A hybrid machine learning-mathematical programming optimization approach for municipal solid waste management during the pandemic

Abstract

This paper provides a mathematical optimization strategy for optimal municipal solid waste management in the context of the COVID-19 epidemic. This strategy integrates two approaches: optimization and machine learning models. First, the optimization model determines the optimal supply chain for the municipal waste management system. Then, machine learning prediction models estimate the required parameters over time, which helps generate future projections for the proposed strategy. The optimization model was coded in the General Algebraic Modeling System, while the prediction model was coded in the Python programming environment. A case study of New York City was addressed to evaluate the proposed strategy, which includes extensive socioeconomic data sets to train the machine learning model. We found the predicted waste collection over time based on the socioeconomic data. The results show trade-offs between the economic (profit) and environmental (waste sent to landfill) objectives for future scenarios, which can be helpful for possible pandemic scenarios in the following years.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10668-023-03354-2.

Introduction

The COVID-19 pandemic has generated problems in most activities where human being develops. The introduction of various social distancing initiatives, the overproduction of different hygiene products, the reorganization of health systems, and even how consumers plan their food purchases and the waste that this implies, have generated direct and indirect impacts on the environment (Vittuari et al., 2021; Zanetti et al., 2022). The apparent positive effects were observable from cleaner lakes, rivers, and beaches, to improvements in air quality, this offers an opportunity to formulate ecological policies that restore environmental health (Chakraborty et al., 2021). On the other hand, the negative effects that this pandemic has caused on the environment are related to the large increase in the production of municipal solid waste (MSW) and how improper handling of it would increase the likelihood of the virus spreading as well as cause it to contaminate regular municipal waste (Nabavi-Pelesaraei et al., 2022), in addition to the low recycling or treatment capacity that existed at the time of the pandemic (Mohamed et al., 2022). The COVID-19 pandemic changed the rules of waste management, since inadequate management practices, poor waste management, and inadequate final disposal can increase the susceptibility to the spread of the virus, standards for the disposal of medical waste have been developed by several environmental and public health groups, but it is highly challenging to execute these guidelines effectively in the public sectors of developing nations (Bhar et al., 2022), especially in those areas where waste disposal was already unsustainable even before the COVID-19 due to ineffective treatment methods, the capacity limitations of healthcare facilities, and insufficient waste disposal techniques (El-Ramady et al., 2021).

It is estimated that the problems in waste management generated as a result of the pandemic will continue for at least five years (Tripathi et al., 2020); for this reason, the implementation of different waste management strategies is increasingly necessary. Due to isolation, changes in the lifestyle of the population, in general, have caused various problems in waste management since the consumption of single-use plastics, and healthcare products, among others, has increased greatly, in addition to the large increases in the generation of medical waste, represent a risk to society if not managed correctly (Sharma et al., 2020).

In recent studies, it has not been possible to determine if infectious waste plays a critical role in the distribution of the virus; however, the deposition of different medical residues in the water and soil ecosystem can cause microbial transformations, which represents a potential threat to the public health system (Ekhaise et al., 2023). For this reason, the enormous amounts of waste generated during the pandemic make processing this waste a priority (Andeobu et al., 2022; Dharmaraj et al., 2021). To minimize the environmental and social impact in the short and long term, implementing efficient waste management strategies is necessary to reduce the long-term effects that the pandemic may generate, solving this challenge and creating technological techniques and knowledge will enable the safe treatment of municipal waste in the current pandemic, and above all to generate prevention strategies in the face of the possibility of future pandemics (Skrzyniarz et al., 2022).

In the search for possible solutions to the management of MSW, various strategies have been proposed, which used different methodologies. From an optimization perspective, Govindan et al. (2021) developed a multi-objective optimization model capable of considering social and economic objective functions simultaneously. In this model, the scheduling of the collection vehicles, possibilities of failures, and fuel consumption, among other factors that allow for establishing the optimal waste transport route, are considered. On the other hand, a mathematical model reported by Valizadeh and Mozafari (2021) uses four cooperative game theory techniques, where genetic algorithms are used to obtain the solution. This strategy offers different incentives to contractors for collecting municipal wastes, allowing for solutions that demonstrate how collaboration among collectors lowers overall costs and encourage cooperation among collectors. A multi-objective optimization model for managing medical waste was proposed by Homayouni and Pishvaee (2020), where by using the epsilon constraint method and a network to distribute different amounts of medical waste to the current processing facilities, this strategy minimizes the cost and health risk associated with the medical waste produced during the pandemic. Although positive results have been noted, the distances between each processing center can cause rather high transportation expenses, which are not taken into account by this strategy.

As part of the search for a definitive solution to MSW management, different alternatives have been explored, with artificial intelligence-based (AI-based) methodologies being one of the most innovative (Andeobu et al., 2022). Smart waste management is a strategy that makes use of advanced technologies to dispose of waste profitably and efficiently. Artificial intelligence provides several methods that can be used to build intelligent waste management systems (Sinthiya et al., 2022; Abdoli et al., 2011). AI-based systems are used to solve challenging issues, deal with uncertainty, and demonstrate the effectiveness of intelligent systems (Ihsanullah et al., 2022). Integrated solid waste management strategies seek to generate methodologies that allow reducing the volume of garbage dumped in landfills. For this purpose, waste management is divided into the following stages: waste separation, collection and transportation, sub-waste separation, waste treatment, and final disposal (Antonopoulos et al., 2012). Within these stages, it is possible to incorporate machine learning (ML) models with different objectives; Rubab et al. (2022) proposed different alternatives for the use of AI-based models that allow for improving integrated solid waste management, the use of AI for the optimization of collection and transport routes, assignment of locations, and optimal numbers of incinerators and sanitary landfills are some examples of the proposed alternatives.

Learning about what happened in the current pandemic and taking advantage of all the information generated will mark the current and future challenges in waste management where a different set of tools will be used, which, being used creatively, will allow better planning in the face of future scenarios of emergency.

The main contributions of this work are based on the implementation of ML models to a mathematical model of multi-objective optimization that explores the plan of building an industrial park to handle the various types of generated MSW. This hybridization of the model will allow the prediction of different parameters over time to evaluate the long-term viability of installing different industrial parks under different scenarios. This will provide alternatives to the decision maker that, based on the observable benefits, will facilitate the choice of whether to construct an industrial park for the treatment of different wastes following a strategy based on the intensification of processes and the circular economy.

Problem statement

The increase in the generation of MSW during the pandemic carries different social and environmental risks (Luhar et al., 2022). Face masks, syringes, and surgical gloves, among others, were the first line of defense against COVID-19, and because of this, once used, they represent a great risk to anyone who may come into contact with these residues (Singh et al., 2022), at the same time, it reduces the possibilities of reuse or treatment thanks to established medical waste treatment guidelines, which makes medical waste a growing problem in the world (Hou et al., 2022); since the disposal and utilization of medical waste, even in developed countries, has not been explicitly planned (Le et al., 2022).

Social distancing and the change in lifestyle in general during the pandemic were also reflected in an increase in the use of disposable plastics (Haque & Fan, 2022; Igalavithana et al., 2022), as well as in food waste mainly in large cities (Çavuş et al., 2022; Iranmanesh et al., 2022). In developed countries, different strategies were implemented to deal with these new amounts of waste, new waste treatment facilities were installed, and policies were implemented in favor of prioritizing the treatment of medical waste (Andeobu et al., 2022). However, in underdeveloped countries there was no planning that could mitigate the problem represented by these new rates of generation of toxic waste; therefore, a large part of the waste generated ended up in open-air landfills, which represents great health and environmental risk for the region (Masud et al., 2023).

Although various approaches to waste management have been investigated, the COVID-19 pandemic-related conditions altered the dynamics of how waste must be managed (Ali & Parvin, 2022). Currently, it is possible to take advantage of the information generated during a health emergency that allows us to generate better waste management strategies (Chen, 2022), in order to be better prepared for the possibility of a future pandemic. The supply chain for waste management mostly consists of stages with high levels of uncertainty, such as classification, collection, and transportation, separating sub-waste, treatment, and final disposal (Fathollahi-Fard et al., 2020; Santibañez-Aguilar et al., 2013). Therefore, a deterministic approach may not be enough to generate robust waste management strategies. To address this problem, the use of hybrid mathematical models (mathematical optimization and machine learning) can be helpful to optimize an MSW management system during sanitary emergencies (Valizadeh et al., 2021).

Methodology

The methodology used in this work is based on a set of tools that allows for solving a specific part of the problem. The approach for the general solution is shown in Fig. 1 and consists of the cyclical solution of a mathematical optimization model that describes the supply chain, assigns the processing technologies for each sub-residue, and generates a green tax rate that seeks to promote the recycling even of those residues with low economic potential, this model is coded in the General Algebraic Modeling System (GAMS) while storing its results in GAMS Data Exchange (GDX) files to later be fed to an ML model programmed in Python that will be responsible for the prediction of the useful parameters for future iterations of the optimization model. Among these parameters, the waste generation rates are estimated based on different sociodemographic attributes such as unemployment, average family income, and the population over 45 years of age, characteristics of the case study. This optimization strategy based on “closed loop” data allows an organic integration of ML and mathematical programming, this “hybrid” system generates information on both sides (ML and mathematical programming) offering an efficient alternative for optimization problems under uncertainty (Ning & You, 2019). Below is a detailed description of the parts of the optimization model.

Fig. 1.

General optimization approach based on modeling and data systems

Data-based system

For the first part of the optimization model, the use of prediction tools is explored, particularly ML models that have shown good results in predicting the generation of MSW in different regions. According to the results in the work presented by Jahandideh et al. (2009) in terms of waste prediction, using ML algorithms present better behavior in complex nonlinear type problems than traditional regression methods. Figure 2 shows the graphic scheme of the methodology used for the data-based system. In the following section, the development of the ML model proposed for this work is discussed in detail.

Fig. 2.

Proposed scheme of the workflow of the machine learning model

Selection of significant socioeconomic parameters

Databases have become an essential tool in modern times, they allow access to a huge amount of data over time; however, these data do not initially express information, or there may be so much data that can reach to be overwhelming to obtain something useful from them, it is for this reason that a data mining must be carried out that allows us to extract a delimited set of useful data from which it is possible to extract relevant information. According to data presented by Ghinea et al. (2016), age plays a fundamental role in the generation of waste, this is mainly due to different social behaviors such as expenses, savings, or even changes in the increasingly sedentary lifestyle as the population approaches adulthood. Among other relevant socioeconomic parameters for the generation of waste is the quality of life, since it has been shown that a better quality of life also implies a greater generation of waste (Monavari et al., 2011). To be able to estimate the quality of life of a region is possible through different characteristic data of the region such as unemployment, level of education of the population, and life expectancy, among others. Knowing these data allows us to find a correlation between various social behaviors and waste generation; however, one of the main problems is precisely the availability of data, for this work different data sets available in the City of New York Data Database (NYC open data, 2022) were used, the selected socioeconomic data were annualized to homogenize the available data. Table 1 shows the list of socioeconomic indicators selected for further analysis and the possible selection of parameters for the ML model.

Table 1.

Selected socioeconomic indicators and their acronyms

Socioeconomic indicator	Census area	Abbreviation
Population over 45	Demographics	PO45
Median household income	Earnings and income	MHI
Unemployment ratio	Employment	UmR
School dropout	Education	ScD

Preprocessing of socioeconomic data

Figure 3 describes the different steps to perform the preprocessing of the data collected in this work. First, data preprocessing must be carried out, this being one of the most important stages. The data is usually obtained in a raw format (from a data lake) and is not specifically prepared for the task at hand. The data preprocessing is carried out through a series of steps, starting with taking the collected data and generating an adequate data structure, later a normalization of the data sets that present very different scales between their components is carried out, and if necessary, a filtering of the data must be carried out whenever atypical or abnormal data is presented. Frequently, the socioeconomic data collected, coming from censuses, is usually taken in different temporalities, so it is necessary to carry out interpolations, and extrapolations in some cases, for this work the data sets were reduced to an annual data set. For the data preprocessing in this work, Pandas and NumPy were used, both being Python libraries.

Fig. 3.

Data preprocessing methodology used to generate the training and validation data sets

Training and validation of models

During the modeling stage, different models were tested for each data set seeking to find the best correlation between variables. Given that ML algorithms can produce over-fit models, that is, they seem to have a very good fit with the training set, it was decided to divide the data sets in a ratio of 80:20 training–testing, being this data set division one of the most common (Azadi & Karimi-Jashni, 2016). To determine the significant variables of the model, different modeling configurations were tested, the validation criteria used were p value (p_value < 0.025) and the adjusted coefficient of determination (R²_adj), which are calculated as follows (Hastie et al., 2009):

$$R^2=\frac{{\sum }_{n=1}^N{\left({\widehat{Y}}_n-\overline{Y}\right)}^2}{{\sum }_{n=1}^N{\left(Y_n-\overline{Y}\right)}^2}$$ 1

$$R_{\text{adj}}^2=1-\left[\frac{\left(1-R^2\right)\left(n-1\right)}{n-k-1}\right]$$ 2

where ${\widehat{Y}}_n$ represents the value of the variable estimated by the model, $\overline{Y}$ is the average value of the variable, $Y_n$ is the real value of the variable for case n of the set of cases N, and k is the number of independent regressors (the number of variables in the model). The use of the adjusted coefficient of determination on the coefficient of determination (R²) should be highlighted. This is because R² has a disadvantage since R² increases its value for each variable added to the model, which may appear to be a better fit for a model with a greater number of variables, and this is not always the case; which does not happen when using R²_adj (Karch, 2020).

The p_value and R²_adj were calculated on each model for each training and testing set. As expected, the training sets obtain better results, that is, a better fit, this is mainly because the model parameters are adjusted based on the training set. Finally, the optimal complexity of the model (the one that best fits to evaluate unseen data) turns out to be a model composed only of 3 socioeconomic variables, PO45, MHI, and UmR, this model is selected based on the fact that it turns out to be the one that calculates the lowest p_values and best R²_adj values. To estimate the value of the socioeconomic parameters in years after the application of the strategy, different regressions were carried out for this set of independent data.

Machine learning strategy

Considering the data sets of the addressed case study, we decided to use random forest (RF) algorithms. However, for other case studies (including different types of data sets), other algorithms may need to be used. In RF algorithms, each decision tree is built from samples taken from the training set, and the division of the data set was carried out through random subsets, this source of randomness allows for the reduction of the variance of the forest estimator (Genuer, 2012). This randomness added to the model produces different decision tree models with different prediction errors, so, by taking an average of all the predictions it is possible to minimize some errors present in individual decision tree models. In the particular case of the model selected, a total of 10 estimators were used, namely, the regression model is composed of 10 trees, where the depth of each tree is defined until the minimum number of samples is reached to generate a split of samples, for this work it is established as 2.

The proposed ML model is capable of generating estimates of the solid waste produced in the region of the case study, in addition to the portion of that waste that will be disposed of at a landfill, this allows for generating different projections for subsequent years considering different scenarios of the strategy. To generate these projections, it is necessary to feed the solutions obtained in the mathematical optimization model to the ML (closed-loop optimization) (Ning & You, 2019) model and calculate the new rates of waste sent to the landfill as shown in the following equation:

$$\mathrm{\Delta }{\text{LW}}_{y,s}={\text{LW}}_{y,s}^{\text{ML}}-{\text{PW}}_{y,s}^{\text{optm}},\forall y\in Y,s\in S$$ 3

where $\mathrm{\Delta }{\text{LW}}_{y,s}$ represents the decrease in waste sent to the landfill, for year y and scenario s, ${\text{LW}}_{y,s}^{\text{ML}}$ represents the waste disposed of in landfills estimated by the ML model, and ${\text{PW}}_{y,s}^{\text{optm}}$ represents the processed waste estimated by the mathematical optimization model.

Model-based system

For the second part of the optimization strategy, the mathematical model based on the superstructure shown in Fig. 4 is presented. In the superstructure, the different and possible configurations of the supply chain for waste management are displayed, utilizing various technologies for various sub-waste types and penalizing the disposal of waste in sanitary landfills using green taxes at a variable rate.

Fig. 4.

Proposed superstructure for solid waste management through different technologies and disposal in sanitary landfills

Disjunctions to select the processing or treatment technique

One of the most relevant parts of the mathematical model consists of its ability to select the technology and its respective processing capacity with which each type of sub-waste will be treated. To achieve this, a series of disjunctions are proposed. It is important to highlight that the proposed objective function is the primary factor that determines which technology is chosen over others. The assignment of technologies is not limited to those shown in this work, and those selected are solely for illustrative and comparative purposes. The following disjunction is established for the best choice of the technologies suggested in the model:

$$\left[\begin{array}{c}{H}_{j,k}^{}\\ f_{j,k}^{}\ge {\delta }_{j,k}^{min}\\ f_{j,k}^{}\le {\delta }_{j,k}^{max}\\ {\text{cost}}_{j,k}^{}={\text{A}}_{j,k}^{}+{\text{B}}_{j,k}^{}·f_{j,k}^{}\\ \end{array}\right]\vee \left[\begin{array}{c}\neg H_{j,k}^{}\\ f_{j,k}^{}=0\\ cos{t}_{j,k}^{}=0\\ \end{array}\right],\forall j\in J,k\in K$$ 4

The technology to be used is determined by the Boolean variable $H_{j,k}^{}$. If $H_{j,k}^{}$ is true, the processing technique is chosen; otherwise, the processing technology is rejected. The parameter $A_{j,k}^{}$ is used to take into account fixed costs and $B_{j,k}^{}$ represents the variable costs in the disjunction previously described. The reformulated disjunction yields the algebraic relationships shown below:

$$f_{j,k}^{}\ge {\delta }_{j,k}^{min}·h_{j,k}^{},\forall j\in J,k\in K$$ 5

$$f_{j,k}^{}\le {\delta }_{j,k}^{max}·h_{j,k}^{},\forall j\in J,k\in K$$ 6

$${\text{cost}}_{j,k}^{}=kf\left(A_{j,k}^{}·h_{j,k}^{}+B_{j,k}^{}·f_{j,k}^{}\right),\forall j\in J,k\in K$$ 7

$h_{j,k}$ is a binary variable, and when it has a value of 0, the technology is dropped, but when it has a value of 1, it is chosen to be used. In all circumstances, the annualization factor kf is applied to the capital expenses, and the parameter $\delta$ indicates the search limits for the quantities of the material to be processed. These values are established with a lower limit close to 0 and an upper limit depending on the specified objectives.

Taxes to promote recycling and waste processing

Based on a strategy proposed by Ko et al. (2020) for a fictitious scenario in South Korea, where recycling is promoted through fees to mitigate the social and environmental repercussions of the COVID-19 pandemic. “Green taxes” are implemented to encourage environmental preservation (Oates, 1995; Paut-Kusturica et al., 2020). To establish these taxes, in the first place, $T^{\text{Landfill}}$ distinguishes the waste that will be charged with a low or large penalty, and two new criteria are taken into consideration. $T^{\text{land}L}$ denotes waste that will be subject to a moderate tax penalty and $T^{\text{land}H}$ indicates waste that will incur a significant tax penalty.

$$T^{\text{Landfill}}=T^{\text{land}H}+T^{\text{land}L}$$ 8

As a result, the following disjunction is proposed:

$$\left[\begin{array}{c}{H}^{\text{Landfill}}\\ T^{\text{land}H}<T^{\text{II}}\\ \end{array}\right]\vee \left[\begin{array}{c}\neg H^{\text{Landfill}}\\ T^{\text{land}H}\ge T^{\text{II}}\\ T^{\text{land}H}\le T^{\text{III}}\\ \end{array}\right]$$ 9

where $T^{\mathrm{II}}$ is the upper bound for waste produced that is subject to low tax penalties, but it is also the lower limit for waste that is subject to severe tax penalties. $T^{\mathrm{III}}$ is the upper bound for the waste penalized by the high tax. For this work, a tax rate of 5.1 $US/ton (proposed previously by Munguía-López et al., 2020) is established as a high penalization to promote recycling. On the other hand, a tax value of 2 $US/ton is considered as a low penalty. The previous disjunction can be expressed as follows:

$$T^{\text{land}L}<T^{\text{II}}·h^{\text{Landfill}}$$ 10

$$T^{\text{land}L}\ge T^{\text{II}}\left(1-h^{\text{Landfill}}\right)$$ 11

$$T^{\text{land}H}\le T^{\text{III}}\left(1-h^{\text{Landfill}}\right)$$ 12

Lastly, the following relationships can be used to obtain the total taxes:

$${\text{Taxes}}^L={\text{TPT}}^L·T^{\text{land}L}$$ 13

$${\text{Taxes}}^H=TP{T}^H·T^{\mathit{landH}}$$ 14

where ${\mathrm{TPT}}^L$ is the low unitary tax and ${\mathrm{TPT}}^H$ is the high unitary tax.

$$\text{Taxes}={\text{Taxes}}^L+{\text{Taxes}}^H$$ 15

Proposed goals to promote waste processing

According to the location where the superstructure is proposed, it is possible to suggest several objectives, such as minimizing the effect on the environment, maximizing profits, or favoring social development. Reducing the amount of unprocessed waste is necessary to limit the environmental effect.

In contrast, landfills offer a significant environmental concern due to the type of waste that is disposed of there (which also poses a risk to human health) as well as the discharge of dangerous pollutants into the groundwater and soil. These leaks are frequently brought on by the precipitation of water, which creates high-risk leachates that might contain heavy metals, solvents, nitrogen, chlorides, and volatile organic compounds. No matter how many barriers, liners, and pipelines are set up to try to reduce danger, harmful chemicals will always seep into the ground and water from landfills (Pecci, 2018).

Large cities must send a specific quantity of solid waste to a landfill because waste processing capacity is limited. To protect the environment and reduce the amount of green taxes the model assigns, it would be beneficial to reduce the quantity of waste that is received. Therefore, the following objective function is proposed:

$$min{T}^{\text{Landfill}}$$ 16

If increasing economic profit is the goal, the following objective function must be applied to increase overall profit:

$$\text{max}\text{Total}\text{profit}$$ 17

Solution procedure

The proposed approach involves parameter prediction using ML and a deterministic optimization strategy, which is described as follows:

• The prediction of the necessary parameters to run different simulations over time is carried out through an ML model that, based on different socioeconomic data, predicts the amounts of waste generated annually and the amounts of waste that cannot be treated and are sent to the landfill, to make these predictions a random forest algorithm belonging to the supervised learning branch is used, this method generates different decision trees to calculate the final output. This ML model was coded in Python and stored its results in spreadsheets to later be fed to the optimization model to calculate the objective functions of new iterations. After solving the optimization model, the data is stored back in GDX files to be fed back to the ML model that will calculate the new waste generated and sent to the landfill, which allows comparing one scenario against another.

• The GAMS modeling environment is used to solve a mathematical optimization model that is based on the superstructure depicted in Fig. 4. The many technologies that can be used to treat the waste are shown in this figure along with a distribution network for waste management. The input parameters of the model are determined by the ML model. The model is a mixed-integer linear programming problem (MILP) that was solved using the epsilon constraint method (Diwekar, 2008), varying the maximum production capacities of the technologies, this allows for establishing different scenarios where more or less waste is processed. Afterward, the mathematical model is solved to get the maximum profit, which directs the solution to the selection of those technologies that are less expensive and produce more economic benefits. Additionally, using the variable green taxes, the model estimates and penalizes the waste sent to landfills. This strategy enables finding a balance between the economic and environmental benefits since disposing of most of the waste in landfills implies a higher tax payment.

Addressed case study: distribution of urban solid waste in New York City

To apply the proposed methodology, we used New York City as a case study. The generation of infectious waste from COVID-19 has a particularly negative influence on this city because it is one of the cities that produces the most waste each year (DSNY, 2020). Also, this city generates a large amount of data annually (Campbell, 2017), which is ideal for using supervised learning algorithms. Unfortunately, there was an increase in demand for medical products during the COVID-19 epidemic, including masks, goggles, gloves, cleaning supplies, and gowns. Due to these increases and the home trash generation, it became a significant issue for the city (Chand et al., 2021). Nowadays, waste management is done by commercial and public contractors, and waste is divided into three sorts: paper, metal/plastic/glass, and mixed solid waste (waste that cannot be recycled) (Nagle, 2013). About 75% of the paper, glass, plastic, and other materials that are discarded are recycled at the Brooklyn facility for material recovery at Sunset Park, which is the main recycling facility. Nevertheless, near to 75% of the mixed MSW is sent to a landfill 965 km away, and only 20% of it is incinerated to create energy (Galka, 2016). There are currently nine medical waste disposal facilities in New York City, with a 12,000 ton of annual disposal capacity, where COVID-19-related medical waste treatment accounted for 60% of this capacity (Mei et al., 2021). For this work, it is proposed that an enhanced industrial park be built in the Staten Island area, we consider the transportation costs for this region.

Results and discussion

The following section presents the results of the waste management system obtained through the optimization strategy. First, we discuss the results of the deterministic mathematical model formulation. Then, we present the predicted waste collection over time based on the socioeconomic data. Finally, we discuss some selected optimal solutions over time from the projections of the machine learning model. The deterministic mathematical model formulation applied to the New York City case study consists of 63 binary variables, 317 continuous variables, and 341 equations. The solution to the resulting problem (MILP) was obtained by changing the maximum processing volume for each of the cases in the restricted epsilon technique. This model was coded in the GAMS modeling environment using the CPLEX solver. The ML model coding was done in the Python programming environment, the model was trained from an annualized data set collected since 2000, composed of three significant socioeconomic variables PO45, MHI, and UmR. As a prediction tool, RandomForestRegressor from the Sci-kit learn library was used with several estimators of 10 using the P value and R²_adj as validation parameters.

There are multiple Pareto solutions to the established problem; however, 4 of all those possible solutions have been selected to be analyzed, these solutions are found in different regions of the Pareto curve shown in Fig. 5. The most ideal scenario is illustrated by solution A, where it is possible to construct an industrial park with the capacity to completely process all waste produced in the area. However, this is very challenging to accomplish, primarily due to the enormous size and investment that would be necessary to construct an industrial park with such capacities. In contrast, solution B offers a solution that, while differing from solution A, still falls inside the area with the lowest rate of green taxes, resulting in a “low” level of waste transported to the landfill in comparison with the other scenarios, in addition, to generate a good balance between economic and environmental benefits (Fig. 6 shows the technologies used to reach this solution). On the other hand, solution C falls in the region with a higher tax rate, although it still generates economic benefits, these can be low. The final option, solution D, is presented. Under this option, substantial amounts of waste are dumped in landfills resulting in economic losses.

Fig. 5.

Deterministic model results for COVID-19 conditions

Fig. 6.

Solution B: Technologies selected by the model to achieve a solution with the lowest rate of green taxes, maximizing economic benefits

In general, it can be seen that for all the proposed solutions, the main income comes from the sale of recycled materials, while income from energy and compost production begins to increase as scenarios with greater recycling capacity are chosen; on the other hand, the main costs are given by the separation and transport of the waste, these become even higher than the total income in solution D. The treatment costs, as expected, increase in scenarios with a greater processing capacity; on the contrary, the costs associated with the payment of green taxes decrease. In solution D, they represent a significant expense. As the solutions approach a scenario that recycles larger amounts of waste such as solution B, this cost becomes insignificant. The costs involved with treating glass (77% of the waste recollected is treated) make up a significant portion of the solution B treatment costs, which are shown in Fig. 7, along with the revenues obtained for wastes that are used to produce new materials. However, the economic benefits associated with the sale of new glass are only 1% of the total benefits, then from an economic point of view, not processing this type of waste could be a better option, but the inclusion of green taxes would generate penalties that would be more expensive than processing this type of waste with low economic potential.

Fig. 7.

Solution B: Comparison between treatment costs and economic benefits from the sale of new materials produced by the strategy

Figure 5 shows a Pareto curve resolved under the conditions presented in 2018, in which better economic benefits are observed for most solutions, with the established regression models it is possible to develop an ML model that uses an algorithm of random forests that seeks to predict the amounts of MSW collected and waste sent to landfill year by year. Figure 8 shows different useful regressions for each set of socioeconomic data, these regressions allow for generating the complete data set that allows predicting the waste collected in subsequent years, these datasets show clear trends and a low statistical dispersion, which allows us to obtain models and predictions with very acceptable values of R²_adj, where PO45 shows to have a good fit with a linear regression model, MHI, on the other hand, shows a better fit with a Polynomial regression model, and, finally, UmR shows its best fit with a support vector regression (SVR) type model. Figure 9 shows a possible projection for the tons of garbage that will be generated from the year 2022 until the year 2035 based on the projections generated from the aforementioned socioeconomic parameters. These estimates show a slight decrease in the production of waste for years after the pandemic. Figure 10 shows the adjustment obtained from the ML model in addition to the set of solutions B, C, and D. It is worth noting that solution A is on the time axis where all the residues are processed. For this particular case, the year 2018 is proposed for the implementation of the strategy to compare the results with a longer term, where it is noted that by 2020, the amount of waste delivered to the landfill has increased regardless of the suggested solution. This is a result of the COVID-19 epidemic beginning in the New York region; however, even with solution D, there is a significant decrease in the amount of waste delivered to the landfill. Taking into account the risk associated with the waste generated during the pandemic, solution D represents the solution with the lowest social benefit, in addition to being the one that generates the most taxes. This makes solutions B and C the most viable since they provide a better balance between economic and social benefits, as shown in Fig. 5.

Fig. 8.

a Linear regression model for the prediction of the population over 45 years of age. b Polynomial regression model for the prediction of median household income. c Support vector regression model for the prediction of the unemployment ratio

Fig. 9.

Machine learning model for the prediction of municipal solid waste collected based on population over 45 years of age, median family income, and unemployment ratio

Fig. 10.

Solutions obtained over time from the projections of the machine learning model

Conclusions and future research directions

The correct management of MSW generated during pandemics is essential. Improper handling of these residues can generate great environmental and social impacts that can threaten human health. To encourage recycling and the treatment of waste with low economic potential, this paper provides a waste management strategy that employs a variable rate of green taxes. An ML prediction model and a deterministic mathematical optimization model are combined in this approach. The deterministic model enables planning the construction of an industrial park that will be in charge of processing all types of waste produced. The model was able to identify the optimal processing technologies and their capacities according to the established objectives, in addition to using a variable green tax rate relating to the waste that is dumped in a landfill. On the other hand, due to the complexity of the problem, in addition to the uncertainty associated with the generation of waste, it is of great importance for the decision maker to generate projections of the strategy over time that allows for selecting the option that best suits the region. For this reason, useful socioeconomic data are collected to generate an ML prediction model that uses random forest algorithms.

Using New York City as a case study, the implementation of the strategy was demonstrated. According to the findings, it is possible to create solutions that help find a balance between social, environmental, and economic goals by analyzing the scenarios provided and developing an industrial park with the capacity to manage all waste produced. This model is useful in areas with inadequate management of urban waste, which results in high risks for the population. Furthermore, the prediction model helps identify these solutions for future scenarios.

Considering the limitations of the presented study, the following future work is recommended:

• Consider social objectives, such as employment creation in the MSW system.

• Implement a life cycle analysis of the strategy to compare in more detail the environmental impacts associated with each of the proposed process routes.

• Evaluate new case studies with different sets of technologies seeking to generate new waste management structures.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

All authors contributed to the study conception and design, as well as writing and reviewing.

Funding

This work was supported by CONACyT.

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Conflict of interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.