1.1. The National Policy on Urban Solid Waste and Management of Solid Waste and Urban Solid Waste in Brazil

In Brazil, the collection of household and urban public waste is the responsibility of the municipal government. In the National Urban Solid Waste Policy (PNRS), selective collection is defined as the collection of solid waste previously disposed of according to its constitution or composition. It includes the selective collection service of recyclable materials such as paper, glass, plastics, metals, and other materials (^{Besen, 2012}). The PNRS was established by Law No. 12.305 of August 2, 2010 (^{DOU, 2010a}), which was regulated by Decree No. 7.404/2010 (^{DOU, 2010b}), which established principles, objectives, and instruments, as well as guidelines for the management of solid waste, including hazardous waste, as well as the responsibilities of generators and public authorities (^{MMA, 2012}). The following are its guiding principles: 1. no waste creation; 2. reduction; 3. reuse; and 4. recycling. Environmental, social, cultural, economic, technical, and public health elements and the pursuit of sustainable development and ecoefficiency are all factors to examine under the legislation (^{Souza and Orsini, 2013}).

The PNRS Law’s primary concern is sharing responsibility, which recognizes that everyone is liable for waste, planning, and management actions that concretely define their responsibilities. According to Article 25 of the PNRS, “the success of efforts aimed at guaranteeing compliance with the PNRS, and the guidelines and other determinations made by law and regulation is the responsibility of public authorities, the business sector, and the community” (^{Ribeiro, 2012: 557}; ^{MMA, 2012}).

The approval of the National Solid Waste Policy (PNRS) and its regulation gave rise to a new benchmark for integrated and sustainable solid waste management in the country and new challenges for implementing and improving the selective collection service provider in the country. Although without many expressions, progress is being made on a still precarious model of formal selective assortment to provide universal service, with quality and social inclusion, primarily through hiring waste pickers’ organizations, associations, and cooperatives for implementation (^{Besen, 2012}).

Regular collection of solid waste has been the focus of solid waste management in recent years. Although coverage of urban solid waste collection services has improved in all areas, reaching more than 91 percent of households, over 19,000 tons of USW per day are placed in inappropriate places. Despite accounting for 25% of solid waste created, the Northeast of Brazil has the lowest USW collection assortment rate, being the only one below 80% (^{ABRELPE, 2017}).

Integrated solid waste management is to provide guidelines for discipline management actions, taking into account all relevant factors (environmental, cultural, economic, public health, political, social, technical, and urban, to name a few), to ensure that the measures taken are long-term. As a result, management might be viewed as a set of tasks to be completed. This integrated management consists of several actors in order to establish and improve waste management, encompassing all parties involved in the process and enabling a uniform and harmonious development among all stakeholders, in order to achieve the proposed objectives, which are tailored to each community’s needs and characteristics (^{Lopes, 2007}; ^{Pavan, 2010}). However, according to ^{ABRELPE (2017)}, the perception remains that the National Solid Waste Policy, which completed eight years on August 2, 2018, still lacks practical application and effectiveness in all country regions. Furthermore, the lack of resources to fund the planned changes has kept a considerable and growing deficit on the costliest points of the law: maximizing the use and recovery of waste materials and eradicating practices inadequate destination, still present in all units of the federation and with negative health impacts of millions of Brazilians.

Brazilian consumption of such material has been increasing exponentially during recent decades, which has led to the production of solid waste, commonly called garbage, both in urban and rural areas. The widespread consumption of materials resulting from human activities is viewed as a global issue, particularly proper disposal. When improperly disposed of in dumps, landfills, rivers, etc., these substances often contaminate the soil and surface or groundwater (^{MMA, 2012}). Therefore, the National Policy on Solid Waste (PNRS), established by Law No. 12.305/10 (^{DOU, 2010a}), has steadily replaced the notion of waste as ostensibly useless items in the country, as can be seen in its content and in the own definition given to waste.

According to ^{Andrade and Ferreira (2011)}, Brazil has been trying to adopt urban waste management techniques similar to developed countries, although socioeconomic and educational situations are different. Germany, for example, virtually extinguished landfills in significant cities. At the same time, the country invests heavily in educating its citizens about the importance of recycling and “minimization,” controlling the use of packaging (^{Brollo e Silva, 2001}).

In general, developed countries aim to find various waste treatment alternatives before they reach landfills. Composting, recycling, and incineration are just a few examples of what municipalities have been using to mitigate the negative impacts of urban solid waste (^{Andrade and Ferreira, 2011}; ^{Besen, 2012}). However, according to the authors, in Brazil, the selective collection of USW primarily affects the most prestigious neighborhoods of large cities and the lack of technical training.

Both in terms of public policy and USW management, developed and developing countries have somewhat similar orientations. However, cultural and social aspects distinguish the distinction, creating a different end product (^{Dubois et al., 2017}).

In Brazil, urban solid waste management is accompanied by joint actions between the public, private organizations, and community sectors, targeting sustainability so that there is a rational practice of non-renewable natural resources and that the environment is preserved from the random disposal of high potential (dangerous) waste (^{Pinto, 1999}; ^{Lima, 2012}).

According to ^{Andrade and Ferreira (2011)}, expanding home collection and effective waste disposal are obstacles that must be addressed; therefore, municipal resources must be appropriately handled. Because of the subject’s importance, more papers addressing challenges connected to sustainability, including urban solid waste management, are published each year. Between 1995 and 2005, 88 articles appear in the research of CAPES journals on the subject of “Urban Solid Waste.” From 2006 to 2016, this number increased to 1253, demonstrating the general public’s interest in the issue. The following are some recent papers from the CAPES journal:

It is noticeable that the increase of works that explore environmental education in the last decade has substantially increased. (^{Martins et al., 2020}) . Environmental education and awareness are critical factors in this entire waste management process, whether urban or rural. However, the responsibility must rest with the whole society, and no exceptions can be allowed, even those with difficulties in accessing the media. Therefore, it is imperative to find alternatives for access to information.

1.2. Systematic Literature Review on the Urban Solid Waste Management in Brazil

To supplement this theoretical reference, a systematic literature review technique was accomplished. For a systematic review of the literature, many criteria were used to ensure that this study could be replicated. The question that guided this research was: What are the significant studies that address the National Solid Waste Policy (PNSW) and Urban Solid Waste (USW) in the national context? Therefore, it is essential to investigate the flow of information between researchers. Data collection and analysis followed the steps:

The articles were grouped according to the focus with which they addressed the themes of “National Solid Waste Policy” and “Urban Solid Waste.” To establish the categories of analysis, the theme lines were determined by analyzing the information grouped in each article and using the criterion of shared thematic resemblance by area. The thematics were: recyclable material collectors (two articles), selective collection and recycling (one article), inter-municipal consortium (two articles), municipal solid waste management (two articles), dumps and landfills (two articles), and urban solid waste treatment (one article).

As a result of this comprehensive literature study, it was possible to see how the subject has been studied in Brazilian cities.

2.1. Data Collection and Samples

This is an empirical study with a quantitative approach and the use of secondary data. To evaluate the efficiency of Brazilian capitals, from 2002 to 2016, the Data Envelopment Analysis (DEA) was used. The DEA approach is used to assess the effectiveness of production units called Decision Making Units (DMUs) that perform similar activities. When DEA is used, it generates a score that ranges from 0 to 1. The closer the score is to 1, the more efficient the DMU is considered, and scores equal to 1 imply maximum efficiency. Each DMU is treated as a capital in the year in which it is used in this study. In addition, the Variable Returns to Scale (VRS) technique was used in this study, which assumes variable returns to scale by substituting the axiom of convexity for the axiom of proportionality. This element is appropriate, given that the returns to the relation of urban solid waste management are varied.

The sample was non-probabilistic due to the relevance of the cities. Data were collected on November 12, 2018. Although regarding the period selected for analysis, this is a cross-sectional period, as it was based on data available on the National Solid Waste Management Information website (SINIR), it is noteworthy that some cities did not have all the variables available in a given year, so we selected the cities and years that contained all the variables available for the study. The sample consisted of 20 Brazilian capitals. The analysis of the Brazilian capitals is appropriate since these municipalities are the main generators of solid waste in Brazil and are also crucial for the country’s economy. It is also worth noting that, to apply the DEA approach, all of the variables in the study must contain all of the data from the municipalities. Unfortunately, many public statistics in Brazil are out of date, and there is transparency. Therefore, some communities only have access to a few of the variables, making the analysis impractical.

After measuring the efficiency of Brazilian capitals, the logistic regression technique was used to measure the contribution of each variable used in the DEA technique.

2.2. Definition of Variables

In order to define the variables used in this study, we sought previous studies that evaluated the efficiency of USW management in various cities, states, and countries using the DEA technique. Therefore, the variables used in this study were the same as those used by other authors in previous empirical studies. As a result, all the variables employed in this study have been verified in earlier research. Chart 2 presents the variables used in the analysis, their categorization into inputs and products, as well as references in previous research.

2.3. Applications of DEA and Logistic Regression Techniques

Data Envelopment Analysis (DEA) is used to evaluate the efficiency of Decision-Making Units (DMUs) that perform similar tasks. In this study, DMUs are the Brazilian capitals, and each capital in a different year is considered a new DMU, so this study had 202 DMUs. The application of the DEA produces an indicator ranging from 0 to 1, and the closer to 1, the more efficient the DMU is considered, and scores equal to 1 indicate maximum efficiency. In this study, all variables were normalized according to the technique proposed by ^{Müller and Guido (2016)}; thus, all variables were normalized on a scale between 0 and 1; through data normalization, it is possible to measure the data better. The variables were normalized according to equation 1:

After applying the DEA technique, the logistic regression technique was applied to measure the contribution of each variable used in the DEA technique. At first, a histogram with the DEA results was plotted; based on the results, it was decided to consider all scores above 0.90 as 1 in the logistic regression, and all scores below 0.90 considered 0 in logistic regression. Of the 202 DMUs, 18.1% were within the range between 0.90 and 1. In a second moment, the hold-out methodology was used to separate the data in the training group (70%) and the group test (30%). Equation (2) is the linear combination of dependent variables multiplied by their respective parameter. Each parameter characterizes the importance of the respective variable for positive classification prediction, in this case, as efficient. The variables correspond to the variables presented in Table 1, regardless of whether they are isomers or products. There is also a parameter independent of the variables, known as intercept. The model must assign the weights (parameters) for the correct classification of capitals as efficient and inefficient. In principle, inputs are expected to have negative parameters and positive products. Equation (2)

In this study, the logistic regression model was used to model the DEA (efficient/inefficient) result for each capital. The objective was to create an analytical model (Equation 1) of the computational procedure performed by the DEA that mathematically explains the relationship between the variables used and the efficiency score. After the creation of the model, it was possible to estimate the efficiency of other DMUs.

3.1. Application and Analysis of the DEA Technique

Figure 1 shows the boxplot of the variables used in this study. Through the boxplot, it is possible to visualize the distribution of the variables and the distribution of the samples that have divergent behavior of the population (outliers). The sample is composed of 202 data, corresponding to Brazilian capitals, during the 14 years of analysis for each boxplot. It is noteworthy that each variable in the boxplot was normalized by dividing the population of each municipality, i.e., the variables were standardized per capita. It is observed that the municipality that presented the lowest amount of expenses related to sweeping was Manaus in 2002, with R$0.378 per inhabitant. The municipality with the highest total expenses was Florianópolis, in 2010, with R$96.79 per inhabitant.

Source: own elaboration based on interpretation data in software ^{SmartPLS GmbH (2019)}.

Figure 1 Boxplot of Variables 

The municipality of Cuiabá, in 2006, presented the lowest amount of management expenses (R$16.30), and the municipality that presented the highest value with management expenses (R$387.99) was Florianópolis, in 2016. The variables number of workers, the amount of material recovered, and the amount of waste collected was divided per capita and then multiplied by 1000, and this technique was used for better analysis and comparison of data. Regarding the variable number of workers, it is clear that the municipality with the highest value is Goiânia, in 2012, with 3.6 workers.

Regarding the variable quantity of waste collected, it is observed that the median corresponds to 414.37 tons/year, which shows that most municipalities collect approximately 414.37 tons/year of materials. Note that the median of the variable quantity of materials recovered represents 2.84 tons/year, i.e., most municipalities recover approximately 2.84 tons/ year of materials. It is noticed that the number of materials recovered is deficient compared to the number of materials collected. However, the municipality that collected the most materials was Vitória in 2015, and the municipality that recovered the most waste was Florianópolis in 2013. Although the capital city Vitória, in 2015 collected the most significant number of materials, this municipality did not recover a significant amount of waste as it was ranked 76th in the ranking for materials recovery.

After the descriptive analysis of the variables, the DEA technique with variable return approach with input orientation was applied. This approach was chosen as it should prioritize the optimization of available resources. Graph 1 shows the municipalities and the years in which the most efficient municipalities were considered, with 1 being the maximum efficiency.

Source: own elaboration with data obtained on National Solid Waste Management Information website ^{DOU (2010a)}.

Graph 1 Most Efficient Municipalities from 2002 to 2016 

It should be noted that the municipality of Belém received the highest efficiency score the most times, followed by the municipalities of Brasilia, Cuiabá, and Florianópolis. The Northeast is the geographical region with the most efficient capitals, followed by the North and South. It is worth noting that the southern area is the only one where all capitals are considered efficient.

In 2008, ^{Rogge and De Jaeger (2012)} utilized the DEA approach to assess the cost-effectiveness of USW collection and processing in Belgium. Municipal public managers have the problem of managing and implementing budget limitations and restricted resources as effectively as possible without raising taxes and serving most of the people. As a result, the majority of Flemish municipalities are ineffective in terms of USW collection and processing. As a result, non-recyclable waste was burnt or dumped in landfills in Belgium. This may be seen in Brazilian capitals as well.

Considering all the Brazilian capitals and each year under analysis, Table 1 shows the average efficiency of the municipalities over the years. The capital with the highest average efficiency was Macapá (0.720), followed by Porto Alegre (0.712), Belém (0.691), Cuiabá (0.650), Florianópolis (0.642), Fortaleza (0.631), Brasilia (0.621), and Teresina (0.600). Based on this data, it is clear that the geographical region with the highest average efficiency is the South (0.645), followed by the North (0.634), Midwest (0.525), Northeast (0.447), and Southeast (0.236). Considering all municipalities in all the years of analysis, the Southern region remains the geographical region with the highest average efficiency.

MSW is a problem faced in many nations. ^{Chang et al. (2013)} discussed how governments might leverage prior experiences to enhance USW management efficiency. As a result, they believe that organizational learning may help organizations improve their performance over time. The impacts of organizational learning tend to accumulate over time, according to ^{Yeh et al. (2016)}, and so it enables continual development in towns. Municipal managers can use the findings of this study to develop plans for improved urban solid waste management based on previous experiences.

3.2. Application and Analysis of Logistic Regression Technique

Second, the logistic regression approach was utilized to examine the influence of the variables utilized in the DEA methodology (inputs and outputs). This model, which is a mathematical approximation of the DEA methodology’s computer method, provides a more noticeable investigation of the connection between the variables employed in the DEA methodology.

Apart from the efficiency index derived from the DEA, the logistic regression model was created using the variables in Chart 1. It was chosen to proceed with the logistic regression employing binary efficiency values as output variables, with a standard of 1 for Brazilian capitals with efficiency over 0.90 and 0 for the rest of the Brazilian capitals. The hold-out approach was applied, in which the entire sample was randomly divided into two plots: 70% training data and 30% validation data, resulting in the model being validated. Given that models that fit the data are likely to be optimistic when their performance is judged based on training samples, this technique was selected. Such fact can be justified because the models are prone to adjust the individual samples, consequently, do not correspond to the population behaviour. Thus, it was decided to use data that the model (post-training) does not know, thus approaching its actual performance in explaining the relationship between the variables.

The logistic regression model consisted of the intercept and five explanatory variables. Table 2 shows the coefficients generated by the model. From the analysis of the R² statistics (Nagelkerke), it is observed that the model explains 57.9% of the independent variables.

The coefficients of the generated model contribute to the classification of a municipality as efficient. Based on Table 4, it is observed that the variables characterized as inputs in the DEA technique had negative coefficients; in contrast, the variables characterized as products had positive coefficients. This fact can be justified, considering that the greater the number of products and the smaller the number of inputs, the greater the tendency of capital to efficiency. It can be noted that the variables that primarily determine capital as efficient are “quantity of materials recovered” (positively), “quantity of waste collected” (positively), “the number of workers” (negatively), “sweeping expenses,” (negatively) and “handling expenses” (negatively). A classification matrix was created to test the model is predicting capabilities. It shows the number of municipalities categorized correctly and wrongly by the model. Table 3 and Table 4 show the matrices for training samples and model validation samples. Based on these tables, we can observe the number of hits, the number of false positives (inefficient capital understood as efficient), and the frequency of false negatives (efficient capital understood as inefficient). In this study, we used accuracy to evaluate the performance of the generated model, which is the percentage of correct ratings.

In both data sets, the model’s overall performance as measured by accuracy is similar. Validation data performance is expected to decrease. The model’s high performance justifies its usage as a foundation for a comparative evaluation of the variables’ efficiency values determined by the DEA. Observing the number of false positives and false negatives, it is observed that the model tends to be conservative about forecasting municipalities as efficient. The false-negative rate is significantly lower than the false-positive rate in both sets. Thus, the model acts as a filter of municipalities, highlighting a prominent character (represented by the variables considered). This is particularly intriguing since the approach identifies efficient municipalities and may be used as management indicators for other towns.

^{Simões et al., (2012)} examined the USW collection service in Portugal. The USW collection service is provided by the same firm that provides water distribution in this country. Consequently, the authors investigated whether the fact that the same corporation offers both public services to the public saves money. The DEA methodology was employed to assess efficiency. It was discovered that cost reductions might only be found in small municipalities that work together. Public managers might use the findings of this study to develop customized policies for the market under consideration.

Based on the findings of this study, it can be concluded that Brazilian capitals do not manage urban solid waste efficiently. It is also important to note that capitals typically serve large urban centers and metropolitan regions, leading to more significant waste management challenges.