Sustainable Multi-Objective Models for Waste-to-Energy and Waste Separation Site Selection

Abstract

In the past, the Iranian government has excessively relied on fossil fuels, gas, and oil resources, leading to energy-related issues and increasing power outages in the provinces during peak seasons. One of the best opportunities for energy production in Iran is through the establishment of bio-methane and waste-based energy parks. This research aims to determine the optimal locations for waste sorting centers and the establishment of waste-to-energy plants. The coexistence and interaction of these two facilities will enhance system efficiency. To achieve this goal, two mathematical models, with three objectives, have been designed. The static allocation model assigns each industrial park to a waste sorting center, while the dynamic allocation model selects the shortest route from the industrial park to the waste-to-energy center. The first objective is to minimize establishment costs, while the second and third objectives aim to reduce the system’s waiting costs. Waiting for waste shipments leads to pollution, and the desirability and route length can increase the likelihood of organic pollution. Therefore, this research seeks to minimize these factors. The model results indicate that the sorting and energy production centers have been selected to incur the lowest establishment, transportation, and waiting costs. Additionally, the sensitivity analysis section of the model reveals the impact of coefficient changes on the model’s results.

1. Introduction

1.1. Forewords

Turning waste into energy is of great importance as a critical process in waste management and a vital aspect of environmental, economic, and social sustainability. This process addresses two significant challenges in the world: waste management and energy supply [1]. Below, the importance of converting waste into energy is discussed from two main perspectives [2]: environmental and economic. The improper disposal of waste has detrimental consequences for the environment, affecting water, soil, and air quality [3]. Non-degradable waste directly depletes natural resources and introduces environmental pollutants [4]. By converting waste into energy, several of these issues can be addressed [5,6]. Firstly, it reduces the volume of landfilled waste, alleviating pressure on land surfaces and decreasing ground pollution. Secondly, through efficient and controlled waste incineration, air pollution is reduced [7,8]. This waste-to-energy (WtE) conversion can also optimize the utilization of fossil fuel resources and mitigate greenhouse gas emissions [9].

Energy production from waste is considered a high potential and trending energy source [7,10]. Given the growing population and our increasing energy needs [11], the conversion of waste into energy has garnered significant attention from various nations [12]. This approach not only contributes to increasing the energy supply, but it also transforms waste into an economic resource. Consequently, obtaining energy from waste reduces reliance on fossil energy sources and supports a more sustainable approach to energy [1].

1.2. Waste Management Situation in Iran

The municipal solid waste volume per capita in the Qom, Markazi, and Hamedan provinces of Iran is significant in terms of waste management and environmental considerations [11]. These three provinces, located near each other, face diverse challenges in regards to waste and garbage production and require effective measures for waste management [13,14]. Qom Province, with its 4 industrial zones and 7 industrial parks, Markazi Province with its 16 zones and 18 parks, and Hamedan Province, with its 16 zones and 13 parks, are all integral to the social, economic, and environmental planning within their respective zones, serving as essential elements of urban planning and local development.

In Qom Province, approximately 26,616 tons of organic and solid waste are generated monthly, which equates to roughly 810 g per person per day. Waste generation in Qom exceeds the national average; therefore, some efforts have been made to increase the economic value of waste and its segregation. Currently, 10% of waste is segregated, with a focus on recyclables, especially plastics. However, issues remain unresolved regarding industrial waste in the industrial parks. The majority of industrial waste from this area is sent to other provinces for recycling, creating significant environmental issues and higher costs for this province [7,15].

In Markazi Province, approximately 25,110 tons of municipal waste are produced monthly, with 9610 tons allocated to the city of Arak. Of the municipal waste, 1800 tons (equivalent to 7.1%) is sent to the composting plant, while the remainder is disposed of in landfills [16]. Waste in the city of Arak is relatively wet, with some of it being segregated by waste pickers. Approximately 68% of this waste is wet, while the rest is dry and recyclable. Furthermore, Markazi Province is recognized as one of the country’s five industrial provinces [4]. Due to the numerous industrial parks and zones in this province, it requires the development of recycling or energy production infrastructure. In Hamedan Province, daily waste production amounts to 800 g per person, exceeding the national average.

Based on the information regarding the number of industrial consumers in the provinces compared with the national average, as shown in Figure 1a, it can be concluded that Qom, Hamedan, and Markazi provinces comprise a higher number of industrial consumers, indicating significant industrial activity in these provinces [7,16]. However, it appears that the gross energy production in these provinces may not be sufficient (Figure 1b), and there is a need to enhance the capacity of the power plants in these zones.

Furthermore, it is observed that Qom, Hamedan, and Markazi provinces have higher amounts of generated waste when compared to the national average. This could present a suitable opportunity to establish an energy park or WtE plants in these zones. Given the high energy demand in these provinces and the presence of a significant amount of waste, utilizing waste for sustainable energy production can be considered to contribute to increased energy production in these areas. Moreover, these three provinces do not currently exhibit a favorable situation in terms of renewable energy, such as wind and solar energy, production capacity compared to that of other provinces (Figure 2). Therefore, to meet the energy needs in these zones, alternative energy sources, such as energy derived from waste and hydrogen, can be explored [17]. While the specific case being studied may not be ideal for green hydrogen production, it does exhibit potential for blue and turquoise hydrogen. Currently, hydrogen plants are operating on a limited scale in this region. However, there is significant potential to establish new biogas plants in compliance with governmental plans. These initiatives can help improve and strengthen energy infrastructure in these three provinces, leading to increased production of sustainable and environmentally friendly energy in these areas.

1.3. Challenges and Contributions

Considering the existing challenges, which include a significant amount of industrial and municipal waste, a relatively low electricity generation capacity, and the lack of suitable resources in the field of renewable and non-renewable energy production, these three provinces exhibit unique characteristics. Taking into account their geographical proximity to the capital city and their adjacency to high-consumption provinces, these provinces can serve as an essential source in the process of energy production from waste. In addition to meeting their own energy needs, they have the potential to create the capacity for the export of energy to neighboring provinces.

These actions not only contribute to improving the energy situation in these provinces, but they can also help reduce the uncertainty and energy shortage issues in the capital provinces such as Tehran and Isfahan. Energy production from waste presents a significant opportunity for the optimal utilization of resources available in these three provinces. Therefore, this research aims to create a model for selecting the best suitable locations for the development of these energy fields, thus contributing to the improvement and enhancement of energy infrastructure in these three provinces. In the following sections of the study, the literature will be reviewed, the mathematical models described, and the case study explained; the results and conclusions will also be presented.

2. Literature Review

2.1. WtE Background

WtE technologies have garnered significant attention in recent years as a sustainable solution for managing municipal solid waste (MSW) and simultaneously addressing energy demands. Malav, Yadav [18] focused on India’s MSW management challenges, emphasizing the pressing need for effective waste collection and segregation, as well its safe disposal, due to the continuous growth of industrialization, urbanization, and population. The study identified various WtE technologies, such as pyrolysis, gasification, incineration, and bio methanation, as promising methods to convert MSW into useful energy in eco-friendly ways. Moreover, recommendations were provided to enhance the currently implemented solid waste management (SWM) practices in India. This review offers valuable insights for scholars, researchers, authorities, and stakeholders involved in MSW management, guiding them toward informed decision making.

In New Zealand, M.T. Munir, Mohaddespour [19] for a circular economy approach to MSW management, highlighting the importance of safe waste disposal while addressing rising energy demands. They emphasized effective communication and safety measures to gain community acceptance of WtE technologies. Additionally, combining multiple technologies was suggested for achieving efficient waste management and circular economy goals. Conversely, Mukherjee, Denney [8] conducted a comprehensive review of MSW-to-energy trends in the USA, where only 13% of MSW is utilized for energy recovery.

Hoang, Varbanov [20] explored a circular bio-economy concept for MSW-to-energy conversion, categorizing technologies into direct and indirect approaches and highlighting economic indicators. Sharma, Basu [6] focused on hydrogen energy production from waste materials, emphasizing biological methods. Lee, Kim [21] stressed the need for the comparative analysis of hybrid WtE systems, emphasizing the potential of thermochemical waste processing integrated with renewable energy technologies. Khan and Kabir [22] conducted a sustainability assessment, favoring anaerobic digestion as a sustainable technology. Chen, Li [1] introduced an efficient medical-WtE design. Alao, Ayodele [12] proposed a hybrid multi-criteria method for technology selection, favoring anaerobic digestion. Finally, de Campos, Silva [23] compared waste management and WtE practices in Brazil and Portugal, highlighting sustainability and the principles of a circular economy. These collective studies contribute significantly to the global discourse on sustainable waste management and energy production.

2.2. Site Location and Selection in WtE

Several research studies have explored different aspects of WtE facility location, considering various factors such as sustainability, multi-criteria decision making, and suitability analysis. This integrated literature review discusses the findings and contributions of three notable studies in this domain. Hrabec, Šomplák [24] addressed the challenge of sustainable WtE facility location optimization by developing two mathematical models. The first model, a mixed-integer linear method, efficiently minimized costs, but lacked long-term sustainability when plant capacity went underutilized. To address this issue, their second model introduced penalty cost functions associated with reduced energy sales and unused plant capacity. This nonlinear model provided a more sustainable solution by considering the influence of demand on energy sales, emphasizing the need for a balance between facility numbers and capacity utilization.

In another study, Meng, Pang [25] presented a two-stage model for optimal site selection of WtE plants, focusing on Beijing, China. They introduced single-valued neutrosophic sets to handle fuzzy criteria and combined them with the trial evaluation laboratory–analytical network process approach. This innovative model integrated GIS and the extend evaluation based on the distance from average solution method, providing a stable and feasible approach for planning the location of WtE plants based on environmental, economic, technical, and social factors.

Additionally, Al-Ruzouq, Abdallah [26] explored the use of spatial suitability analysis for WtE facility location in Sharjah, UAE, using machine learning algorithms like a gradient boosted tree, a decision tree, and support vector machines. They identified factors such as the distance from landfills, coastline proximity, and elevation as significant influences on optimal WtE facility location. This research demonstrated the potential of advanced analytical techniques and geographic data to effectively guide WtE facility location decisions.

The literature review revealed the ongoing importance of developing an appropriate model for selecting the best locations for establishing energy parks and WtE plants. Upon review, it is evident that recent efforts have resulted in a wide variation in the capacities of waste-to-energy (WtE) facilities, the number of municipalities involved, and the size of the areas served. In some instances, there are more than 200 supplying areas, with only three WtE plants, while there are also different types of scenarios with regards to project constraints. Regardless of the problem’s size, it is crucial to consider the real-world situation and address it within its limitations. In the present study, the problem is confined to provinces, and regional decisionmakers may impose constraints on the transportation outside of designated zones. Furthermore, it is worth noting that WtE plays a relatively minor role in Iran’s overall energy landscape, primarily serving small-scale industrial applications, in most cases.

In this model, the location considerations must encompass construction and maintenance costs and transportation expenses, as well as environmental factors that divert waste away from less traversed routes, preventing pollution. The need for multi-criteria and diverse modeling to select suitable locations for energy resource production and waste management has not been thoroughly examined in the previous literature.

3. Materials and Methods

If it is assumed that the problem is of the graph type, it can be stated that G = (N, S) is a graph consisting of N nodes and a set of edges, S, representing communication pathways between nodes [27]. Some nodes, based on feasibility and other considerations, can serve as candidate locations [28] for setting up WtE centers (energy parks or plants). The distribution for the model was determined using MATLAB R2020b’s distribution fitting tools, with historical data. The arrival of waste at each node for the energy conversion process, originating from industrial centers (waste collection and sorting), adheres to a Poisson process, with a rate denoted as λ_i. Additionally, if the total processing rate at each waste collection and sorting center is considered an average S_j, the waiting time for recycling follows an exponential distribution. If the set formed by the WtE centers is regarded as a connected set, then the set consisting of industrial centers can be seen as an M/M/1 queueing system.

Additionally, waste shipments X to WtE centers, if needed, are proportional to the number of centers and their capacities, with this probability being influenced by the travel desirability between the nodes [27,29]. Since each output from the industrial centers for waste generation are randomly sent to WtE centers, the entry process with regards to the WtE centers will also be Poisson ratios [30]. If the total recovery rate at each WtE center is considered as an average S_k, the recovery time at these centers is also governed by an exponential distribution. Consequently, each WtE center can be regarded as an M/M/1 queueing system [31].

The waiting costs for suppliers, supplier travel, WtE center setup, and ongoing costs must be considered for modeling and solving such a WtE network. It is evident that these costs are not of the same type. Therefore, in this research, multi-objective mathematical models have been proposed for designing a network of centers. The current value of ongoing costs can be easily obtained, based on the project’s lifespan. On the other hand, these costs are somewhat proportional to the WtE capacity, which has been observed in the startup costs. Therefore, these costs have not been considered as a separate objective function. Before introducing the models, the indices, parameters, and variables were defined as follows:

Indices:
i	Index of industrial park/zone (i = 1, 2, …, m)
j	Candidate location for the construction of waste collection and separation centers (j = 1, 2, ..., n)
k	Candidate location for building a WtE center (k = 1, 2, …, l)
Parameters:
λi	Waste production rate of the industrial park i, λi ≥ 0
Ujk	The desirability of the output transported from the waste collection and separation center in the candidate location j to the WtE center in the candidate location k, 0 < Ujk ≤ 1
є	A very small number
${ C}_j^1$	The fixed cost of setting up a waste collection and separation center in the candidate location j, $C_j^1$ > 0
${ C}_k^2$	The fixed cost of setting up a WtE center in the candidate location k, $C_k^2$ > 0
${CS}_j^1$	The fixed cost for each process/transformation in the waste collection and separation center in the candidate location j, ${CS}_j^1$ > 0
${CS}_k^2$	The fixed cost per processing/conversion in the center of WtE in the candidate location k, ${CS}_k^2$ > 0
$w^1$	The cost of waiting for each shipment to receive the service of the waste collection and separation center per unit of time, $w^1$ > 0
$w^2$	The cost of waiting for each shipment to receive service at the WtE center per unit of time, $w^2$ > 0
$TrC$	The cost of sending service waste per kilometer, $TrC$ > 0
$d_{ij}^1$	The distance of the candidate location j from the industrial park i when setting up the waste collection and separation center, $d_{ij}^1$ > 0
$d_{jk}^2$	The distance of the candidate location j from the waste collection and separation center to the WtE, if the waste collection and separation center has been set up, $d_{jk}^2$ > 0
β	An estimate of the percentage of wastes that, after receiving the service from the waste collection and separation center, must be sent to the WtE, 0 < β ≤ 1
Independent decision variables:
$X_j$	If the waste collection and separation center is set up in the candidate location, 1; otherwise, 0.
$Y_k$	If the WtE center is initialized at the candidate location k, 1; otherwise, 0
$S_j^1$	The rate of processing/conversion in the waste collection and separation center of the candidate location j, $S_j^1$ ≥ 0
$S_k^2$	The rate of processing/conversion in the WtE of the candidate location k, $S_k^2$ ≥ 0
Dependent decision variables:
${ \delta }_j^1$	The capacity of the waste collection and segregation center of the j candidate location, ${\delta }_j^1$ ≥ 0
${ \delta }_k^2$	The capacity of the WtE of the candidate location k, ${\delta }_k^2$ ≥ 0
${ p}_{jk}$	The probability that the output from the waste collection and separation center set up in the j candidate location will go to the WtE of the candidate location k, 0 ≤ $p_{jk}$ ≤ 1
$t_{ij}$	The type of decision variable in the fixed allocation model (FAM) and the dynamic allocation model (DAM) is different: $t_{ij}$ industrial park i should be assigned to the waste collection and separation center set up in candidate location j (independent variable in FAM) or industrial park i, based on the closest distance to the waste collection; and the separation center set up in the candidate location should be allocated (dependent variable in the DAM) as 1; otherwise, 0

The investigated system for network of waste management centers includes a set of nodes representing the locations of the separation and conversion centers and the edges of the path between them. Waste management centers consist of two waste collection and separation centers and WtE centers, and all waste collection and separation centers are similar, providing the same process; this assumption also exists for the WtE centers. The nature of the process and the purpose of processing/transformation in the waste collection and separation centers is to separate the waste received from the industrial parks and send it to the WtE centers. The WtE center also has the task of converting organic WtE in the process, the output of which will lead to the production of clean energy, with low carbon dioxide emissions. The waste collection and separation centers are stationary, and the waste is sent to the centers. It is assumed that all the consignment sent to a center is completely separated or used. There is a potential amount of waste shipment from anywhere within the industrial estates. The input rate of each node is a Poisson process. The duration of the processing/transformation in the waste collection and separation centers and the WtE is random and follows an exponential distribution. In the first model, the waste shipment is assigned to a waste collection and separation center in each industrial park, and in the second model, it is assumed that the waste shipment is transported to the nearest waste collection and separation center.

3.1. Mathematical Model

To solve the problem outlined in this article, three objective functions were employed [32]: the first objective function considers the costs of set up of the centers and the processing/transformation of the waste, the second objective function takes into account the waiting time costs at the established centers, and the third objective function incorporates the cost of waste shipment and transportation.

3.1.1. Set-Up Costs of Centers

The set-up costs of the centers consist of the sum of the fixed costs for establishing a waste collection and sorting center, the fixed costs for setting up a WtE center, the fixed costs for sorting at the waste collection and sorting center, and the transformation costs at the WtE center [33].

$$min{Z}_1={ \mathit{C}}_{\mathit{j}}^1\sum _{\mathit{j}=1}^{\mathit{n}}{\mathit{X}}_{\mathit{j}}+{ \mathit{C}}_{\mathit{k}}^2\sum _{\mathit{k}=1}^{\mathit{l}}{\mathit{Y}}_{\mathit{k}}+{\mathrm{CS}}_{\mathit{j}}^1\sum _{\mathit{j}=1}^{\mathit{n}}{\mathit{S}}_{\mathit{j}}^1+{\mathrm{CS}}_{\mathit{k}}^2\sum _{\mathit{k}=1}^{\mathit{l}}{\mathit{S}}_{\mathit{k}}^2$$

(1)

3.1.2. Waiting Costs

This function is intended to reduce pollution levels and the release of pollution into the environment. While there may not be a specific environmental indicator in this case, time is a crucial factor when dealing with organic waste. Organic waste left on the land for prolonged periods will result in the release of GHG into the atmosphere. Therefore, it is imperative to minimize the waiting time and associated waiting costs to mitigate these harmful effects.

Considering that there is no possibility for temporary storage or temporary burial of these wastes, the environmental solution to deal with these problems is to create a quick process with a minimal wait for transportation from the industrial parks to the waste collection and separation centers, and ultimately, to the WtE. Taking into account the random arrival time of waste consignments due to their relay from the industrial parks to the centers, according to the Poisson distribution and following the duration of separation and transformation of the waste consignments from the exponential probability distribution, each of the centers can be considered as a system M/M/1 queue. The total average wait time of the waste shipment in a certain period is equal to the entry rate in the average wait time of each waste shipment for separation or conversion. Therefore, the sum of the average wait time of the waste shipment is equal to $\left(\frac{\mathrm{Input}\mathrm{Ratio}\times 1}{\mathrm{Dissociation}\mathrm{rate}-\mathrm{Input}\mathrm{Ratio}}\right)$.

If the wait time cost per unit time for each shipment at each of the waste collection and sorting centers is denoted as $w^1$ and $w^2$, respectively, the following equation presents the total average wait cost of the waste shipment at the established waste collection and sorting and WtE centers:

$$min{Z}_2=w^1{\sum }_{j=1}^n\left(\frac{{ \delta }_j^1}{S_j^1-{ \delta }_j^1}\right)+ w^2\sum _{k=1}^l\left(\frac{{ \delta }_k^2}{S_k^2-{ \delta }_k^2}\right)$$

(2)

3.1.3. Distance and Travel Costs for Waste Shipments

Another important objective function is the distance that waste shipments must travel to reach the sorting or processing facilities. This objective function is of paramount importance because waste shipments should be dispatched in a way that covers the shortest distance to minimize potential environmental pollution. Moreover, considering that organic waste materials typically have a high moisture content, it is better to avoid long-distance transport [28], especially during very hot or very cold seasons. Icing can lead to difficulties in waste sorting, and exposure to heat and dry conditions can result in moisture loss and reduced WtE efficiency. Therefore, efforts are made to locate facilities in a manner that minimizes the total distance traveled by waste shipments.

Since waste collection and sorting centers provide the opportunity to separate waste materials, the parameter β estimates the percentage of organic waste materials that are separated at the collection and sorting center and then sent to the WtE centers. The parameter TrC represents an approximate cost per kilometer of transporting a 10-ton waste shipment. The following objective function calculates the total cost of the distance traveled by the waste shipments:

$$min{\mathit{Z}}_3=TrC\sum _{\mathit{i}=1}^{\mathit{m}}\sum _{\mathit{j}=1}^{\mathit{n}}{\lambda }_{\mathit{i}}{\mathit{t}}_{ij}{\mathit{d}}_{ij}^1+TrC\sum _{\mathit{j}=1}^{\mathit{n}}\sum _{\mathit{k}=1}^{\mathit{l}}{ \beta \delta }_{\mathit{j}}^1{\mathit{p}}_{jk}{\mathit{d}}_{jk}^2$$

(3)

3.2. Fixed Allocation Model (FAM)

Assuming that each industrial estate is assigned to a waste collection and sorting center, and waste shipments must be allocated to the waste collection and sorting center corresponding to their estate, the mathematical model is presented as follows:

$${minZ}_1={ \mathit{C}}_{\mathit{j}}^1\sum _{\mathit{j}=1}^{\mathit{n}}{\mathit{X}}_{\mathit{j}}+{ \mathit{C}}_{\mathit{k}}^2\sum _{\mathit{k}=1}^{\mathit{l}}{\mathit{Y}}_{\mathit{k}}+{\mathrm{CS}}_{\mathit{j}}^1\sum _{\mathit{j}=1}^{\mathit{n}}{\mathit{S}}_{\mathit{j}}^1+{\mathrm{CS}}_{\mathit{k}}^2\sum _{\mathit{k}=1}^{\mathit{l}}{\mathit{S}}_{\mathit{k}}^2$$

$$min{\mathit{Z}}_2={\mathit{w}}^1{\sum }_{\mathit{j}=1}^{\mathit{n}}\left(\frac{{ \delta }_{\mathit{j}}^1}{{\mathit{S}}_{\mathit{j}}^1-{ \delta }_{\mathit{j}}^1}\right)+{\mathit{w}}^2\sum _{\mathit{k}=1}^{\mathit{l}}\left(\frac{{ \delta }_{\mathit{k}}^2}{{\mathit{S}}_{\mathit{k}}^2-{ \delta }_{\mathit{k}}^2}\right)$$

$$min{\mathit{Z}}_3=TrC\sum _{\mathit{i}=1}^{\mathit{m}}\sum _{\mathit{j}=1}^{\mathit{n}}{\lambda }_{\mathit{i}}{\mathit{t}}_{ij}{\mathit{d}}_{ij}^1+TrC\sum _{\mathit{j}=1}^{\mathit{n}}\sum _{\mathit{k}=1}^{\mathit{l}}{ \beta \delta }_{\mathit{j}}^1{\mathit{p}}_{jk}{\mathit{d}}_{jk}^2$$

$$\begin{array}{cc}s.t:\hfill & \\ { \delta }_{\mathit{j}}^1={\displaystyle \sum _{\mathit{i}=1}^{\mathit{m}}}{\lambda }_{\mathit{i}}{\mathit{t}}_{ij}\hfill & \forall \mathit{j}\end{array}$$

(4)

$${ \mathsf{\delta }}_{\mathrm{k}}^2=\sum _{\mathrm{j}=1}^{\mathrm{n}}\mathsf{\beta }{\mathrm{p}}_{\mathrm{jk}}{ \mathsf{\delta }}_{\mathrm{j}}^1\forall \mathrm{k}$$

(5)

$${\mathit{t}}_{ij}\le {\mathit{X}}_{\mathit{j}}\forall \mathit{i},\mathit{j}$$

(6)

$${\sum }_{\mathit{j}=1}^{\mathit{n}}{\mathit{t}}_{ij}=1 \forall \mathit{i}$$

(7)

$${\mathit{S}}_{\mathit{j}}^1<{ \delta }_{\mathit{j}}^1+є \forall \mathit{j}$$

(8)

$${\mathit{S}}_{\mathit{k}}^2<{ \delta }_{\mathit{k}}^2+є \forall \mathit{k}$$

(9)

$${\mathit{p}}_{jk}=\frac{{\mathit{Y}}_{\mathit{k}}{\mathit{U}}_{jk}}{{\sum }_{ḱ}^{\mathit{l}}{\mathit{Y}}_{ḱ}{\mathit{U}}_{\mathit{j}ḱ}}\forall \mathit{j},\mathit{k}$$

(10)

$${\sum }_{\mathit{k}=1}^{\mathit{l}}{\mathit{Y}}_{\mathit{k}}\ge 1 \forall \mathit{i}$$

(11)

$${\mathit{X}}_{\mathit{j}}\in \left\{0,1\right\}, {\mathit{Y}}_{\mathit{k}}\in \left\{0,1\right\} , {\mathit{t}}_{ij}\in \left\{0,1\right\}$$

(12)

Equation (4) presents the capacity rate of the established waste collection and sorting center at candidate location j. Equation (5) calculates the total capacity rate at candidate locations for establishing WtE centers. The capacity at each WtE center depends on the percentage of waste shipments that are candidates for conversion to energy (β) and the potential of each of the WtE centers for the shipment of waste from the waste collection and sorting centers, which is estimated as a probability (${\mathit{p}}_{jk}$). Constraints (6) and (7) ensure that each waste shipment is only sent to one collection and sorting center. For the stability of a queueing system, the processing/conversion rate must always be less than the capacity at the established centers. Constraints (8) and (9) have been added to the model for this purpose. Constraint (10) indicates the probability of waste traveling from the waste collection and sorting center to the WtE center if the WtE center has been established at candidate location k. This probability depends on the desirability of the waste shipment sent to each of the candidate locations for establishing WtE centers. Constraint (11) ensures that at least one WtE center is established, and constraint (12) shows the type of decision variables included.

3.3. Dynamic Allocation Model (DAM)

As mentioned, in the first model, each industrial estate is assigned to a waste collection and sorting center, and the waste shipments must be allocated to the assigned waste collection and sorting center. In the second model, it is assumed that waste shipments travel to the nearest center. Thus, the following two constraints are added to the FAM:

$${\mathit{t}}_{ij}+(1-{\mathit{X}}_{\mathit{j}})\le 1 \forall \mathit{i},\mathit{j}$$

(13)

$${\mathit{t}}_{ij}\ge {\mathit{t}}_{ij\prime }\hspace{1em}if\hspace{1em}{\mathit{d}}_{ij}^1<{\mathit{d}}_{ij\prime }^1\forall \mathit{i},\mathit{j}$$

(14)

Constraints (13) and (14) ensure that waste shipments from each industrial estate travel to the nearest established waste collection and sorting center. It worth noting that since the decision maker is a governmental organization, there are instances in which provincial governments choose to allocate their waste to their preferred WtE facility. However, in the DAM, these limitations were not taken into account, and the model was allowed to select the nearest WtE facility.

4. Results

4.1. Case of Three Provinces in Iran

Since waste management centers provide one of the most essential urban infrastructures, the proposed waste management center location model’s performance was evaluated in three Iranian provinces: Hamadan, Markazi, and Qom. As mentioned in the introduction section, these three provinces, particularly Markazi at the area’s center, contribute significantly to the country’s production levels. Below (Figure 3) is a map illustrating the industrial zones and parks found in these three provinces.

Furthermore, in terms of definition, there is not much difference between industrial estates and industrial zones. However, industrial estates usually have larger dimensions and extents compared to industrial zones. Considering the establishment of industrial estates in various locations, there are large industrial estates, ranging from 200 to 3000 hectares, in the country. Still, an industrial zone initially starts with an area of less than 50 hectares and gradually expands through development projects and may eventually become an industrial estate.

4.2. Determining Parameter Values

Eight industrial zones located in these three provinces were considered as candidates centers for the mentioned facilities. The reason for selecting these areas is the availability of space, the potential for further growth, and the absence of pollution. Additionally, eight industrial zones with fewer active factories and workshops, taking into account road access and government budget constraints, were chosen. To calculate the waste shipment arrival rate at the waste collection and sorting centers (λ), Equation (15) is used, in which, on any given day, each industrial estate or zone contributes:

$${\lambda }_i=\mathrm{Residual}\mathrm{shipment}\mathrm{rate}\times \mathrm{Production}\mathrm{volume}$$

(15)

The entry rates of waste from industrial estates or industrial zones to the waste collection and sorting centers in one day have been calculated in

Table 1. The rate of arrival of waste consignments to waste collection and separation centers (λ_i) in one day.

i	C1	C2	C3	C4
λ	313	89	127	402
i	C5	C6	C7	C8
λ	1358	69	128	102

.

Because the centers for all eight candidates are considered to be located at the selected industrial zone’s center, the distance from each industrial park or industrial area to the candidate locations for establishing waste collection and sorting centers ($d_{ij}^1$) is calculated as the distance between the centers in kilometers. The corresponding table is an 8 × 74 matrix that specifies the distances between nodes. It is important to note that it is possible to establish a waste collection and sorting center and a WtE center at the same node. Therefore, similarly, the distance between candidate locations for establishing waste collection and sorting centers to candidate locations for establishing WtE centers ($d_{jk}^2$) is calculated in kilometers, according to

Table 2. Distance between candidate locations for setting up waste collection and separation centers and locations for setting up WtE centers (${\mathit{d}}_{jk}^2$).

	C1	C2	C3	C4	C5	C6	C7	C8
C1	0
C2	119	0
C3	11	122	0
C4	69	78	70	0
C5	120	39	90	87	0
C6	66	87	48	42	39	0
C7	124	123	134	114	87	88	0
C8	208	127	192	187	111	155	178	0

. These distances are calculated in terms of road kilometers and represent traversable distances.

A portion of the waste shipment designated for processing by WtE facilities, as determined from available statistics in the reports of the environmental organization, accounts for 18% (β) of the total waste shipment entering the waste collection and separation centers. Although it appears that these shipments should contain a larger amount of organic materials capable of being converted into energy, the provided were employed. The number of waste shipments, each with a probability associated with the desirability of their transport to each of the candidate locations for WtE facility deployments, refers to the WtE facilities. This desirability value depends on factors such as distance, road quality, and environmental pollution risk. The effective factors and the mathematical relationship of desirability were obtained through surveys. Initially, the influential factors were examined and surveyed. Then, inquiries were made regarding desirability, considering these factors. The values presented were normalized, and a function for the desirability of travel was fitted, based on the responses of five experts working in the industrial parks of the mentioned provinces. Equation (16) provides the resulting desirability function.

$${\mathit{U}}_{jk}={\left(\frac{50-{\left({\mathit{d}}_{jk}^2\right)}^{\frac{2}{3}}}{50}\right)}^3·{\mathit{k}}_1·{\mathit{k}}_2$$

(16)

k₁: Road quality factor and low risk in terms of pollution, 0.5 ≤ k₁ ≤ 1.

k₂: Coefficient of desirability of energy production in terms of usability and the possibility of contributing to the energy network, 0.7 ≤ k₂ ≤ 1.

The k₁ and k₂ values are calculated based on expert estimations using a Likert scale ranging from 1 to 9. Subsequently, these values are normalized corresponding to the consensus among the experts, according to their upper and lower limits. The results of the calculations are shown in

Table 3. The desirability of sending waste from waste collection and separation centers to candidate locations for WtE centers (U_jk).

	C1	C2	C3	C4	C5	C6	C7	C8
C1	0.95	0.011	0.607	0.028	0.03	0.038	0.007	0.003
C2	0.014	0.9	0.012	0.028	0.064	0.022	0.009	0.011
C3	0.607	0.012	0.95	0.024	0.035	0.044	0.008	0.003
C4	0.032	0.024	0.024	0.95	0.031	0.043	0.008	0.003
C5	0.026	0.045	0.03	0.022	1	0.051	0.015	0.013
C6	0.049	0.022	0.05	0.043	0.073	0.9	0.015	0.006
C7	0.007	0.009	0.009	0.008	0.021	0.015	0.9	0.003
C8	0.003	0.011	0.003	0.003	0.019	0.006	0.003	0.9

and as can be seen, the convenience of traveling from each center to the same center, that is, the center for the separation and conversion into energy, is the most convenient.

The fixed cost of establishing waste collection and separation centers and WtE facilities is estimated to be 180 units ($C_j^1$) and 630 units ($C_k^2$), respectively, based on conducted investigations. The fixed cost of processing/conversion for each waste collection and separation center is approximately 0.67 units (${CS}_j^1$), and the fixed cost of each processing/conversion at the WtE facility is approximately 1.5 units (${CS}_{\mathit{k}}^2$). The waiting cost of waste shipments at the waste collection and separation and the WtE center for both facilities is estimated at 22.5 units (w¹ and w²). The cost per kilometer traveled by waste shipments between population nodes to candidate locations for waste collection and separation centers and candidate locations for WtE facility deployment is also determined to be 0.47 units (TrC). Finally, a small value of 0.00001 (є) is assigned for solving the model. The estimation of these costs is based on conducted investigations and involve assessments, quotes, and financial planning by the comprehensive waste management center in the Department of the Environment in Iran. Regarding the data values, scaled data was used, and as a result, no specific units were assigned to the costs.

The results obtained after solving the models:

To analyze the proposed models, the problem presented in the case study section was solved using a weighted sum method in MATLAB, using a genetic algorithm. Equal importance was given to all three objective functions.

Z_Total = min(Z₁ + Z₂ + Z₃)

(17)

As observed, solving both models provided relatively similar solutions, according to

Table 4. Values of objective functions.

	ZTotal	Z1	Z2	Z3
FAM	12,774.43	7746.171	851.085	4177.176
DAM	12,774.43	7746.16	851.097	4177.176

. All 8 proposed locations for establishing waste collection and separation centers, as well as the proposed locations for the WtE facilities, except for C2, C3, and C6, are listed. The value of variable ${\mathit{t}}_{\mathit{i}\mathit{j}}$ (the allocation of industrial parks or industrial areas to the waste collection and separation centers) is relatively consistent for both models, according to

Table 5. Locations of waste collection and separation and WtE centers, the service rates in each established WtE and WtE collection and separation center, and the capacity of the WtE collection and separation centers launched.

		C1	C2	C3	C4	C5	C6	C7	C8
FAM	Xj	1	1	1	1	1	1	1	1
	Yk	1	0	0	1	1	0	1	1
	${\mathit{S}}_{\mathit{j}}^1$	478.018	144.061	240.532	513.773	1512.458	129.974	182.298	153.248
	$S_k^2$	149.169	0	0	122.379	310.731	0	47.945	41.469
DAM	Xj	1	1	1	1	1	1	1	1
	Yk	1	0	0	1	1	0	1	1
	${\mathit{S}}_{\mathit{j}}^1$	478.017	144.061	240.532	513.773	1512.448	121.359	182.298	153.248
	$S_k^2$	149.168	0	0	122.377	310.731	0	47.945	41.469

and Appendix A.

As this was a case study, the number of selected locations and distances do not allow for enough dispersion under real conditions; thus, both the static and dynamic models yield approximately the same results. In the following sections, in line with the sensitivity analysis, the capabilities and changes will be observed.

4.3. Sensitivity Analysis

In the location of waste management centers within the framework of the proposed models, determining the parameters has a direct effect on the calculation of the main variables (locations of centers and processing/conversion rates). The purpose of presenting this section is to review and compare the results with changes in several parameters in the proposed models.

At first, the cost per time unit of waiting for each consignment to the waste collection and separation centers and the WtE (w¹ and w²) is considered. It can be seen in

Table 6. Changes in the values of the objective functions with respect to different values of the waiting cost.

	${\mathit{w}}^1$	${\mathit{w}}^2$	ZTotal	Z3	Z2	Z1
FAM	10	10	12,148.81	4177.176	538.267	7433.366
DAM			12,148.81	4177.176	538.274	7433.359
FAM	25	25	12,774.43	4177.176	851.085	7746.171
DAM			12,774.43	4177.176	851.097	7746.16
FAM	40	40	13,225.38	4177.176	1076.554	7971.627
DAM			13,225.36	4177.176	1076.549	7971.632

that with the increase in the cost of waiting, the values of objective functions 1 and 2 (functions of the cost of setting up centers and the average total cost of waiting) increase in both models. The reason for the increase in the values of objective functions 1 and 2 is the increase in the processing/conversion rate that has been set up in the centers. This issue can be observed in Appendix B. With the increase in the cost of waiting in the centers, the processing/conversion rate of the centers set up in both models increases so that the waste consignor spends less time on average waiting to receive the service, and in this way, the spread of pollution to the environment is prevented.

In the second phase of the study, a percentage of the waste shipments sent to the waste collection and sorting centers requiring the WtE process (β) was considered. To investigate the effect of the β parameter, its value was changed from 0.18 to 0.3, 0.45, and 0.53, respectively. The results obtained for the variables after applying this change are presented in

Table 7. Objective function values resulting from the β change.

β	Model	ZTotal	Z1	Z2	Z3
0.18	FAM	12,774.43	7746.171	851.085	4177.176
	DAM	12,774.43	7746.16	851.097	4177.176
0.3	FAM	18,459.34	8320.25	924.309	8329.345
	DAM	18,590.29	8325.51	939.128	8329.345
0.45	FAM	26,949.24	11,513.25	1152.602	14,283.39
	DAM	28,985.84	12,781.48	1320.86	14,883.5
0.53	FAM	32,126.84	13,053.78	1333.334	17,415.01
	DAM	35,661.48	14,096.15	1426.712	19,810.74

. According to Figure 4, the values of all three objective functions in both models increased with an increase in the amount of waste sent to the WtE centers, as expected due to the response to the demand of the population nodes. In Appendix C, the number of established waste collection and sorting centers in the static allocation model decreased from 13 centers to 10 centers, while in the DAM, the number of established WtE centers increased by one unit, reaching a total of 14 centers. This change in the β parameter demonstrates the sensitivity of the results to this parameter and highlights its impact on the establishment and operation of waste management facilities, particularly WtE centers.

As illustrated in Appendix C, in the solutions obtained for both models, a reduction in the waste transportation cost parameter leads to a decrease in the number of established centers. With an increase in the value of this parameter, the total number of established centers in both models increases, but after several increments in the cost of travel parameter, the number of established centers gradually stabilizes, and the value of the variable for the processing/transformation rate does not change significantly.

5. Discussion and Managerial Insights

As shown in the sensitivity analysis section, the differences between the two models for the case studies of the three Iranian provinces are not significant. This is because the assumed capacities for the centers in these case studies are suitable. However, the reason for considering both static and DAM variables is that in real-world situations, there may be a need for either static or dynamic allocation, based on decision maker’s needs.

The previous works by Refs. [24,26,34] have explored various aspects of WtE facility location, addressing issues of sustainability, multi-criteria decision making, and suitability analysis. Their studies focused mainly on optimizing the WtE facility locations by employing considerations such as sustainability, environmental factors, and advanced analytical techniques like machine learning. In comparison, this research specifically targets the Iranian context, emphasizing the coexistence and synergy between waste sorting centers and waste-to-energy plants. Two mathematical models are employed to minimize establishment, transportation, and waiting costs, with an emphasis on environmental factors to prevent pollution and optimize waste resource management in Iran. While the previous works have provided valuable insights, the present research tailors the approach to the Iranian energy landscape, offering a unique and localized perspective on WtE facility location.

Furthermore, since these facilities have not yet been established, and the models have been developed based on available data from the environmental organization, we suggest recommendations for the construction and operation of waste management and WtE facilities in line with the study’s results:

• The largest cost incurred by the system is the establishment cost. While this cost is undeniable, selecting the optimal location will significantly reduce transportation costs and distances. The presented model provided a trade-off situation for the policy makers to achieve a better decision.
• Proper and systematic location planning, as provided by the proposed model, may lead to a reduction in environmental pollution, as mentioned in the second objective function, and reduce pollution emissions in the third objective function, whether considering waiting costs or traffic costs.
• Minor changes in the separation ratio and the wastes sent to the WtE led to significant changes in the costs of the system. While this parameter may not be changeable at will by the decision maker, it is recommended that experts emphasize and pay more attention to achieving the accurate value for this parameter, as relatively small changes to this constraint can result in significant changes in the objective functions.
• As indicated in the sensitivity analysis results, a significant portion of the costs is related to the transportation and movement of materials. Therefore, it is recommended that in industrial areas or industrial parks candidates, conditions for the establishment of waste separation, collection, and WtE facilities be provided collectively. This will lead to lower transportation costs between centers and a further reduction in waiting costs.
• Another suggestion of this study is to pay more attention to the quantity and accurate separation of the types of industrial park waste collected. If this data is identified more accurately and in larger quantities, the proposed model can provide more precise answers for decision making.

6. Conclusions

This study has addressed the modeling of the problem of locating waste management networks consisting of two types of waste collection and separation centers, along with WtE centers. For the problem raised, two models were proposed. In the first model, the assignment of each park or industrial area to each waste collection and separation center is fixed, and waste dispatchers in each park or zone can only send waste to the assigned center. In the dynamic model, it was assumed that waste shipments from parks or zones are transported to the nearest waste collection and separation center. The order of service delivery in both models was considered as follows: the waste received in the waste collection and separation centers, depending on its desirability (low risk of the road from a pollution emission point of view, and the desirability coefficient of energy production in terms of usability and the possibility of contributing to the energy network), is sent to each location of the established WtE centers. It is also possible to send the waste to the waste disposal sites without the need to send it to the WtE centers, an option which is not included in the model.

There are several recommendations which should be seriously considered for future research. The first is that researchers should consider the costs of transporting and burying waste that cannot be converted to energy. The second is that it is possible to send recyclable inorganic waste to the recycling centers in the separation centers, and considering the previous point, a complete network can be created. Also, the most important basic research involves determining who should be involved in waste separation. This requires research that will ascertain what the public–private partnership relationship should look like.