in the MWCS and the MWTS, indicating that these five cities have certain reference values for other cities in MW recycling.However, Hangzhou have the lowest MWCS and MWTS efficiency in the past five years, at 0.4861 and 0.4535, respectively.As shown in Fig.10, the efficiency of MWCS show a gradual increase from 2017 to 2018, with 10 cities achieving a score of 1 in 2018.The efficiency of MWTS continue to increase from 2017 to 2019, with 12 cities achieving a score of 1 in 2019.Both the MWCS and the MWTS experience their lowest efficiency in 2020, with a gradual recovery observed in 2021.