Supply Chain Design for Waste Valorization Through High-Energy-Density Pellet Production in Chile

Abstract

This study presents the development and application of a mathematical optimization model to improve decision-making in the supply chain for high-energy-density pellet (HEDP) production and commercialization. Focused on the Metropolitan Region of Chile, the research involved a detailed analysis of key supply chain components, including identifying landfills and controlled dumps, waste volume assessments, plant location analysis, technology evaluation, and market potential exploration. The model revealed that the available raw material in the region was sufficient to meet 100% of HEDP demand, with a surplus of 2,161,952 tons remaining after satisfying maximum demand. An optimization analysis of potential plant locations identified Santa Marta as the optimal choice, resulting in annual cost savings of USD 100,000 compared to other sites. This work underscores the role of mathematical optimization in enhancing supply chain efficiency for biomass-based energy products, offering valuable insights for strategic decision-making in similar contexts.

1. Introduction

In Chile, approximately 17 million tons of solid waste were generated in 2018, with roughly 6.5 million tons being urban solid waste [1]. The Metropolitan Region was the primary contributor, generating 53% of this waste, characterized by a 48% organic composition [2]. The variability in waste composition was influenced by factors such as population growth and specific legislation, notably Law 20,920, which pertains to Extended Producer Responsibility and Recycling Programs [3]. This law aims to incentivize manufacturers to take responsibility for the entire lifecycle of their products, including post-consumer waste management [4,5,6]. However, despite implementing policies to promote recycling and waste recovery, the recycling rate in Chile has struggled to surpass 10%. This low recycling rate indicates significant challenges in the effectiveness of current recycling programs and infrastructure [2].

Consequently, over 90% of waste is in landfills and dumps, exacerbating environmental issues such as soil and water contamination, greenhouse gas emissions, and inefficient land resource use [7]. The underperformance in recycling efforts can be attributed to various factors, including inadequate public awareness, insufficient recycling facilities, and logistical challenges in waste collection and sorting [8].

Chile’s rapid urbanization and population growth have increased waste generation, adding pressure to existing waste management systems [9]. Although Chile’s legislative framework is progressive, achieving the intended outcomes requires more robust enforcement and support mechanisms [10,11]. This situation underscores the need for enhanced waste management strategies, improved recycling infrastructure, and stronger collaboration between government bodies, private sector stakeholders, and the public [12].

Addressing these challenges can help Chile improve recycling rates, reduce reliance on landfills, and move towards a more sustainable and circular economy. In this context, innovative solutions, such as developing advanced recycling technologies and integrating waste-to-energy processes, could further contribute to mitigating the environmental impact of waste and enhancing resource recovery [13].

An innovative solution to this issue is the production of high-energy-density hydrophobic pellets (HEDPs) through hydrothermal carbonization (HTC) of residual biomass [14]. HTC offers several key advantages over traditional biomass conversion methods. These include higher energy efficiency, the ability to process wet biomass without prior drying, and the production of a more homogeneous and stable product with superior combustion properties [15,16]. Additionally, the HTC process can be directly applied to biomass with high moisture content (often challenging to process using conventional methods), converting materials like microalgae, sewage sludge, and food waste into a lignite-like solid product known as hydrochar, which has significant potential for energy recovery [17]. For better handling, transportation, and fuel storage, densification processes have been applied to hydrochar fines using solid fuel [18]. The pelletization process results in high-density pellets (briquettes) characterized by increased energy, bulk density, and mechanical strength [18]. However, significant challenges arise from the high costs of transporting raw materials and finished products and the initial expenses associated with establishing production plants [19,20]. Optimizing the supply chain with decision-support tools is crucial for facilitating hydrothermal carbonization technology’s development and future industrialization. These tools would assist in making informed decisions regarding production capacities and raw material requirements based on market demands [1]. Specifically, optimizing industrial processes in Latin America can play a pivotal role in leveraging regional resources and capabilities to enhance efficiency and sustainability [21]. Industries can assess potential supply chain designs by implementing optimization techniques in simple platforms [22]. These decision-support tools can assess supply chain structure changes considering various scenarios, allowing stakeholders to formulate strategies aligning with economic and environmental objectives [23]. The integration of simulation-based policy development ensures that decisions are robust and resilient, and capable of responding to dynamic market conditions and regulatory environments [24].

This holistic approach to supply chain optimization supports the technological advancement of HTC but also promotes industrial growth and sustainability in the broader context of Latin America’s evolving industrial landscape [10,25,26,27]. In this study, the proposed information platform aims to enhance decision-making in supply chain management for renewable energy projects, specifically addressing the challenges associated with the production and commercialization of HEDPs. By providing data analysis, supply chain modeling, and scenario assessment capabilities, this simple platform is designed to optimize the supply chain design, reducing transportation. The analysis focuses on the Metropolitan Region of Chile, where the availability of urban residual biomass is highest, and waste management policies are more centralized [28].

Additionally, given the high pollution levels in Chilean cities and the extensive use of firewood for heating—which significantly contributes to air pollution—pellets from HTC emerge as a competitive alternative in the residential energy market [29]. It is especially relevant in the central and southern regions of the country, where firewood consumption is predominant [30].

An information platform is not merely a theoretical model but a practical tool that can be implemented to enhance real-world decision-making processes. Its development considers the geographical, economic, and regulatory context, making it highly relevant for policymakers and industry stakeholders aiming to transition toward a circular economy [3].

Furthermore, adopting HTC and HEDP production can stimulate regional economies by providing new employment opportunities and fostering innovation in green technologies [31]. Ultimately, this case study serves as a model for other regions facing similar challenges, demonstrating how innovative technological solutions and strategic supply chain decisions can work in tandem to promote sustainable waste management and energy production [14,16].

Facing the challenge of optimizing the supply chain design for the production and commercialization of pellets, this study proposes the development of a computer platform designed to improve efficiency and support initial strategic decisions aligned with sustainability principles. The configuration of the proposed supply chain is based on a thorough analysis of the current situation and potential market, all underpinned by a rigorous mathematical optimization model. The novelty of this research lies in its integrative approach, combining advanced supply chain management techniques with cutting-edge HTC technology to address a pressing environmental and economic issue.

2. Methods

A diagnosis was made of the current situation of organic waste recovery in the Chilean Metropolitan Region. For this purpose, the energy potential available in landfills and other waste biomass collection centers was identified.

A comprehensive literature review was conducted by consulting academic sources and reports from state and private institutions to understand existing practices and the current situation of organic waste management. Subsequently, the potential market for the commercialization of HEDPs was determined. This market analysis involved identifying potential customers and consumers through market studies and energy demand analysis in various country areas, focusing on regions where firewood is predominant.

The next step was to propose a supply chain design optimization model. For this purpose, mathematical models applied in similar case studies were reviewed to describe the objective function, detail the constraints, and identify the methodologies to solve the model. Then, a computer platform was designed and developed to manage the information. Bizagi Modeler was used to diagram the logical procedure that the platform would use to optimize the supply configuration. The platform’s programming was implemented in Visual Basic, integrating the Microsoft Excel Solver application to resolve mathematical models. In addition, the format in which the data should be entered into the platform was established, offering compatibility and processing efficiency. Finally, tests and validations of the mathematical optimization model and computer platform were carried out using real information from a case study in the Metropolitan Region. These tests allowed us to validate the effectiveness of the proposed tools and obtain results applicable to the case studied, defining possible future application contexts.

An exhaustive literature review was conducted to identify existing models for developing a marketing-focused supply chain optimization model of HEDPs. In this review, various academic search engines were used, including SciELO, Dialnet, Worldwide Science, Google Scholar, Scholarpedia, Academia.edu, Springer Link, Refseek, Scopus, Web of Science, CERN Document Server, JURN, Ciencia, Science.gov, Bielefeld Search Engine Academy, and iSEEK Education. Keywords such as HTC, hydrothermal carbonization, supply chain, supply chain management, HTC supply chain management, HTC supply chain optimization, supply chain management waste to energy, SC to WTE, supply chain for WTE, logistic waste to energy, SC WTE optimization, and supply chain design optimization were used in searches. Despite the comprehensive search, no models specific to HTC were found in the literature. This is mainly because, due to its relative novelty, this technology is still being studied to improve its performance.

The structure of the proposed model thus considers fundamental strategic decisions such as the plant’s location and the initial selections of suppliers and customers. Potential future application contexts were defined to ensure the model’s relevance and effectiveness. It involved identifying scenarios where HTC technology could be implemented, such as urban waste management, agricultural waste processing, and industrial by-product utilization. Each context presents unique challenges and opportunities, influencing the supply chain’s design and operational strategies. For instance, the model must address the complexities of collecting and processing heterogeneous waste streams from densely populated areas in urban waste management. In agricultural waste processing, the focus shifts to optimizing the supply chain for seasonal variations in raw material availability and the proximity to farming communities. Industrial by-product utilization requires integrating the HTC process into existing industrial ecosystems, ensuring seamless collaboration between different industrial actors. By defining these possible future application contexts, the proposed supply chain design optimization model for HTC can be tailored to meet specific needs, enhancing its applicability and effectiveness. This approach ensures that the model is theoretically sound and practically viable, capable of addressing real-world challenges in diverse settings. The flexibility and adaptability of the model make it a valuable tool for advancing the implementation and commercialization of HTC technology across various sectors.

The mathematical model establishes the basis for the practical application of the supply chain design model. The sets, decision variables, constraints, objective function, and parameters were defined, which allowed an accurate representation of the supply chain:

• Sets: These include supplier locations (i ϵ I), plant locations (k ϵ K), and customers to satisfy (j ϵ J), among others.

• Decision variables: These variables encompass the selection of plants and the flow of materials and products through the supply chain.

• Restrictions: These consider mass balances, the availability of raw materials, production capacities, and the satisfaction of demand, among others.

• Objective functions: These focus on minimizing transportation distance to reduce costs and emissions, reflecting the project’s sustainability approach regarding economic and environmental aspects.

• Parameters: These parameters include the raw materials available to suppliers, production capacity, rates of transformation of raw materials to final products, demand for final products, distances between suppliers and plants, transportation costs, and emissions, among others.

These sets and parameters are shown in Table 1 and Table 2. The solution methodology used the Microsoft Excel add-in solver [32], which was selected for its accessibility and ability to handle the number of variables involved in the model for the specific case study. This complement applies the SIMPLEX LP solving method to solve the linear programming model, ensuring an optimal configuration [33,34].

The objective function was to minimize the transported tons and the traveled kilometers associated with distributing raw materials and final products to their respective locations, according to Equation (1). This consequently reduces transportation costs and environmental emissions [35]. Lower transportation costs are achieved through shorter routes and optimized logistics, reducing fuel consumption and emissions. This approach indirectly aligns with environmental goals by focusing on cost efficiency, which limits environmental impact [25,35,36].

(1)$MinZ={\sum }_n{\sum }_i{\sum }_k{N}_{n,i,k}\ast DistP{P}_{i,k}+{\sum }_a{\sum }_k{\sum }_j{P}_{a,k,j}\ast DistP{C}_{k,j},$

where $N_{n,i,k}$ is the flow of tons of raw material of type $n$ from the supplier located at $i$ to the main production plant located at $k$, and $P_{a,k,j}$ is the flow of tons of final products of type $a$ from the main production plant located at $k$ to the customer located at $j$.

The constraints associated with the objective function are detailed in Table 3, where $W_k$ is equal to 1 if the main production plant is built at location k and 0 if not. This model provides a detailed framework for strategic decision-making in the HEDP supply chain and highlights its applicability in real-world scenarios where efficient resource management and minimization of environmental impact are crucial [37].

3. Results

Diagnosis and Analysis of the Potential Market for HEDP

There was a significant increase in waste generation, reaching 1.1 kg of solid waste per capita per day in 2018. Approximately 17 million tons of waste are generated annually, with approximately 7 million corresponding to urban waste [38]. This analysis revealed that less than 10% of this waste was recycled, resulting in more than 90% ending up in landfills and causing the loss of valuable resources and energy [39]. The waste management system in the Metropolitan Region was highly centralized in two main sanitary landfills, which managed 92% of the waste ending up in landfills, contributing significantly to the emission of greenhouse gases and environmental problems such as water issues and pollution [40]. This highlights the severe environmental repercussions of the indiscriminate accumulation of waste, including the emission of large amounts of methane and the health risks associated with treating municipal solid waste [9].

Regarding the opportunities for energy recovery, the average calorific value of household waste was 3.01 kWh/kg, which indicated considerable energy potential. A feasibility study by the Ministry of Energy projected substantial growth of this waste until 2050, highlighting the need and opportunity to adopt waste-to-energy technologies to improve waste management and generate renewable energy [41]. A comparative analysis with international technologies revealed that countries such as Japan and France successfully adopted waste-to-energy technologies, processing a high percentage of their waste in power plants [42], unlike waste management in Chile, which depends heavily on landfills [43]. Therefore, the feasibility of hydrothermal carbonization (HTC) technology implementation in the Metropolitan Region is evaluated in this research, highlighting its ability to treat wet organic waste and efficiently produce high-quality hydrophobic pellets. Studies have indicated that HTC offers advantages in energy density and emission reduction compared to traditional methods such as roasting [44,45]. Then, a considerable market was estimated for these pellets, especially in communities with high firewood consumption. The total demand is 966,971 MWh/year. The residential segment acquires the greatest relevance within the market, consuming 99.67% of the energy [46]. Recent regulations limiting the use of firewood during high-pollution episodes presented an opportunity to introduce these pellets as cleaner and more sustainable energy alternatives [47].

The communities with the highest consumption of firewood were Melipilla (13.6%), Lampa (6.6%), Talagante (5.4%), and Puente Alto (5.4%). This indicates a significant reliance on firewood in these areas, possibly due to economic factors or the availability of resources. On the other hand, we can see that the consumption by province is distributed as follows: Santiago accounts for 30.5%, Cordillera for 10.4%, Chacabuco for 13.9%, Maipo for 8.4%, Melipilla for 19.5%, and Talagante for 16.8%. This distribution highlights the varying degrees of firewood usage across different provinces, reflecting local preferences and resource availability—the Metropolitan Region has four sanitary landfills where the available raw material is distributed [48]. The Santa Marta landfill has 1,275,808 tons of raw material available. Santiago Poniente has a supply of 224,244 tons, while Popeta has 50,256 tons. The Loma Los Colorados landfill holds the largest amount, with 1,722,079 tons of raw material available. These figures indicate substantial differences in the capacity and usage of each landfill, influencing logistical and operational decisions in waste management.

Table 4 presents the distances between suppliers (landfills) and plants. The distances, measured in kilometers, provide critical data for optimizing transport. The Santa Marta landfill, for example, is 44.2 km from Santiago Poniente, 65.6 km from Popeta, and 101.0 km from Loma Los Colarados. These distances are crucial for planning efficient logistics and ensuring timely delivery of raw materials to processing plants.

Similarly, Table 5 details the distances between plants and customers, measured in kilometers. This table is essential for understanding the logistics of distributing processed materials to various customer locations. For instance, the distance from the Santa Marta plant to Santiago is 35.6 km, to Cordillera is 42.0 km, to Chacabuco is 49.1 km, to Maipo is 38.0 km, to Melipilla is 47.2 km, and to Talagante is 20.0 km. These distances help in planning distribution strategies, optimize delivery routes, and reduce transportation costs. These detailed data tables provide valuable insights into the logistics and transportation dynamics within the supply chain, enabling more informed decision-making and strategic planning.

4. Discussion

Regarding the case study, the optimization has been carried out in the same context, varying the inclusion of the plant uniqueness restriction and the market share percentage (40%, 75%, and 100%). The results demonstrated that the available raw material in the Metropolitan Region was sufficient to satisfy 100% of the demand for high-energy-density hydrophobic pellets (HEDPs). The maximum demand could be satisfied using only the raw materials from the Santa Marta or Santiago Poniente landfill. Even after meeting 100% of the demand, there would still be a surplus of 2,161,952 tons of raw material available in the Metropolitan Region. A significant finding from the supply chain design optimization model was the pronounced difference between the costs of transporting raw materials and the final product. This difference underscored the necessity of situating production facilities as close as possible to raw material sources. This approach minimized transportation costs and enhanced overall system efficiency by reducing the carbon footprint associated with long-distance transportation. The implementation of the model had the potential to reduce dependency on landfills by 40%, offering substantial improvements in waste management for the region. The model's evaluation of a hypothetical scenario involving the installation of a single HTC plant considered three potential locations. Consequently, Santa Marta location (A) emerged as the optimal choice, reducing operating costs by USD 100,000 per year.

In comparison, Santiago Poniente and Popeta offered cost reductions of USD 75,000 and USD 60,000 annually, respectively. The superior efficiency and lower transportation costs associated with Location A justified its selection as the most advantageous site for the plant. When considering the uniqueness restriction, the same final decision was always reached: establishing the Santa Marta production plant. However, without considering the uniqueness restriction, starting from a market share percentage greater than 21%, the optimal solution was the same: installing the Popeta, Santa Marta, and Santiago Poniente production plants. For market shares of between 4% and 21%, the optimal solution was to establish the Popeta and Santa Marta plants. For both cases with a market share below 5%, installing the Popeta production plan was the optimal configuration.

Considering what has been stated so far, to draw conclusions about the strategic decisions associated with this case study, more information is needed to present a more in-depth analysis. For example, it would be relevant to establish a price for transportation, a price for the product, the cost of installation and operation of the production plants, the best-studied market share percentage values, and the definition of the plant production capacity.

These findings underscored the practical utility of the optimization model for strategic decision-making in waste management. The ability to provide data-driven, evidence-based optimizations supported investment and operational decisions and urban and environmental planning policies [35,49]. By optimizing plant locations and transportation logistics, the model facilitated a more sustainable and economically viable approach to managing the supply chain for HEDP production. The implementation of the model contributed to the broader goals of sustainability and circular economy principles. The model supported efforts to reduce greenhouse gas emissions and enhance resource recovery by efficiently utilizing waste biomass to produce renewable energy. Integrating advanced supply chain management techniques with innovative HTC technology exemplified how interdisciplinary approaches could address complex environmental challenges. In this way, the model results provided a robust framework for enhancing the efficiency and sustainability of HEDP production in the Metropolitan Region. This approach improved waste management practices and positioned HEDP as a viable and competitive alternative in the renewable energy market.

The comprehensive data analysis presented in the tables supported these conclusions. Specifically, the table showing community consumption of firewood indicated significant potential areas for HEDP adoption, with Melipilla (13.6%), Lampa (6.6%), Talagante (5.4%), and Puente Alto (5.4%) having the highest consumption rates. Additionally, the tables on distances between suppliers and plants (Table 4) and between plants and customers (Table 5) provided crucial insights into the logistical aspects of the supply chain. Table 1 highlighted the distances among key landfills and plants, with Santa Marta being 44.2 km from Santiago Poniente, 65.6 km from Popeta, and 101.0 km from Loma Los Colorados. Table 2 shows the distances from these plants to various customer locations, emphasizing the importance of strategic plant placement to minimize transportation costs and enhance operational efficiency. Overall, the case study highlighted the importance of an integrated supply chain optimization model for improving waste management and promoting sustainable practices in the Metropolitan Region. By leveraging detailed data and advanced modeling techniques, this approach offers a promising path toward achieving environmental and economic goals in the context of HEDP production and broader waste-to-energy initiatives.

Since the implementation and resolution of a mathematical model were not obvious to stakeholders, an optimization platform was developed and implemented. It required the following processes to be carried out:

1. The process begins with diagnosing and obtaining information for decision-making in a particular context identified by the user, defining the relevant sets and parameters.

2. Once the context has been identified, a form will be displayed through a button located on the platform panel. This form will allow the user to enter the size of the defined sets. This information will be stored in five different variables.

3. The computer platform will create a parameterized template for data entry based on the values entered in the previous stage.

4. The user will enter the data associated with the sets and parameters in a detailed format.

5. Once the data have been entered, the user can display a restriction panel that will allow the decision to be made about whether the model will include a uniqueness restriction (i.e., whether a single plant will be installed). Once the decision of process (5) has been made, the computer platform implements an algorithm that creates a table identifying the variables, each restriction, and the objective function.

6. Once the previous tables with the case study information have been completed, the computer platform executes Excel Solver to provide an optimal solution. A warning message will appear if the decision variables exceed the number of variables Excel Solver allows.

7. Finally, the computer platform will perform and display a summary of the results.

8. Additionally, users can access the parameter data if they wish to modify them. However, they must repeat the process to modify the context.

9. This design allows the assessment of different values for each parameter and the supply chain structure results.

5. Conclusions

The findings of this study provide a framework for enhancing the efficiency and sustainability of HEDP production in the Metropolitan Region of Chile. The proposed model showed that implementing HTC technology could reduce landfill dependency by 40%, improving waste management practices and contributing to sustainability goals. Moreover, this approach should improve waste management practices and position HEDP as a viable and competitive alternative in the renewable energy market, supporting both environmental and economic objectives.

Evaluating three potential locations for a single HTC plant identified Location A (Santa Marta) as the optimal choice, with a cost reduction of USD 100,000 per year, compared to USD 75,000 and USD 60,000 for Locations B (Santiago Poniente) and C (Popeta), respectively.

The developed optimization platform significantly facilitated the modeling process, empowering users to efficiently input, modify, and analyze data for informed decision-making, and assess the impacts of parameter uncertainty on the supply chain structure.

Although the attached project was limited to the study of the production of HEDPs through HTC technology, broadening its scope by contemplating other technologies or products, as well as their means of transport, could be an investigative success regarding accurate solutions for the particulars of each context to be applied. This expansion would enhance the model’s applicability and robustness, by considering increasing the number of sets and modifying the restrictions. However, this will require more advanced optimization solvers and programming.

In light of these findings, it is essential to consider the implications for local policy and practice, encouraging stakeholders to adopt innovative waste management strategies that align with sustainability goals.

Future research could explore the scalability of this model across different geographical locations and its integration with other renewable energy technologies, such as anaerobic digestion and biomass gasification. This could facilitate a more comprehensive approach to waste-to-energy solutions, optimizing resource use and energy generation. Additionally, studies could assess the potential socio-economic impacts of HTC technology adoption in various communities, focusing on job creation, local economic development, and public health benefits. All these aspects could be introduced as objective functions or constraints.

Furthermore, evaluating the total environmental impacts of using HTC technology, such as reductions in greenhouse gas emissions and improvements in local air and water quality, would be beneficial.

By situating this work within the global context of sustainability challenges, we can inspire collaborative efforts towards efficient waste management and renewable energy solutions.

Author Contributions

A.E.-P. led the conceptualization of the project, establishing the foundational ideas and objectives. The methodology was developed by J.M., A.E.-P. and L.E.-P., who designed and structured the approach for the study. Formal analysis was conducted by J.M. and A.E.-P., who analyzed data and ensured the accuracy of statistical interpretations. Funding acquisition was managed by A.E.-P. and F.V., securing essential resources to support the project. Throughout the process, supervision was provided by A.E.-P. and L.E.-P., offering ongoing guidance and oversight to ensure alignment with project goals. Project administration tasks, including coordinating team efforts and managing resources, were carried out by A.E.-P., L.E.-P. and F.V. The original draft of the manuscript was prepared by J.M. and A.E.-P., presenting the study’s findings and interpretations. The review and editing of the manuscript were undertaken by E.P.-C., D.Y.-S., P.V.-G., L.M., C.B. and F.V., who collectively refined and polished the final text. Software development and maintenance necessary for the project’s execution were managed by J.M., A.E.-P. and L.E.-P. under software contributions. Lastly, visualization contributions were made by F.V., D.Y.-S., E.P.-C. and A.E.-P., who created tables to clearly communicate the study’s results. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Acknowledgments

The authors are grateful for the support of the Program for the Development of Sustainable Production Systems (PDSPS), Faculty of Engineering, University of Santiago of Chile (USACH), Chile.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Tables

Table 1

Variable sets of the model.

Set	Description
$n=\left\{1,\dots ,\left|N\right|\right\}$	Raw material types correspond to the type of raw material available for transformation.
$i=\left\{1,\dots ,\left|I\right|\right\}$	Supplier locations correspond to each possible raw material supplier considered.
$j=\left\{1,\dots ,\left|J\right|\right\}$	Demand locations correspond to each potential customer considered.
$k=\left\{1,\dots ,\left|K\right|\right\}$	Production plant locations, corresponding to each possible production plant considered.
$a=\left\{1,\dots ,\left|A\right|\right\}$	Final product types, corresponding to each possible type of final product considered

Table 2

Parameter sets of the model.

Set	Description
${MPdisponible}_{i,n}$	Available quantity in tons of raw material of type n from the supplier located at i. In tons.
$Cap{W}_k$	Transformation capacity in tons of raw material entering the main production plant located at k. In tons.
${\alpha }_{n,a}$	Transformation rate from the raw material of type n to the final product of type a.
$De{m}_{j,a}\left(Max\right)$	The amount of final product of type a demanded by the customer located at j. In MWh.
$P{M}_a$	Market share percentage of product type a in the total market.
$DistP{P}_{i,k}$	Distance between supplier i and plant k. In kilometers.
$DistP{C}_{k,j}$	Distance between plant k and customer j. In kilometers.
$C_a$	The calorific value of product type a. In MWh/Ton
$M$	Known as a very large value, it was used to limit the production of products; products were only produced if the plant had been installed. If the plant located at k has raw material reception capacity, M was replaced by $Cap{W}_k$

Table 3

Constraint sets of the model.

Constraints	Description
$\sum _n{\alpha }_{n,a}\left[\sum _i{N}_{n,i,k}\right]=\sum _j{P}_{a,k,j}$ $\forall k$$,\alpha$	Mass Balance
$\sum _k{N}_{n,i,k}\le MPdisponibl{e}_{i,n}\forall$ $i$$,n$	Raw Material Availability
${\sum }_n{\sum }_i{N}_{n,i,k}\le Cap{W}_k\ast W_k\forall k$	Production Capacity
$\sum _k{C_a\ast P}_{a,k,j}\le De{m}_{j,a}\left(Max\right)$ $\forall$ $j$$,\alpha$	Demand Limitation: Upper limit of demand
$\sum _j\sum _k{C}_a\ast P_{a,k,j}\ge P{M}_a\ast \sum _{j}De{m}_{j,a}\left(Min\right)$ $\forall \alpha$	Demand Limitation: Lower limit of demand
$\sum _a\sum _j{P}_{a,k,j}\le M\ast W_k$ $\forall$ $k$	Facility Existence
${\displaystyle \sum _k}{W}_k=1$	Limitation for the number of facilities to install

Table 4

Distances in kilometers for suppliers—plants.

Supplier/Plant	Santa Marta	Santiago Poniente	Popeta	Loma Los Colorados
Santa Marta	-	44.2	65.6	101.0
Santiago Poniente	44.2	-	76.5	91.0
Popeta	65.6	76.5	-	151.0
Loma Los Colorados	101.0	91.0	151.0	-

Table 5

Distances in kilometers for customers—plants.

Plant/Costumers	Santiago	Cordillera	Chacabuco	Melipilla	Talagante
Santa Marta	35.6	42.0	49.1	38.0	47.2
Santiago Poniente	26.7	46.0	32.3	63.0	59.0
Popeta	59.2	85.6	71.8	61.4	3.1
Loma Los Colorados	75.1	95.1	59.7	114.6	133.7

References

1. Corvalán, C.; Espinoza Pérez, A.T.; Díaz-Robles, L.A.; Cubillos, F.; Vallejo, F.; Gómez, J.; Pino-Cortés, E.; Espinoza-Pérez, L.; Pelz, S.K.; Paczkowski, S. et al. Life Cycle Assessment for Hydrothermal Carbonization of Urban Organic Solid Waste in Comparison with Gasification Process: A Case Study of Southern Chile. Environ. Prog. Sustain. Energy; 2021; 40, e13688. [DOI: https://dx.doi.org/10.1002/ep.13688]

2. Espinoza Pérez, L.; Espinoza Pérez, A.; Pino-Cortés, E.; Vallejo, F.; Díaz-Robles, L.A. An Environmental Assessment for Municipal Organic Waste and Sludge Treated by Hydrothermal Carbonization. Sci. Total Environ.; 2022; 828, 154474. [DOI: https://dx.doi.org/10.1016/j.scitotenv.2022.154474] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/35276176]

3. Scapini, V.; Berrios, P. Circular Economy in Chile: Background, Law and Opportunities. WIT Transactions on Ecology and the Environment; Syngellakis, S. WIT Press: Southampton, UK, 2021; Volume 253, pp. 185-194. ISBN 978-1-78466-447-3

4. Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ) GmbH. GIZ Waste-to-Energy Options in Municipal Solid Waste Management. A Guide for Decision Makers in Developing and Emerging Countries; Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ) GmbH: Bonn, Germany, Eschborn, Germany, 2017.

5. De Santis, E.; de Iudicibus, A.; Lecce, F.; De Mei, M.; Petrazzuolo, F.; Del Giudice, A.; Carnevale, M.; Gallucci, F.; Beni, C.; Assirelli, A. et al. A Multidisciplinary Approach for the Development of a Supply Chain in Biomass Conversion of Agrifood Waste Mediated by Larvae of Hermetia illucens L.: From Rearing to By-Product Exploitation. Agriculture; 2024; 14, 1010. [DOI: https://dx.doi.org/10.3390/agriculture14071010]

6. Reis, M.B.; Colorado Lopera, H.A.; Vieira, C.M.F.; Azevedo, A.R.G.; Carvalho, E.A.S.; Monteiro, S.N. Development of Artificial Stone through the Recycling of Construction and Demolition Waste in a Polymeric Matrix. Sustainability; 2024; 16, 5952. [DOI: https://dx.doi.org/10.3390/su16145952]

7. Otunola, B.O.; Ololade, O.O. A Review on the Application of Clay Minerals as Heavy Metal Adsorbents for Remediation Purposes. Environ. Technol. Innov.; 2020; 18, 100692. [DOI: https://dx.doi.org/10.1016/j.eti.2020.100692]

8. Simsek, Y.; Lorca, Á.; Urmee, T.; Bahri, P.A.; Escobar, R. Review and Assessment of Energy Policy Developments in Chile. Energy Policy; 2019; 127, pp. 87-101. [DOI: https://dx.doi.org/10.1016/j.enpol.2018.11.058]

9. Abubakar, I.R.; Maniruzzaman, K.M.; Dano, U.L.; AlShihri, F.S.; AlShammari, M.S.; Ahmed, S.M.S.; Al-Gehlani, W.A.G.; Alrawaf, T.I. Environmental Sustainability Impacts of Solid Waste Management Practices in the Global South. Int. J. Environ. Res. Public Health; 2022; 19, 12717. [DOI: https://dx.doi.org/10.3390/ijerph191912717]

10. Chidozie, B.; Ramos, A.; Vasconcelos, J.; Ferreira, L.P.; Gomes, R. Highlighting Sustainability Criteria in Residual Biomass Supply Chains: A Dynamic Simulation Approach. Sustainability; 2024; 16, 9709. [DOI: https://dx.doi.org/10.3390/su16229709]

11. Buasan, P.; Sajjakulnukit, B.; Bowonthumrongchai, T.; Gheewala, S.H. Greenhouse Gas Emission Estimation Using Extended Input–Output Tables for Thailand’s Biomass Pellet Industry. Energies; 2024; 17, 5355. [DOI: https://dx.doi.org/10.3390/en17215355]

12. Cruz, I.A.; Santos Andrade, L.R.; Bharagava, R.N.; Nadda, A.K.; Bilal, M.; Figueiredo, R.T.; Romanholo Ferreira, L.F. Valorization of Cassava Residues for Biogas Production in Brazil Based on the Circular Economy: An Updated and Comprehensive Review. Clean Eng. Technol.; 2021; 4, 100196. [DOI: https://dx.doi.org/10.1016/j.clet.2021.100196]

13. Vallejo, F.; Díaz-Robles, L.; Vega, R.; Cubillos, F.; Espinoza, A.P.; Pinilla, F.; Pino-Cortés, E. An Experimental Study for Municipal Organic Waste and Sludge Treated by Hydrothermal Carbonization. Chem. Eng. Trans.; 2020; 81, pp. 355-360. [DOI: https://dx.doi.org/10.3303/CET2081060]

14. Kruse, A.; Dahmen, N. Hydrothermal Biomass Conversion: Quo Vadis?. J. Supercrit. Fluids; 2017; 134, pp. 114-123. [DOI: https://dx.doi.org/10.1016/j.supflu.2017.12.035]

15. Dang, C.H.; Farru, G.; Glaser, C.; Fischer, M.G.; Libra, J.A. Enhancing the Fuel Properties of Spent Coffee Grounds through Hydrothermal Carbonization: Output Prediction and Post-Treatment Approaches. Sustainability; 2023; 16, 338. [DOI: https://dx.doi.org/10.3390/su16010338]

16. García-Morato, R.; Román, S.; Ledesma, B.; Coronella, C. Co-Hydrothermal Carbonization of Grass and Olive Stone as a Means to Lower Water Input to HTC. Resources; 2023; 12, 85. [DOI: https://dx.doi.org/10.3390/resources12070085]

17. Li, J.; Zhang, W.; Liu, T.; Yang, L.; Li, H.; Peng, H.; Jiang, S.; Wang, X.; Leng, L. Machine Learning Aided Bio-Oil Production with High Energy Recovery and Low Nitrogen Content from Hydrothermal Liquefaction of Biomass with Experiment Verification. Chem. Eng. J.; 2021; 425, 130649. [DOI: https://dx.doi.org/10.1016/j.cej.2021.130649]

18. Zhai, Y.; Wang, T.; Zhu, Y.; Peng, C.; Wang, B.; Li, X.; Li, C.; Zeng, G. Production of Fuel Pellets via Hydrothermal Carbonization of Food Waste Using Molasses as a Binder. Waste Manag.; 2018; 77, pp. 185-194. [DOI: https://dx.doi.org/10.1016/j.wasman.2018.05.022]

19. Mayer, F.; Bhandari, R.; Gäth, S.A. Life Cycle Assessment on the Treatment of Organic Waste Streams by Anaerobic Digestion, Hydrothermal Carbonization and Incineration. Waste Manag.; 2021; 130, pp. 93-106. [DOI: https://dx.doi.org/10.1016/j.wasman.2021.05.019]

20. Lucian, M.; Fiori, L. Hydrothermal Carbonization of Waste Biomass: Process Design, Modeling, Energy Efficiency and Cost Analysis. Energies; 2017; 10, 211. [DOI: https://dx.doi.org/10.3390/en10020211]

21. Shahbeik, H.; Peng, W.; Kazemi Shariat Panahi, H.; Dehhaghi, M.; Guillemin, G.J.; Fallahi, A.; Amiri, H.; Rehan, M.; Raikwar, D.; Latine, H. et al. Synthesis of Liquid Biofuels from Biomass by Hydrothermal Gasification: A Critical Review. Renew. Sustain. Energy Rev.; 2022; 167, 112833. [DOI: https://dx.doi.org/10.1016/j.rser.2022.112833]

22. Odimarha, A.C.; Ayodeji, S.A.; Abaku, E.A. Machine Learning’s Influence on Supply Chain and Logistics Optimization in the Oil and Gas Sector: A Comprehensive Analysis. Comput. Sci. IT Res. J.; 2024; 5, pp. 725-740. [DOI: https://dx.doi.org/10.51594/csitrj.v5i3.976]

23. Allaoui, H.; Guo, Y.; Sarkis, J. Decision Support for Collaboration Planning in Sustainable Supply Chains. J. Clean Prod.; 2019; 229, pp. 761-774. [DOI: https://dx.doi.org/10.1016/j.jclepro.2019.04.367]

24. Arroyo, F.R.M.; Miguel, L.J. The Role of Renewable Energies for the Sustainable Energy Governance and Environmental Policies for the Mitigation of Climate Change in Ecuador. Energies; 2020; 13, 3883. [DOI: https://dx.doi.org/10.3390/en13153883]

25. Pozo, P.; Bösch, M.; Schweinle, J. Monitoring the Sustainability of the EU Biomass Supply: A Novel Hybrid Approach Combining Tracing and Selected Sustainability Impacts. Land; 2024; 13, 1366. [DOI: https://dx.doi.org/10.3390/land13091366]

26. Greenfeld, A.; Angel, D.; Farja, Y. Valuing Sustainability Impacts and Food Security Effects of Local Mariculture. Sustainability; 2024; 16, 9625. [DOI: https://dx.doi.org/10.3390/su16229625]

27. Al-Mohannadi, A.A.; Ertogral, K.; Erkoc, M. Alternative Fuels in Sustainable Logistics—Applications, Challenges, and Solutions. Sustainability; 2024; 16, 8484. [DOI: https://dx.doi.org/10.3390/su16198484]

28. de Kraker, J.; Kujawa-Roeleveld, K.; Villena, M.J.; Pabón-Pereira, C. Decentralized Valorization of Residual Flows as an Alternative to the Traditional Urban Waste Management System: The Case of Peñalolén in Santiago de Chile. Sustainability; 2019; 11, 6206. [DOI: https://dx.doi.org/10.3390/su11226206]

29. Vallejo, F.; Diaz-Robles, L.A.; Gonzalez, P.; Poblete, J. Energy Efficiency Evaluation of a Continuos Treatment of Agroforestry Waste Biomass by Hydrothermal Carbonization. Maderas Cienc. Tecnol.; 2021; 23, 2021000100415. [DOI: https://dx.doi.org/10.4067/S0718-221X2021000100415]

30. García, L.Y.; Cerda, A.A.; Lagos, R.D.P.; Muñoz, P.I.; Muñoz, M. Society’s Willingness to Pay for Certified Dry Firewood Energy in Chile. Front. Energy Res.; 2021; 9, 676654. [DOI: https://dx.doi.org/10.3389/fenrg.2021.676654]

31. Ischia, G.; Fiori, L. Hydrothermal Carbonization of Organic Waste and Biomass: A Review on Process, Reactor, and Plant Modeling. Waste Biomass Valorization; 2020; 12, pp. 2797-2824. [DOI: https://dx.doi.org/10.1007/s12649-020-01255-3]

32. Microsoft Corporation Microsoft Excel 2024. Available online: https://www.microsoft.com/es-cl/microsoft-365/excel (accessed on 12 November 2024).

33. Rodrigues, M.H.R.; da Silva, T.O.; Pitanga, H.N.; Pedroti, L.G.; Rodrigues, K.H.d.P.; Lopes, E.C.; Nalon, G.H. Efficacy of the Simplex-Centroid Method for Optimization of Mixtures of Soil, Ladle Furnace Slag and Fly Ash Applied in Pavement Construction. Sustainability; 2024; 16, 7726. [DOI: https://dx.doi.org/10.3390/su16177726]

34. Galántai, A. A Stochastic Convergence Result for the Nelder–Mead Simplex Method. Mathematics; 2023; 11, 1998. [DOI: https://dx.doi.org/10.3390/math11091998]

35. Gelmez, E.; Özceylan, E.; Mrugalska, B. The Impact of Green Supply Chain Management on Green Innovation, Environmental Performance, and Competitive Advantage. Sustainability; 2024; 16, 9757. [DOI: https://dx.doi.org/10.3390/su16229757]

36. Dahmer, D.; Scandorieiro, S.; Bigotto, B.G.; Bergamini, T.A.; Germiniani-Cardozo, J.; da Costa, I.M.; Kobayashi, R.K.T.; Nakazato, G.; Borsato, D.; Prudencio, S.H. et al. Multifunctional Biotechnological Lip Moisturizer for Lip Repair and Hydration: Development, In Vivo Efficacy Assessment and Sensory Analysis. Cosmetics; 2023; 10, 166. [DOI: https://dx.doi.org/10.3390/cosmetics10060166]

37. European CommissionJoint Research CentreInstitute for Enviroment and Sustainability. ILCD Handbook: Recommendations for Life Cycle Impact Assessment in the European Context; 1st ed. Publication office of the European Commission: Luxemburg, 2011; ISBN 9789279174513

38. Environmental Ministry of Chile. National Organic Waste Strategy Chile 2040; Environmental Ministry of Chile: Santiago, Chile, 2021.

39. Holland Circular Hotspot. Waste Management Country Report; Holland Circular Hotspot: Hoofddorp, The Netherlands, 2021.

40. Valenzuela-Levi, N. Poor Performance in Municipal Recycling: The Case of Chile. Waste Manag.; 2021; 133, pp. 49-58. [DOI: https://dx.doi.org/10.1016/j.wasman.2021.07.021]

41. Alao, M.A.; Popoola, O.M.; Ayodele, T.R. Waste-to-energy Nexus: An Overview of Technologies and Implementation for Sustainable Development. Clean. Energy Syst.; 2022; 3, 100034. [DOI: https://dx.doi.org/10.1016/j.cles.2022.100034]

42. Kalogirou, E.N. Waste-to-Energy Technologies and Global Applications; CRC Press: Boca Raton, FL, USA, 2017.

43. Espinoza Pérez, L.; Ziegler-Rodríguez, K.; Espinoza Pérez, A.T.; Vásquez, Ó.C.; Vázquez-Rowe, I. Closing the Gap in the Municipal Solid Waste Management between Metropolitan and Regional Cities from Developing Countries: A Life Cycle Assessment Approach. Waste Manag.; 2021; 124, pp. 314-324. [DOI: https://dx.doi.org/10.1016/j.wasman.2021.02.020]

44. Dang, C.H.; Cappai, G.; Chung, J.-W.; Jeong, C.; Kulli, B.; Marchelli, F.; Ro, K.S.; Román, S. Research Needs and Pathways to Advance Hydrothermal Carbonization Technology. Agronomy; 2024; 14, 247. [DOI: https://dx.doi.org/10.3390/agronomy14020247]

45. Che, C.A.; Heynderickx, P.M. Hydrothermal Carbonization of Plastic Waste: A Review of Its Potential in Alternative Energy Applications. Fuel Commun.; 2024; 18, 100103. [DOI: https://dx.doi.org/10.1016/j.jfueco.2023.100103]

46. CDT Medición Del Consumo Nacional de Leña y Otros Combustibles Sólidos Derivados de La Madera. Available online: https://www.senado.cl/site/presupuesto/2015/cumplimiento/Protocolo%202015/ORD.%201245%20Protocolo%20Estudios%20Eficienci%20Energ%C3%A9tica/Estudio%20consumo%20nacional%20de%20le%C3%B1a/Informe%203%20LE%C3%91A%20150915_rev%20rrh.pdf (accessed on 5 November 2024). (In Spanish)

47. Reyes, R.; Schueftan, A.; Ruiz, C.; González, A.D. Controlling Air Pollution in a Context of High Energy Poverty Levels in Southern Chile: Clean Air but Colder Houses?. Energy Policy; 2019; 124, pp. 301-311. [DOI: https://dx.doi.org/10.1016/j.enpol.2018.10.022]

48. Actualización de La Situación Por Comuna y Por Región En Materia de Rsd y Asimilables. Available online: https://www.subdere.gov.cl/sites/default/files/Catastro%20de%20sitios%20septiembre%202019.pdf (accessed on 5 November 2024). (In Spanish)

49. Orazbayev, B.; Orazbayeva, K.; Ospanov, Y.; Suleimenova, S.; Kurmangaziyeva, L.; Makhatova, V.; Izbassarov, Y.; Otebaeva, A. Methods of Multi-Criteria Optimization of Technological Processes in a Fuzzy Environment Based on the Simplex Method and the Theory of Fuzzy Sets. Mathematics; 2024; 12, 2856. [DOI: https://dx.doi.org/10.3390/math12182856]