A Heuristic Procedure for Improving the Routing of Urban Waste Collection Vehicles Using ArcGIS

Abstract

This paper proposes a heuristic procedure created to improve the collection routes obtained with the support of the ArcGIS software and its complement, Network Analyst. After a series of experiments, it was found that the software presents several inconsistencies with logistical and operational management concepts, such as the unnecessary realization of U-turns in a dead end and unnecessary access to areas with difficult access to a single customer. These are issues that a collection route planner must consider to make a good decision that considers the cost of visiting areas with difficult access and the benefits of reaching that area. In this sense, our heuristic procedure considers a set of best practices in operational and logistical strategies that could be programmed within the Network Analyst. As it is well known in the science of vehicle routing, U-turns and sub-tours in the routes travelled by vehicles increase distances and operating costs, so in our work, we propose a systematic heuristic procedure to reduce the number of U-turns performed by a municipal waste collection truck, while using the ArcGIS-Network Analyst add-on to reduce the number of sub-tours in the route under the Directed-Capacitated Arc Routing Problem approach. It is then shown how the routes improved using our conceptual heuristic procedure, which provides better quality than the original routes obtained with ArcGIS and Network Analyst. Specifically, reducing the total distances travelled by the vehicle fleet, increasing the coverage of sidewalks visited by the truck in the urban perimeter of a city, and minimizing the time used in municipal solid waste collection operations. The importance of our work lies in the fact that effective MSW management is an essential municipal service whose regulation can drive innovation, sustainability, and efficiency in the MSW sector.

1. Introduction

There is great interest worldwide in developing an integrated municipal solid waste (MSW) management model that considers the entire life cycle of MSW to prevent and minimize waste while contributing to sustainable community development and climate change mitigation. According to this approach, MSW collection is essential to ensure proper population health management and should, therefore, be carried out optimally and sustainably [1].

In several North American countries and developing countries in Latin America, municipal solid waste management is the responsibility of government agencies. In some cases, however, this responsibility is assumed by private companies that derive most of their revenue from waste collection using fleets of vehicles [2]. As a result, this issue has traditionally concerned the various departments responsible for the operations of these companies [3], leading them to conduct in-depth analyses of their internal processes. These analyses led them to conclude that it was possible to reduce operating costs by using their assets better (i.e., by having an integrated system for planning appropriate vehicle routes for waste collection) [4].

The vehicle routing problem associated with collecting residential, commercial, and industrial solid waste is technically known as the Waste Collection Vehicle Routing Problem (WCVRP). It is primarily concerned with the simultaneous collection and sorting of different types of waste and their transportation to landfills for final disposal. Both public and private entities can perform these operations. Key elements of the WCVRP include a fleet of vehicles, transfer stations, disposal facilities, a depot, and waste containers that serve as collection points. Most WCVRP-related research is aimed at minimizing the distances travelled by waste collection vehicles [5,6,7].

Geographic Information Systems (GIS) are computer-based tools that collect, store, analyze, manage, and present spatial or geographic data. They allow the visualization and analysis of data in a geographic context, making them a valuable tool for various applications, including MSW collection [6,8,9]. Several studies have explored the application of GIS in optimizing the location and management of waste accumulation points (GAPs) and collection routes [10]. Several Geographic Information System (GIS) software applications have been used in studies related to municipal solid waste collection, such as ArcGIS software, ArcGIS Network Analyst, R the osmar package, and QGIS open-code software [11], among others [12,13].

Network Analyst is an extension to ArcGIS that enables the modelling and analysis of transportation networks such as roads, streets, railways, etc. It proved to be an invaluable tool for routing municipal solid waste collection trucks. Network Analyst allows the development of a detailed transportation network that accurately represents the hierarchy of roads, traffic directions, turn restrictions, and other relevant factors. This network facilitates the analysis of optimal routes for collection trucks, minimizing distances, travel times, and operating costs. In addition, it allows the incorporation of the locations of waste containers and their requirements, allowing for the generation of balanced routes that effectively cover the entire service area. Network Analyst also allows the exploration of different scenarios by evaluating different collection strategies [12,13].

In this sense, this paper aims to contribute to research conducted on the case study of Canton Ibarra, which our research group has addressed since 2016 [14,15,16,17]. We propose an experimentally obtained heuristic procedure that attempts to minimize vehicle routes to improve the results automatically generated by geographic information systems such as ArcGIS. The importance of our research lies in the recognition that competent management of MSW is a core municipal service. Its proper regulation not only catalyzes innovation, but also promotes sustainability and increases efficiency within the MSW sector.

Therefore, the specific objectives of this paper are to propose a procedure aimed at:

• Reducing total route distances travelled by the vehicle fleet.
• Increasing the coverage of sidewalks used by trucks in the urban periphery of the Ibarra Canton.
• Minimizing time spent on MSW collection operations in said canton.

A Brief Literature Overview of Implementation of SIG in MSW Routing

For the literature review on the implementation of GIS in the optimization of municipal solid waste collection routes, we consulted the Scopus database using the following search terms: “(title (geographic AND information AND systems) OR title (gis) AND title (waste AND collection) AND title (routing) OR title (routes))”. Below are the results of recent implementations in this important area.

First, Karadimas et al. (2005) used an ArcGIS-based GIS system to integrate waste production modelling in Athens, Greece [18]. Eugster and Schlesinger (2013) introduced $osmar$, an R package that allows interaction with OpenStreetMap data, which could be useful for analyzing urban waste collection scenarios [19].

Rada et al. (2013) analyzed the implementation of a web-GIS system to optimize the selective collection of municipal solid waste in two Italian municipalities using RFID-tagged bins, GPS-tracked collection vehicles, and route optimization software. In the northern municipality, the implementation of such a system increased recycling from 28% to 80% in a decade. In the southern municipality, selective collection was introduced to increase very low recycling rates. Rada et al. emphasized the need for user communication and explored its applicability in developing countries such as China and Malaysia. One limitation was increased system costs [20].

Boskovic and Jovicic (2015) used Network Analyst, consisting of a recently introduced add-on for ArcGIS, to design the optimal location of waste collection points in a sector of Kragujevac, Serbia [21].

Gallardo et al. (2015) proposed a GIS-based methodology to design a complete waste collection network in Castellon, Spain, using ArcGIS software [22].

Later, Titrik (2016) proposed a sign-in time-based info-communication system to detect full waste containers and optimize collection routes in Hungary using measuring devices, transponders, and web GIS technology. This made it possible to add additional collection stops and redefine routes. Key innovations were saturation measurement and rea-l-time communication to ignore unnecessary emptying. The main benefits were reduced environmental impact, improved road safety, and operational optimization. Limitations were increased collection times and the need for different vehicle sizes [23].

Cavdar et al. (2016) designed and piloted a smart waste collection system in Kestel, Turkey, combining optimized routing, sensor-equipped containers, and a centralized monitoring portal. Over two years, they adapted the system for 50,000 residents and demonstrated savings of 50–80% compared to traditional collection. Their system is an example of an integrated smart city infrastructure [24].

Erfani et al. (2018) also used ArcGIS Network Analyst to rearrange the distribution of garbage collection points and determine the number of bins needed in Dhanbad, India, and Mashhad, Iran [25].

Rizvanoglu et al. (2019) implemented linear programming and geographic information system (GIS) analysis using ArcGIS to optimize municipal solid waste collection and transportation routes in Şanlıurfa, Turkey. They evaluated an existing collection route and proposed optimized alternatives, which resulted in 28–33% savings in route distance. Their study contributed to applying optimization methods to improve MSW collection efficiency [26].

Quiñones et al. (2019) developed TapeYty, an open-source software that integrates mathematical programming and GIS, to generate optimal waste collection routes in Asunción, Paraguay. By applying it to an existing waste route, they achieved a 20% reduction in the distance travelled. Their tool allows for customization for different cities and route constraints [27].

Ferronato et al. (2020) used QGIS in La Paz, Bolivia, to evaluate the implementation of selective waste collection and the integration of informal waste pickers. They found that including waste pickers could reduce costs by 10%, increase recycling by 3.5%, and reduce collection distances by 7%. Their analysis demonstrates the benefits of incorporating informality into MSWM planning [28].

Amal et al. (2020) proposed a GIS-based multi-criteria decision analysis using the ELEC-TRE III methodology to evaluate municipal waste collection scenarios in Sfax, Tunisia. Comparing four service options, they found that the consolidation of transfer stations optimizes distances and costs. Their methodology facilitates a standardized comparison of alternatives. They built GIS models and used the ELECTRE III methodology to evaluate four MSW collection scenarios for Sfax, Tunisia. When compared on six criteria, a route consolidating to one transfer station achieved the lowest distances and costs. Their integrated framework allowed for standardized comparison, sensitivity analysis, and identification of a robust solution but lacked dynamic elements [29].

Vu et al. (2020) modelled changes in waste density over time to assess the impact on dual-compartment truck routing in Austin, Texas. Density significantly affected route distances and times across 48 scenarios varying in collection frequency, truck size, capacity, and compartment ratio. Notably, a 50/50 truck ratio performed best. They highlighted relationships missing from other geospatial studies that could inform truck selection and rerouting policies [30].

León et al. (2020) [14] present a proposal to optimize the municipal solid waste collection routes in the canton of Ibarra, Ecuador, using geographic information systems (GIS). The methodology consisted of consolidating an updated geographic database and processing the information in ArcGIS software. Based on a previous study that divided the canton into collection districts, 11 micro-routes were designed, considering aspects such as waste generation rates, collection frequencies, and the operating costs of collection trucks [8]. The results were compared with the current empirical model implemented in the canton, using indicators of the cost per tonne collected in each route. The proposed model reduced the average collection cost.

Smita (2021) used ArcGIS to map waste flows, design optimal MSW routes, and site facilities in Nagpur, India. Comparing the current decentralized collection system with the proposed centralized routing via transfer stations, they projected a reduction in transport distance and cost of over 9%. Their ward-level data and GIS platform could improve local planning and policy. But they did not include informal recycling [31].

Samra et al. (2023) applied GIS network analysis in Pakistan to optimize municipal solid waste transport routes based on travel time. Statistical analysis revealed relationships between travel time, population, and route stops. Their predictive model could aid MSW planning in Pakistani cities and other transportation optimization contexts. However, they did not compare existing and optimized routes or quantify potential time savings [32].

More recently, Bošković et al. (2024) highlighted regulations and trends in municipal solid waste (MSW) collection services. In recent years, there has been an exponential increase in global efforts to improve MSW management systems, with a particular focus on the waste collection and transportation segments. These initiatives have aimed to drive innovation, sustainability, and efficiency within the MSW sector. Key regulations and trends included using digital technologies such as GIS, IoT, and data analytics to optimize waste collection routes, reduce energy consumption and environmental protection, improve service quality, and promote circular economy practices. In addition, there was a growing emphasis on cost-saving measures, route optimization strategies, and the reduction in greenhouse gas emissions in the MSW collection and transportation processes [33].

Table 1. Recent implementations of SIG in MSW routing.

Reference	Place	Principal Results
Karadimas et al. (2005) [18]	Athens, Greece	Reduction in the number of waste bins to be placed in sub-areas of the city. The bins are better distributed to ensure optimal quality of waste collection services, which also means fewer waste transport routes.
Eugster and Schlesinger (2013) [19]	Auckland, New Zealand	They presented a GIS environment that can be analyzed from R, specifically waste collection networks for the University of Aukland.
Rada, et al. (2013) [20]	Italy	Increase in recycling from 28% to 80% within a decade in the northern municipality; introduction of selective collection in the northern municipality; increase in recycling from 28% to 80% within a decade in the northern municipality; introduction of selective collection in the northern municipality.
Boskovic and Jovicic (2015) [21]	Kragujevac, Serbia.	The application of the methodology in the Kragujevac area made it possible to optimize the location of collection points and the number of containers, resulting in economic savings, increased efficiency, and reduced emissions. Specifically, the time required for waste collection was reduced by approximately one hour, which translates into annual fuel savings of approximately 1700 euros.
Gallardo et al. (2015) [22]	Castellón, España.	Optimal locations for waste disposal points (door-to-door, curbside, clean points) were determined using a Geographic Information System (GIS). Furthermore, a detailed design of the waste pre-collection system for Castellón was obtained.
Titrik (2016) [23]	Hungary	Innovations in saturation measurement and real-time communication; reduced environmental impact and improved traffic safety.
Cavdar et al. (2016) [24]	Kestel, Turkey	Savings of 50–80% over traditional collection for 50,000 residents.
Erfani et al. (2018) [25]	Mashhad-Iran.	Several models were applied to improve a given MSW management system, then these models were compared in terms of minimizing the number of facilities required to cover up to 98.56% of the demand points but maximizing the coverage of these facilities to place the optimal number of facilities so that the distance from a generator to the facility is not excessive; specifically, the large percentage of inhabitants were located between 50 and 100 m. Finally, the service area was analyzed to determine the population’s accessibility to the stations.
Rizvanoglu et al. (2019) [26]	Sanliurfa, Turquia	Savings of 28–33% in route distance through linear programming and GIS analysis.
Quiñones et al. (2019) [27]	Asuncion, Paraguay	A total of 20% reduction in waste collection routes with TapeYty software.
Ferronato et al. (2020) [28]	La Paz, Bolivia	A total of 10% reduction in costs, 3.5% increase in recycling and 7% reduction in collection distances.
Amal et al. (2020) [29]	Sfax, Tunisia	Identification of optimized service options through multi-criteria decision analysis. Evaluation of waste collection scenarios with an integrated approach but without dynamic elements.
Vu et al. (2020) [30]	Austin, Texas, EE. UU.	Analysis of waste density and its impact on collection routes, highlighting the relationship between truck size and efficiency.
León et al. (2020) [14]	Ecuador	Reduction of the average collection cost from 37.53 $/t to 8.27 $/t using ARC-GIS, achieving a more balanced distribution of costs across routes, and increasing service levels by ensuring that collection trucks visit all areas daily.
Smita (2021) [31]	Nagpur, India	Projected reductions of 9% in distance and transportation costs, improving local planning.
Samra et al. (2023) [32]	Pakistan	Development of a predictive model for MSW route optimization, but without quantitative comparison.
Bošković et al. (2024) [33]	Servia	Decrease in total distance travelled ranges from 5.1 to 15.1%

below summarizes recent implementations in this important area.

While most studies have focused on specific aspects of waste management, such as GAP location or route optimization, some researchers have proposed more comprehensive methodologies using GIS capabilities [22]. However, the integration of GIS with other optimization techniques, such as mathematical programming or metaheuristics, could further improve the efficiency and applicability of these approaches [34]. This fact shows the importance of modelling in vehicle routing problems [35]. In addition, the above studies collectively illustrate the transformative impact of GIS and Web-GIS technologies on improving MSW management. They highlight the potential for significant efficiency gains, cost savings, and environmental benefits. However, challenges such as system cost, operational complexity, and the need to integrate informal sectors remain. These research efforts provide a roadmap for future innovation and policy formulation in sustainable waste management. In addition, there are new projection strategies that are currently being used to solve the path planning problem, such as the complex network method, graph neural networks, and others, which we plan to explore in future work [36,37]. However, these strategies are not yet available in the ArcGIS software, so they are beyond the scope of this study.

Given the above background, the main objective of our research will be to propose and validate a heuristic procedure to improve the performance of the routes provided by ArcGIS software and its complement Network Analyst. Specifically, to reduce the use of subtours and U-turns on the route to be travelled by the MSW collection truck.

The paper is structured as follows: First, general aspects of MSW collection systems are reviewed, emphasizing Latin America and the Caribbean (LAC) aspects. Then, recent research on the implementation of GIS in MSW collection is reviewed, trying to find common aspects and highlighting the results obtained in such implementations. Subsequently, Section 2 describes the main tools and methodologies for optimizing MSW collection, such as macro- and micro-routing, with special attention to the Directed Capacitated Arc Routing Problem (CARP) model, which by its nature captures most of the characteristics of the problem in collection systems in LAC cities. Subsequently, in this section, and considering the impact of U-turns and subtours in the generation of an optimal micro-routing of MSW collection trucks, a systematic heuristic procedure is proposed to improve the result of such routing, specifically when such micro-routing is performed under the DCARP approach in a GIS environment by means of ARC-GIS. Then, using a case study of a small city in Ecuador, we implement the micro-routing of a municipal solid waste collection truck crew using ARC-GIS, and then we implement our heuristic improvement procedure to compare the results obtained by applying our heuristic procedure. Finally, we present the results obtained and the conclusions of our proposal.

2. Materials and Methods

2.1. Macro-Routing and Micro-Routing of Waste Collection Vehicles

2.1.1. Macro-Routing

Macro routing refers to a municipal area’s high-level division and allocation into distinct subzones or districts for waste collection, Macro-routing will take place within the residential, commercial, rural, or industrial zones of a city, depending on how it is previously divided. As defined by Herrera-Granda et al. (2019), macro-routing strategically divides a zone or region to balance the workload across collection subzones, reduce operational costs, and increase service levels. It considers population growth, waste generation rates, truck capacity, terrain, and regulatory policies to delineate feasible districts. Equitable distribution of waste collection workloads facilitates planning and monitoring of subsequent micro-routing tasks [17,38,39]. This concept can be observed in Figure 1.

2.1.2. Micro-Routing

Micro-routing involves detailed street-level routing to optimize individual collection vehicle paths within each subzone. Like León-Jácome et al. (2020) [14], micro-routing tackles the capacitated arc routing problem to minimize route distances and times across a subzone’s entire road network graph. It incorporates granular data on road layouts, weights, directions, and waste volumes at the stop-level to find cost-effective trajectories that visit all waste nodes. By sequencing roads based on constraints such as truck size and frequency, micro-routing ensures that truck capacity is fully utilized to provide reliable service. Integrated with macro-routing zoning, optimized micro-routes balance workloads, reducing costs and emissions. It is important to note that the first step in performing micro-routing is to divide the territory into n subzones with similar collection service needs, and within each subzone we define a route for the collection truck to travel to cover the greatest number of roads within that subzone while respecting existing road and geographic constraints [14,40,41,42]. The concept of micro-routing can be observed in Figure 2.

2.2. Capacitated Arc Routing Problem (CARP)

The Capacitated Arc Routing Problem (CARP) is a type of vehicle routing problem where the demand for service is located at the edges, or arcs, of a network rather than at the nodes. In CARP, the goal is to find the optimal set of routes to serve all required arcs in a network while respecting vehicle capacity constraints [43,44]. Some key elements of CARP include:

• A network of roads/streets represented as arcs or edges between nodes.
• A fleet of vehicles with limited capacity.
• Demand for services located on the arcs (e.g., garbage collection, street sweeping).

The goal is to find routes that cover all required arcs exactly once without exceeding vehicle capacity.

CARP is well suited to modelling problems such as garbage collection, where service demands are along road segments rather than at specific collection points. It extends concepts from the Chinese postman problem to capacitated vehicles. CARP models have been applied to waste management, street sweeping, snow removal, and other public sector operations. By solving CARP, municipalities and contractors can optimize route plans to reduce costs and emissions. Recent advances in metaheuristics and GIS analysis have increased the size and complexity of the problems that can be effectively addressed.

More specifically, the Capacitated Arc Routing Problem (CARP) is a routing problem that considers vehicle capacity and ensures that the sum of demands on each arc (edge) does not exceed it, starting from a depot. The goal is to traverse or make a tour through all arcs (streets and avenues) within a given graph (route) G with minimum cost. Each arc $(vi, vj)$ has a positive demand $qij$, and there is a fleet of m homogeneous vehicles with capacity $W$ based at vertex $v1$.

CARP is a generalization of the Capacitated Chinese Postman Problem (CCPP) with $qij>0$ for all $(vi, vj)$ established by Eiselt et al., 1995b [45]. Three main formulations have been proposed for CARP: the directed formulation by Golden and Wong [46], the undirected formulation by Belenguer and Benavent (1991) [47], and the lower bound formulation by Benavent (1992) [48]. These generalizations provide a resolution structure for the routing problem through mathematical algorithms and heuristic methods.

The directed CARP formulation uses binary variables $xijk$ and $yijk$ to denote if an arc $(vi, vj)$ is traversed from $vi$ to $vj$ by vehicle $k$ and if it is serviced, respectively. Constraints ensure flow conservation, service requirements, capacity limits, and the elimination of illegal subtours.

The undirected CARP formulation by Belenguer and Benavent defines $xijk$ and $yijk$ only for $i<j$, with $xijk$ representing the number of times vehicle k traverses the edge $(vi, vj)$ without servicing it. Constraints guarantee that required arcs are serviced exactly once, as well as capacity limitations and connectivity requirements.

Benavent’s lower bound formulation LB4 directly accounts for vehicle capacity constraints. It uses a dynamic programming algorithm to generate a lower bound on the cost of a route from the depot to a given vertex with a total load, where each required edge is served only once, as shown in Figure 3.

Due to the existence of directed arcs in the roadmap of a city, we decided to use the Directed CARP, and we will explain this model, which is the most suitable for the WCVRP.

Formulation of the Directed CARP (DCARP)

For the formulation of the directed CARP (DCARP), the binary variables ${\mathit{x}}_{\mathit{i}\mathit{j}\mathit{k}}$ are equal to $\mathbf{1}$ if and only if the edge $\left({\mathit{v}}_{\mathit{i}},{\mathit{v}}_{\mathit{j}}\right)$ is traversed from ${\mathit{v}}_{\mathit{i}}$ to ${\mathit{v}}_{\mathit{j}}$ by the vehicle k, and the binary variables ${\mathit{y}}_{\mathit{i}\mathit{j}\mathit{k}}$ are equal to $\mathbf{1}$ if and only if $\left({\mathit{v}}_{\mathit{i}},{\mathit{v}}_{\mathit{j}}\right)$ is served by vehicle $\mathit{k}$ while travelling from de ${\mathit{v}}_{\mathit{i}} to {\mathit{v}}_{\mathit{j}}$ [46]. Note that ${\mathit{x}}_{\mathit{i}\mathit{j}\mathit{k}}$ is bounded by $\mathbf{1}$, since it is never optimal for a vehicle to traverse an edge more than once in a given direction. All arcs $\left({\mathit{v}}_{\mathit{i}},{\mathit{v}}_{\mathit{j}}\right)$ with ${\mathit{q}}_{\mathit{i}\mathit{j}}>\mathbf{0}$ must be served, just as the remaining arcs can also be traversed [45,49].

Further, E(S) is defined $\mathit{E}\left(\mathit{S}\right)=\{\left({\mathit{v}}_{\mathit{i}},{\mathit{v}}_{\mathit{j}}\right):{\mathit{v}}_{\mathit{i}}\in \mathit{S},{\mathit{v}}_{\mathit{j}}\in \mathit{V}\backslash \mathit{S}\mathit{o}{\mathit{v}}_{\mathit{i}}\in \mathit{V}\backslash \mathit{S},{\mathit{v}}_{\mathit{j}}\in \mathit{S}\}$ y ${\mathit{E}}^{+}\left(\mathit{S}\right)=\mathit{E}\left(\mathit{S}\right)\cap \left\{\left({\mathit{v}}_{\mathit{i}},{\mathit{v}}_{\mathit{j}}\right)\in \mathit{E}:{\mathit{q}}_{\mathit{i}\mathit{j}}>\mathbf{0}\right\}$. The formulation of DCARP is as follows.

Minimize:

$$\sum _{k=1}^m\sum _{ \left(v_i, v_j\right)\in \mathit{A}}({c_{ij}x}_{ijk})$$

(1)

Subject to:

$$\sum _{ \left(v_j, v_i\right)\in \mathit{A}}{x}_{jik}-\sum _{ \left(v_i, v_j\right)\in \mathit{A}}{x}_{ijk}=0 (v_i\in V,k=1,2,\dots ,\mathit{m})$$

(2)

$$\sum _{k=1}^m{(y}_{ijk}+y_{jik})=\left\{\begin{array}{c}0 if {\mathit{q}}_{\mathit{i}\mathit{j}}=0 \\ 1 if {\mathit{q}}_{\mathit{i}\mathit{j}}>0\end{array}\right.$$

(3)

$$\begin{array}{cc}{x}_{ijk}\ge y_{ijk} (\left(v_i, v_j\right)\in \mathrm{A},k=1,2,\dots ,\mathrm{m})& \left(\left(v_i, v_j\right)\right)\in \mathrm{A}\end{array}$$

(4)

$$\sum _{ \left(v_i, v_j\right)\in \mathit{A}}{q}_{ij}{y}_{ijk}\le W(k=1,2,\dots ,\mathit{m})$$

(5)

In this formulation, constraints (2) are flow conservation equations for each vehicle. Constraint (3) ensures that arcs are served when they have positive demand. Constraint (4) states that an arc is served if it is traversed by the same vehicle. Moreover, constraint (5) ensures that the vehicle capacity is not exceeded. The following constraints complete the model:

$$\begin{array}{cc}\left.\begin{array}{c}\begin{array}{c}{\displaystyle \sum _{v_i, v_j\in \mathit{S}}}{x}_{ijk}\le \left|S\right|-1+{\mathit{n}}^2{{\mathit{u}}^S}_k\\ {\displaystyle \sum _{v_i\in \mathit{S}}}{\displaystyle \sum _{v_j\notin \mathit{S}}}{x}_{ijk}\ge 1-{w^S}_p\end{array}\\ \begin{array}{c}{u^S}_k+{w^S}_k\le 1\\ {u^S}_k, {w^S}_k\in \left\{0, 1\right\}\end{array}\end{array}\right\}& \begin{array}{c}(\mathit{S}\subseteq \mathit{V}\backslash \left\{v_1\right\};\mathit{S}\ne \mathit{Ф};\\ \mathit{k}=1,2,\dots ,\mathit{m}\end{array}\end{array}$$

(6)

$$\begin{array}{cc}{x}_{ijk}, y_{ijk} \in \left\{0, 1\right\} & (\left(v_i, v_j\right)\in \mathrm{A};k=1,2,\dots ,\mathrm{m})\end{array}$$

(7)

The restriction $\left(6\right)$ ensures that there are no illegal subtours. To understand how these restrictions operate, note that for given $\mathit{S}$ and $\mathit{k}$, only one of the two binary variables ${w^S}_k$ or ${ u^S}_k$ can take the value of 1 correspondingly. Then, any cycle with the set of vertexes $\mathit{S}$ and arcs traversed by a vehicle $\mathit{k}$ must be connected to $\mathit{V}$\$\mathit{S}$ (and hence to ${\mathit{v}}_{\mathrm{1}}$)), from:

$$\sum _{ v_i, v_j\in \mathit{S}}{x}_{ijk}>\left|S\right|-1⟹{{\mathit{u}}^S}_k=1⟹{{\mathit{w}}^S}_k=0 ⟹\sum _{ v_i\in \mathit{S}}\sum _{ v_j\notin \mathit{S}}{x}_{ijk}\ge 1.$$

(8)

2.3. Challenges and Implications of Subtours and U-Turns in Urban Traffic and Waste Collection Operations

Urban traffic congestion is a pervasive problem in cities worldwide, and the phenomenon of subtours and U-turns in vehicle routes contributes significantly to this problem. This paper explores the complexities associated with subtours and U-turns in urban traffic and their impact on waste collection operations, particularly during peak hours, in the context of Latin America and the Caribbean (LAC). Academic articles from Scopus provide valuable insights into the challenges posed by these phenomena and their implications [3,50].

2.3.1. Subtours and U-Turns in Urban Traffic

Subtours, partial and unnecessary deviations from optimal routes, and U-turns, which are abrupt direction changes, are recurring problems in urban transportation networks [51]. These phenomena lead to increased travel times, fuel consumption, and emissions and exacerbate peak-hour congestion [52]. In LAC, where rapid urbanization and population growth contribute to increased traffic volumes, the management of sub-turns and U-turns is crucial for effective traffic management [53].

The results show that even combining OSRM with a GIS environment such as OpenStreetMap is not efficient enough to optimize routes, emphasizing the need for human expertise to refine and improve the routing process [14]. Notably, route optimization problems are inherently complex and classified as NP-hard [54]. This complexity, as observed in the garbage truck routing case study in a small Latin American city, highlights the intricate nature of urban logistics challenges and emphasizes the importance of integrating human intelligence with technological solutions for effective route optimization. Acknowledging the NP-hard nature underscores the inherent challenges in achieving optimal routing outcomes and warrants a comprehensive approach that considers both algorithmic advances and human decision making to address the intricacies of waste collection logistics. An example is shown in Figure 4.

2.3.2. Traffic Congestion in LAC and Its Impact

Cities in Latin America and the Caribbean face unique challenges related to traffic congestion, exacerbated by inadequate infrastructure, population density, and limited public transportation options [55]. Subs and U-turns exacerbate these challenges, contributing to longer travel times and reduced overall road network efficiency during peak hours [56]. This congestion has profound implications for economic productivity, air quality, and overall urban livability.

2.3.3. Linking Traffic Issues to Waste Collection Operations

The link between traffic congestion and waste collection is evident during peak hours when increased vehicle density impedes the efficient movement of waste collection trucks. Sub-optimal routes and frequent U-turns further increase delays, adversely affecting the timely and effective collection of municipal solid waste [57]. This, in turn, results in longer operating hours, increased fuel consumption, and increased environmental impacts.

2.3.4. Proposed Heuristic Procedure to Improve the Routing of Collection Trucks in ArcGIS

The heuristic procedure used to optimize the collection routes followed by the collection trucks is described below. This procedure is based on concepts used in previous work by the authors, such as the subdivision of the Canton of Ibarra into subzones [17], the definition of initial collection routes in the different subzones [14], and the result of the routing proposed by the ArcGIS software without any extensions.

The proposed heuristic procedure (see Figure 4) aims to minimize the distance travelled based on the number of capacitated arcs, focusing primarily on reducing both the distance travelled and the associated cost per tonne on the designated route. It is defined by considering key factors such as road quality, the requirement for the number of capacitated bends (which should be greater than 4), and the maximum allowable distance from the collection vehicle to the capacitated bend, which should not exceed 100 m.

The degree of the arc is the number of houses, also known as waste generators, that are in the same arc and can be greater than 1.

Capacited arc is an arc where there is at least one house that generates waste to be visited for collection service. Then, the neighbouring arc with the highest degree of capacity is basically the previous adjacent node or neighbour in the route that is gradually formed by adding arcs in the general tour travelled by truck. It is said that this is a higher degree of capacity because it is assumed that this node has previously passed through the filter of the heuristic procedure, and obviously, there will be at least four generators or houses in this arc.

The steps of an algorithm to improve the routing of a garbage truck are described below:

Select Capable Arcs: The algorithm starts by selecting all capable arcs (road segments) from the planned route for analysis. The arcs consist of road sections between two corners of a city block. In addition, these arcs are where the residents deposit their waste (from the household’s generators) and where the truck must collect it.

Eliminate Low-Capability Arcs: Orders for collection associated with arcs with a capability degree less than or equal to 1 are eliminated from the route. Considering higher operational costs, these arcs are deemed unsuitable for the trucks to navigate.

Classify Orders by Arc Capability Degree: The remaining orders are classified based on the capability degree of their associated arcs:

• Add orders with arc degree ≥2 ≤4 to the neighbour arc with a higher highest degree of capacity.
• Add orders with arc degrees ≥4 and <10 to their nearest neighbouring arc when arcs require U-turns (U-Turn Check) and do not exceed 100 m. If a U-turn is not required and the next arc exceeds 100 m (Arc Length Check), only the passage to the next arc is allowed.
• For orders ≥ 10 located in U-turns, the passage is only allowed up to the midpoint of that arc. If a U-turn is not required, only allow the passage to the next arc.

Arc Length Check: If the length of an arc exceeds 100 m, the passage is only allowed up to the midpoint of that arc.

U-Turn Check: If entering an arc requires the truck to make a U-turn, passage on that arc is restricted. U-turns may be deemed unsafe or impractical for the waste collection trucks.

Road Quality and Width Check: The algorithm checks if the quality and width of the road are adequate for the waste collection trucks. If the conditions are suitable, the passage is allowed; otherwise, the passage is restricted on that arc.

Review Assigned Arcs and Restrictions: After applying the necessary restrictions and reassignments, the decision maker reviews the assigned arcs and restrictions, such as legal or geographical impediments to entry or high risks when entering waste collection trucks in such an arch, for example, when the road is incomplete in an arc. To ensure the route is safe and feasible for collection trucks to travel.

Execute and Solve Optimized Micro-Route: Finally, the algorithm executes and solves the optimized micro-route using the ArcGIS Network Analysis tool. This step calculates the most efficient route for the waste collection trucks based on the DCARP model and considers the applied restrictions and arc capabilities.

The overall objective of this algorithm is to optimize the routing of waste collection trucks by considering various factors such as road conditions, arc capabilities, manoeuvrability constraints, and potential obstacles like U-turns. By systematically analyzing and classifying the arcs, the algorithm aims to create a safe and efficient route that minimizes operational challenges and maximizes productivity for waste collection operations. This procedure is depicted in Figure 5.

2.3.5. Proposed Pseudocode to Improve WCVRP Micro-Routing

Based on the proposed heuristic procedure, we developed a pseudocode (Algorithm 1) with the steps involved in analyzing and optimizing routes based on arc capability degrees, road quality, and other factors such as U-turns and arc lengths. The algorithm selects feasible arcs, classifies orders based on arc degrees, applies passage restrictions or order reassignments accordingly, and finally executes and solves the optimized micro-route.

3. Validation in a Case Study

The Ibarra canton, located in the northern region of Ecuador, has experienced sustained population growth in recent years. As a result, it has experienced a high rate of MSW generation, with current figures indicating approximately 114 tonnes per day. National regulations state that waste collection is the responsibility of decentralized, autonomous municipal governments. Initially, the Municipality of Ibarra established a system of 17 collection routes served by a fleet of 11 trucks and a transfer station.

In 2018, Ibarra began implementing a container-based collection system. However, despite the efforts of the municipality and the research centre, residents have not fully taken responsibility for depositing waste in these containers. This makes it difficult to determine the best truck routes and requires trucks to collect waste from sidewalks throughout the city.

Recent evidence shows that Ibarra’s current collection service lacks technical micro-routing studies or records to facilitate efficient operations. Route planning has been performed empirically based on the criteria and experience of municipal sanitation managers and collection truck drivers.

The lack of micro-route, characterization, or waste generation studies makes determining waste generation rates per route difficult. This prevents a balanced distribution of work across routes, resulting in problems such as overflowing containers, route and truck overload, overtime usage, and inflated collection costs. In summary, the lack of technical route analysis and data, reliance on ad hoc empirical practices, unbalanced collection workloads, and resulting cost and operational issues highlighted the needs and challenges facing Ibarra’s waste collection service efficiency and planning.

Considering the challenges presented, a conceptual methodology has been developed that includes various logistics and operational excellence techniques, specifically designed for application in the case study. Furthermore, this methodology considers the entire supply chain of a small to medium-sized waste collection company, which is appropriate to the social context of Latin America and the Caribbean. An operational management methodology is first proposed to improve the waste collection system at strategic and tactical levels in small to medium-sized cities in LAC.

The conceptual methodology involves redesigning the waste collection network for a municipality or city in Latin America and the Caribbean with a population of less than 200,000. It includes key components such as a truck depot located in the urban sector of the municipality or city, a fleet of trucks assigned to collect solid waste in specific subzones, and specific times based on the needs of the residents. In addition, there is a transfer station where all the trucks converge when their collection capacity is reached. At this station, recyclable materials are separated using waste separation equipment, while non-recyclable waste is transported by industrial trucks to a landfill (disposal). The landfill uses measures such as covered cells with geomembranes to prevent contact between the waste and the environment, including water sources, thereby minimizing the pollution of these valuable resources.

In our proposed model, we used Compactor Garbage Trucks in the residential zone, equipped with hydraulic presses to reduce waste volume and have a load capacity of around 12 tonnes. Front Load Garbage Trucks, efficient in collecting containerized waste from commercial zones, with a capacity of up to 18 tonnes, and Roll-Off Trucks, commonly used to transport non-usable waste from transfer station to disposal, have a capacity of up to 30 tonnes. All of the above are in compliance with the Euro 4 standard. These trucks play a crucial role in waste management by offering versatility, efficiency, reduction in fuel consumption and emissions, and durability in handling various waste materials, contributing significantly to sustainable waste collection and disposal.

Regarding the schedules for waste collection in our proposed methodology, we have previously analyzed the hours of greatest vehicular congestion in the Canton of Ibarra to avoid collecting MSW during those hours and to avoid exacerbating the traffic generated in typical Latin American and Caribbean cities. Thus, in the residential area, schedules have been established from 8:00 p.m. to 5:00 a.m., avoiding the hours with the greatest traffic congestion in the Canton of Ibarra, so that since the waste is collected at night, a minimum time is required to complete the route and fuel consumption is minimized. For the trucks that collect MSW in the commercial zone, the collection schedule will be from 18:00 to 22:00. A schematic representation of the conceptual methodology is shown in Figure 6.

In the context of our improvement model, we focus on the challenge of routing garbage trucks within the urban subzones of a small city in Latin America. Specifically, we advocate using capacitated arc routing, a type of problem known in the literature as the Chinese postman problem (CPP).

This type of vehicle routing problem assumes that customers can be located anywhere along the arcs of a network composed of nodes located at the corners of city blocks. This assumption aptly captures the complexity of waste collection in small cities in Latin America. In these cities, waste collection is often performed manually along the sidewalks or curbs of city blocks [58,59]. The concept of capacitated arc routing is illustrated in Figure 2.

This approach to vehicle routing, particularly through capacitated arcs, addresses the unique challenges of waste collection in small cities in Latin America. By assuming customer distribution along network arcs, we align with the practicalities of waste collection in these urban areas. The use of capacitated arc routing provides a strategic framework for optimizing waste collection routes, contributing to improved efficiency and resource utilization in the waste management systems of small cities in Latin America, as shown in Figure 7.

In the context of the current study, our study will only be limited to the residential and commercial zones of Ibarra. The investigation started with the definition of subzones as established by Herrera et al. [17]. This activity involves an equitable distribution of the territory in the Canton of Ibarra into nine residential subzones and one commercial subzone. The distribution considers factors such as the population growth in the canton, as well as its waste generation rates, and the territorial and legal policies defined within the canton. In addition, terrain constraints are considered. At the macro-territorial level, this proposal aimed to achieve the following objectives:

• Balancing the workload among the various subzones,
• Reducing operational costs,
• Enhancing the level of service in urban waste collection operations within the canton.

The subzone definition served as the basis for implementing a vehicle routing algorithm to optimize waste collection routes within the small Latin American city. The algorithm effectively achieved a fair distribution of the workload, minimized operating costs, and improved the efficiency of the waste collection operations in the urban areas of the canton by considering the specified objectives.

Integrating the subzone definition and applying the routing algorithm provides a comprehensive approach to the waste management challenges of small cities in Latin America, contributing to more sustainable and effective waste collection practices.

Built upon the methodology proposed by Herrera et al. [17,60]. Geographic Information Systems (GIS) were used to define optimal vehicle routes within each subzone. The ArcGIS software version 10.5 provided a tool within its Network Analyst plugin that allowed the analysis and design of collection routes, considering various parameters and constraints to structure them effectively.

Input Information

First, it was necessary to determine the amount of waste generated in each subzone.

Table 2. MSW generation in the case study [17].

Zone	Subzone	Generated Waste (t/d)
Residential zone	Subzone 1	13.56
	Subzone 2	13.11
	Subzone 3	13.67
	Subzone 4	12.41
	Subzone 5	15.38
	Subzone 6	12.42
	Subzone 7	12.4
	Subzone 8	12.7
	Subzone 9	13.36
Commercial zone	Subzone 10 N	12.46
	Subzone 11 S	8.48
Total		142.43

provides details on waste generation in tonnes for both residential and commercial zones.

Specifically, our heuristic procedure was adapted to the DCARP model using Network Analyst in this research. The “Centroids” tool was used to determine the locations of waste generators and generate orders for the capacitated arcs in the road network (see Figure 8). This approach facilitated the routing of trucks to these orders throughout the city of Ibarra along their respective micro-routes.

To conduct this study, certain input parameters required by the Network Analyst tool were defined, including;

• Orders (capacitated arcs);
• Depots (starting and ending points of routes);
• Routes (routes under analysis);
• Route Renewals (waste disposal locations);
• Line and Point Barriers (passage restrictions on the roadway).

Subsequently, five primary parameters were specified, detailed in

Table 3. Input Parameters.

Parameter	Input Field	Value
Orders	Name	Text
	Collection Quantity	Numeric
	Sidewalk collection approach	Without turning and with pickup on both sides of the vehicle
Depots	Name	Transfer Station or Truck depot
	Description	Exit or Entry
Routes	Name	Micro-route N
	Description	Subzone N
	Name of initial Depot	Truck Parking
	Name of final Depot	Transfer Station
	Capacity	11 or 12 t
	Cost per Unit of Time	7.66 ($/h)
	Cost per Unit Distance	0.456 ($/km)
Route Renewals	Depot name	Transfer Station
	Route name	Micro-route N
	Service Time	5.45 min
Line Barriers	Name	Track Quality or Track Width
Point Barriers	Name	Track Quality or Track Width

, outlining valid input fields for each parameter to be read and executed by the software. Each Micro-route N is carried out within its respective Subzone N.

Initially, the jobs were segmented for each subzone to develop each route independently of the others, as shown in Figure 8. Since the waste generation in the commercial zone exceeds the truck’s working day, it was decided to divide it into two subzones: North (10 N) and South (11 S). Once the jobs were delimited by subzone, the routing problem was addressed based on the parameters outlined in Table 3.

4. Results and Discussions

The proposed heuristic procedure aimed at minimizing the travelled distance produced the main results presented in

Table 4. Results obtained with and without the proposed heuristic.

Micro-Routes	1	2	3	4	5	6	7	8	9	10 N	11 S	Total
Routing in ArcGIS without Heuristic procedure
Orders in capacited arcs	463	400	439	302	272	398	378	294	435	495	337	4213
Time on route (h/d)	3.35	2.77	3.21	3.15	3.49	3.13	3.06	2.48	3.76	3.09	1.91	33.4
Total distance (km/d)	108.11	91.42	108.13	117.63	114.93	107.12	101.16	83.72	123.25	110.75	65.78	1132
Routing in ArcGIS with the Heuristic procedure
Orders in capacited arcs	194	240	190	172	190	207	244	189	215	188	198	2227
Time on route (h/d)	2.47	2.28	2.62	2.33	2.96	2.51	2.85	2.3	2.42	2.02	2.01	26.77
Total distance (km/d)	75.35	67.85	86.33	74.47	87.12	82.26	84.89	71.34	74.4	66.42	65.71	836.16

, compared to the routing by GIS developed by the same author. These results consider the reduction in the distance travelled, the route time, and the number of orders for capacitated arcs. Graphically, we can see how our heuristic procedure proposed to improve the micro-routing proposed by Network Analyst works as a basis for its solution. We then proceed to improve this solution, creating more feasible solutions to be executed by the collection vehicles and, above all, more economically profitable, avoiding the unnecessary entry of the truck into bends with low capacity or with unnecessary U-turns and unsafe situations for the truck, which is extremely important considering that we are using trucks with more than 12 tonnes of load capacity and a limited turning radius. This is depicted in Figure 9 and Figure 10.

With the implementation of the micro-routing heuristic, significant results were observed in several key parameters during the optimization process. The parameters considered included distance travelled (km), time on route (h/d), and orders served by the micro-route, all of which played a critical role in determining and selecting more optimal and efficient routes for the optimized model.

The workload distribution could be related to the number of orders served by micro-route; it was successfully balanced based on the operational capacity of the trucks. Each truck was assigned a load of 10 to 12 tonnes per trip, ensuring a fair distribution of tasks throughout each working day. An effort was made to standardize the distance travelled, considering the amount of waste generated in each area. As a result, our heuristic procedure defined 11 micro-routes, each with a distance of between 80 and 95 km per trip during each working day. These results highlight the effectiveness of the micro-routing heuristic procedure in optimizing vehicle routes, contributing to improved operational efficiency and resource utilization in the transportation system, as shown in Table 4.

Results Regarding the Reduction in Environmental Impact

The emissions of carbon dioxide (CO₂) and nitrogen oxides (NOx) from municipal solid waste (MSW) collection trucks had a negative impact on the environment. These emissions contributed to air pollution, causing respiratory problems, and exacerbating existing health problems in nearby communities. In addition, the release of CO₂ and NOx contributed to smog and ground-level ozone formation, further degrading air quality. The widespread use of inefficient internal combustion engines in waste collection trucks exacerbated these emissions, highlighting the urgent need for cleaner and more sustainable transportation solutions in urban waste management systems. In this sense, considering the study by Monteros et al. 2018, carried out in the same city as the case study and included in the framework of our research project, it was possible to determine the level of emissions from municipal solid waste collection trucks, specifically in terms of carbon dioxide (CO₂) [61].

Using the Testo 350 gas analyzer, it was possible to determine the average CO₂ emissions of the trucks used in the MSW collection, which averaged 0.295 kg/t/km [62,63,64]. In addition, the emission analysis confirmed that the trucks used in our methodology comply with the Euro 4 emission standards [65,66,67,68].

We have reviewed the relevant literature on CO₂ generation worldwide for comparison purposes. For example, in the work of Yaman et al. (2019), conducted in Saudi Arabia, the authors state that the greenhouse gas emissions (GHG) of MSW collection trucks in terms of carbon dioxide (CO₂) should be estimated in terms of kg of CO₂ generated when moving one tonne of MSW over one kilometre (kg/t/km). Subsequently, it will be possible to determine the Global Warming Factor (GWF) of our entire MSW collection system, expressed in (kg/t), and thus be able to compare it with other collection systems applied in different cities worldwide. Those values are shown in

Table 5. Gas emissions estimation from solid urban waste collection trucks, based on [61,62].

Subzones	Population (ca)	MSW Amount (ty−1)	Distance to Landfill (km)	Number of Trips	GHG Emissions (t CO2-eq)	GWF (kg CO2-eqt-1)
1	19,796	4949.40	75.35	412.45	137.52	27.79
2	19,139	4785.15	67.85	398.76	119.72	25.02
3	19,956	4989.55	86.33	415.80	158.84	31.83
4	18,117	4529.65	74.47	377.47	124.39	27.46
5	22,453	5613.70	87.12	467.81	180.34	32.13
6	18,131	4533.30	82.26	377.78	137.51	30.33
7	18,102	4526.00	84.89	377.17	141.68	31.30
8	18,540	4635.50	71.34	386.29	121.94	26.31
9	19,504	4876.40	74.4	406.37	133.78	27.44
10 N	18,190	4547.90	66.42	378.99	111.39	24.49
11 S	12,380	3095.20	65.71	257.93	75.00	24.23
Total	204,307	51,081.75	836.14		1442.1
Average	18,574					28.03

.

For comparison purposes and based on the Yaman et al. (2019) model, we calculated the amount of GHGs no longer emitted to the environment by applying our proposed heuristic (

Table 6. Reduction in GHG from solid urban waste collection trucks, based on [61,62].

Subzones	Population (ca)	MSW Amount (ty−1)	Distance to Landfill (km)	Number of Trips	GHG Emissions (t CO2-eq)
Routing in ArcGIS without Heuristic procedure	204,306.57	51,081.75	1132	4256.81	21,322.80
Routing in ArcGIS with the Heuristic procedure	204,306.57	51,081.75	836.16	4256.81	15,750.24

). The GWFs are also included in our collection model, where we apply the proposed heuristic and compare them with the results obtained in the work of Yaman et al. (2019) [62], as shown in Figure 11.

In addition, it is worth mentioning that we have demonstrated a significant reduction in execution time when using the heuristic approach, which, on average, after ten executions, showed us to be able to solve the problem in about 12 min, while solving the same problem without the proposed heuristic approach took on average 63 min. All of these experiments were performed on a Toshiba Thinkpad laptop (Toshiba, Tokyo, Japan) equipped with an Intel^® Core^TM i5-4210U CPU @ 2.40 GHz (Intel, Santa Clara, CA, USA) and 8 GB of RAM, running a Windows 10 64-bit operating system.

5. Conclusions

When the ArcGIS software and its Network Analyst plugin are used without the heuristic algorithm, the software simply defines and calculates vehicle routes based on travel time without considering the workload or the number of times a truck traverses the same capacitated arc. In other words, the ArcGIS software and its Network Analyst plugin do not consider that distance should be optimized and maximized by avoiding inconveniences in the truck’s route, such as unnecessary U-turns to enter areas that are difficult for the truck to access. This limitation prompted the development of our heuristic procedure, which proposes an extension to the Network Analyst plugin.

Our heuristic approach addresses these shortcomings by introducing workload distribution considerations and optimizing distance use. This improvement ensures that the algorithm minimizes travel time and considers the practical challenges that may arise along the route. Incorporating these elements leads to more effective and efficient vehicle routing in a small city environment, ultimately improving transportation logistics and resource utilization.

Addressing subtours and U-turns in urban traffic reduces congestion, especially during peak hours in Latin America and the Caribbean. The impact goes beyond transportation, affecting critical services such as waste collection. Strategic urban planning, infrastructure investment, and intelligent transportation systems are essential components of a holistic approach to reducing traffic congestion and improving the efficiency of waste collection in the region.

In addition, to evaluate the reduction in environmental impact, the variance of 295.84 km/d in the total distance travelled between the proposed model and the established model was considered, measuring the emissions generated by the difference between the two scenarios. That is, with and without the application of the heuristic. The results show that applying the Routing in ArcGIS model with the heuristic procedure reduces the total distance travelled. This reduced distance travelled significantly reduces 5572.56 t CO₂-eq in greenhouse gas (GHG) emissions.

To validate our proposed MSW collection and management model, we estimated the average GWF of 28.03 kg CO₂-eq per tonne in our collection model. We compared it with the work of Yaman et al. (2019) [62], which estimated an average GWF of 29.14 kg CO₂-eq per tonne. With this, it was possible to say that our model presents a lower CO₂ generation per tonne than the abovementioned model calculated in Saudi Arabia.

Reducing exhaust gas emissions in urban environments can also be achieved using garbage trucks powered by ecological fuels, such as natural gas [69]. Therefore, as future work, we propose to evaluate this or similar models by applying a vehicle fleet that uses this fuel type that is more ecologically friendly to the environment.