Sustainable optimization of waste management network over extended planning time horizon

Correspondence Yousef Saif, Department of Chemical Engineering, Khalifa University of Science and Technology, Sas Al Nakhal Campus, PO Box 127788 Abu Dhabi, UAE. Email: yousef.almohairi@ku.ac.ae Abstract This study proposes a multiperiod mixed integer linear programming model for the management of a single municipal solid waste (MSW) treatment plant with sustainability as the objective. Discrete and continuous variables define the capacity selections for diverse MSW technologies, and the operation of the MSW network, respectively. The economic target is considered to maximize the net present value. The environmental impact is the minimization of a normalized environmental objective function (NEOF). The social target is the maximization of jobs. An interesting feature about the research work is the requirement of biodrying technologies for MSW moisture content control. Due to the conflicted nature among the sustainability components, a multiobjective optimization (MO) is carried out to find the Pareto optimal solutions. The MO results show that the Pareto optimal solutions vary around profit range of $4.9–8.5 billion, NEOF impact range of 3.2–3.6 units, and social benefit range of 2700–4828 jobs.

Existing MSW management studies were focused on several assessment criterions such as economic, environmental, and efficiencies of technologies. Decision support models were developed in the past based on several mathematical programming formulations which include linear programming (LP) and mixed integer LP (MILP), non-LP (NLP), mixed integer non-LP (MINLP), stochastic programming, and hybrid models, for the assessment of optimal MSW management. 10 Other studies also applied the life cycle assessment tools for the MSW management. 11,12 The MSW optimization studies covered in the following literature review are focused on centralized and decentralized mathematical programming-based models for the MSW management under deterministic and stochastic model parameters.
Centralized MSW management has received research attention to examine different MSW management issues. Single site optimization of MSW management was addressed to assess optimal processing pathways of MSW under deterministic conditions. 13 The optimization framework was based on superstructure optimization to extract the best optimal economic structure for processing MSW constituents. A multiobjective optimization model was later examined the tradeoff between the economic and environmental objective functions. 14,15 These studies considered the transformation of recyclable waste, and nonrecyclable waste to electricity and biofuels. Another study considered the tradeoff between the economic and risk objective functions while optimizing the MSW network. 16 Single site optimization of organic MSW treatment was examined by multiperiod NLP model with only incineration technology for integrated heat and power production. 17 The selection of optimal processing technologies for the transformation of organic MSW to power production was addressed under uncertainties of economic and technical parameters through Monte Carlo simulation over long time planning horizon. 18 Decentralized MSW management addressed many issues which include the effect of transportation through distributed sites. A multiobjective MILP formulation was developed to maximize the profit from MSW treatment network while maximizing the conversion of MSW constituents. 19 Another superstructure optimization study addressed the sustainable utilization of MSW in Malaysia with four treatment technologies (e.g., composting, material recycling facility (MRF), incineration, landfill gas recovery system). 20 An MILP model is also developed for Hong Kong situation to assess the feasibility of incineration technology. 21 Other studies considered supply-demand and power price uncertainties effects on the MSW supply chain configuration to obtain power from the organic MSW part, and general MSW supply chain management in Mexico. [22][23][24] Research studies in the literature that is focused on MSW single site management considering sustainability issues are limited. 25,26 These research studies focused either on a single treatment technology, 18,[27][28][29][30] or on a network involving diverse treatment technologies. [13][14][15][16]18 By examining the sustainability indicators from these studies, one can notice that the optimization models were driven by a single economic objective function, or combined economic and environmental objective functions.
Some of these studies minimized the CO 2 emissions as an environmental sustainability indicator. In addition, these research studies ignored the sustainability evaluation over time, and neglected the social responsibilities. These limitations were highlighted as important issues that should be considered while designing an integrated MSW treatment facility. 7,31 A single MSW treatment technology is not an attractive option for the holistic treatment of MSW constitutents. 26 Furthermore, MSW treatment projects are costly especially for developing countries with limited financial resources. Therefore, financial planning at the early stages of MSW projects should bring insights about proper fund arrangements.
Moisture content of the MSW constituents is another important problem during the MSW treatment which imposes MSW pretreatment before processing the MSW stream, especially with thermal treatment technologies. 7,26,31 To the best of our knowledge, the pretreatment step of MSW stream before the treatment by the MSW technologies was not incorporated in the optimization studies so far. Therefore, our research objective is to address the abovementioned limitations by an MILP optimization model which is focused on a single integrated MSW treatment site taking into account sustainability as a major target. Interested readers about the MSW management studies (e.g., collection, storage, segregation, processing, distribution of products) can cover several review paper in this area. [10][11][12]25,26 In this research study, a capacity expansion planning model is presented as a multiperiod MILP model for the treatment of MSW on a single site. The model examines the optimal selection of treatment capacities for diverse MSW treatment technologies (e.g., biological, and thermal technologies). Furthermore, the study explores the tradeoff between the conflicted objective functions (e.g., economic, environmental, and social) through ε-constraint approach in order to find efficient Pareto optimal solutions. The economic objective function is to maximize the net present value (NPV). The environmental objective function is to minimize an aggregate function reflecting global warming potential (GWP), acidification potential (AP), furan and dioxin equivalent emissions, and side-solid waste generation (SSWG). In addition, the social aspect of the treatment network is to maximize job creation. Pretreatment of MSW is an important step prior to energy extraction by the thermal MSW treatment technologies. 7,[32][33][34] Pretreatment is considered in this study for moisture content control in order to find suitable input flow of material with acceptable moisture content for the thermal treatment technologies. The case study for Abu Dhabi city is examined during the time period of 2025-2055 to show the optimization model application.
The following section describes the MSW treatment network and the research objectives. In Section 3, an MILP model is developed for the capacity expansion of MSW treatment, and MO optimization approach description. In Section 4, Abu Dhabi city is considered as a case study for the proposed model. Finally, we provide research conclusions and future research directions in Section 5.

| Overview
MSW generation volume and composition vary significantly around the world. These variations can be attributed to different factors such as socioeconomic profile, climatic conditions of a given geographical region, extent of recycling, waste collection efficiency. 35 In addition, the MSW generation volume varies over time which imposes optimal strategic and tactical planning. It is an important task to know the volume, the characteristics (e.g., moisture content, calorific value), and composition of a given MSW in order to design an effective MSW treatment facility. 36 There are many potential technologies for the treatment of MSW 7 ; however, a legitimate question remains about which technology or combination of technologies that will serve positive economic, environmental, and social impacts over time. These treatment technologies normally present different capital and operation cost, environmental impact, technical constraints, and social impact. Therefore, it is essential to build a systematic decision framework to evaluate these technologies simultaneously. In this research, we base our analysis of MSW management on network optimization which helps in developing a decision-based optimization model as given in the following sections.

| Network representation
Graph theory has been a useful tool to represent material flow through networks for a single site or multiple distributed sites with various engineering applications. 37,38 These networks can be assembled by certain sets of nodes and arcs. It is assumed that the modeler has economic data, technical efficiency for technologies, technology operation restrictions, emissions and environmental data, and social data. The modeler can set up a network which includes large design alternatives that should be evaluated according to a given criterion. Usually, the modeler specifies certain connectivity between the nodes by arcs within the network in order to obtain large number of design alternatives. Our objective is first to give a treatment network representation for the MSW treatment. It is assumed that a set of nodes and another set of arcs are given. It is desired to construct an MSW treatment network based on given information about a set of technologies (tc). These technologies are further decomposed to a set of pretreatment technologies and another set of treatment technologies. Figure 1 depicts an MSW treatment network with consecutive stages star ting from a starting node of an MSW source to final nodes of valuable desired products (p).
The figure shows that a single mixed MSW stream represents an input to the MSW network. The MSW is assumed to be with known flowrate and characteristics (e.g., composition, moisture content, etc.).
After the collection step, the mixed MSW stream is segregated into its corresponding components. A secondary step involves mixing of MSW constituents according to a designer prejudgment in order to insure suitability of predefined mixed constituents with respect to the MSW treatment technologies. In the pretreatment section, the mixed constituents undergo pretreatment to achieve certain predefined characteristics in order to improve the operation of downstream MSW treatment technologies (e.g., moisture content). The final step involves the transformation of several mixed MSW constituents in the treatment section to final desired end products. Also, it can be noticed that there are some MSW constituents which bypass the treatment technologies. These streams represent recyclable materials which flow through MRFs to deliver final recycled products. In addition, SSWG (e.g., bottom and fly ash) can be generated during the MSW processing and requires final treatment. In this study, we assume SSWG is an inert material that can be disposed in landfills. Therefore, the MSW treatment network represents different alternatives of MSW management which requires simultaneous evaluation to achieve desired goals set by the designer. The following section describes the research problem statement.

| Problem structure
The proposed research methodology for the optimal MSW management on a single site passes through different hierarchical stages which comprise data collection, MSW system identification, model development, generation of results, analysis of the results, and final recommendations. These steps are explained briefly in this section. It is assumed that a given region or a city facing growth of population and MSW generation over time. It is desired from a public authority or private investors to evaluate potential benefits from the treatment of MSW. Obviously direct MSW dumping in landfills is not an acceptable solution, and the sustainable utilization of MSW is an ultimate target. Therefore, it is assumed that the following is given: • A planning time horizon (t) that involve yearly time increments.
• Projection of MSW generation and its characteristics over the planning time horizon.
• Set of treatment technologies (tc) with economic and technical data.
• Set of desired products that should bring benefits.
It is desired to identify; • The optimal MSW treatment network from Figure 1.
• Projection of the capacity expansion of the selected treatment technology over time.
• Assessments of the operational and environmental impact for the selected technologies.
• Evaluation for the tradeoff between the economic, environmental, and social impacts.
• Recommendations from the obtained results.
The following section provides details for the proposed mathematical programming formulation.

| MILP MODEL
In this section, the MILP capacity expansion model is explained. Section 3.1 covers the design constraints, and Section 3.2 presents the operation constraints. Section 3 presents the objective functions covered in this study, and Section 4 shows the MO optimization approach for the MSW constrained problem.

| Design constraints
The MILP model describes the capacity expansion of MSW network by discrete and continuous variables. Capacity expansion models require selection of efficient technologies among a set of available technologies for the MSW treatment over the planning time horizon. [39][40][41] The selected optimal values will affect eventually the economic, environmental, and social impacts for the MSW treatment facility. Technology selection is described by a binary variables (y), and the required capacity installation at a given time period (t) is given by a continuous variable (ex). Furthermore, the accumulative capacity of a given technology at a given time period is described by a continuous variable (ac). ex LO y tc,t ≤ex tc,t ≥ex UP y tc,t 8tc,t ð1Þ ac tc,t = ac tc,t− 1 + ex tc,t 8tc, t ð2Þ Equation (1) states that the expansion of a treatment technology is constrained by an upper (ex UP ) and lower (ex LO ) bounds of a desired capacity available in the market. It is also implies that a given technology will have zero capacity if it is not selected (e.g., the value for the binary variable y is zero). In addition, Equation (2) describes the accumulative capacity of a given technology over time.

| Material flow constraints
The network depicted by Figure 1 shows material flow from an MSW node source to final terminal nodes that provide saleable products. The model represents any stream within the network with total waste flow (f to ), and an individual MSW component flow (f sw ).
For any given node, it is required to conserve material flow balance.
The network shows several mixer (mn) and splitter (sn) nodes.
Therefore, total and individual material flow can be conserved for the mixer nodes, and the splitter nodes. Equations (3) and (4) conserve the total material flow, and individual MSW constituent flow balance requirements for a splitter node, respectively. Similar equations can be set easily for the mixer nodes following the same concept. Equation (5) states that a product flow (f pr ) from a given technology is related to the input flow through a conversion factor.
Furthermore, the input flow to a given technology should not exceed the available capacity as described by Equation (6) f to sn,t =  43 GWP is expressed as carbon dioxide equivalent and it is given by Equation (7). β represents the emission factor for a given pollutant (e.g., CO 2 , CH 4 , N 2 O) from a given technology. g represents the global warming ratio for a given pollutant (e.g., CH 4 , N 2 O) with respect to CO 2 .
AP is considered as equivalent of sulfur dioxide (SO 2 ) impact, and it is attributed to SO 2 , hydrogen chloride (HCl), and ammonia (NH 3 ).
The AP is expressed by Equation (8) Jobs = X tc,t η tc ex tc,t ð10Þ

| Carbon avoidance constraints
Diversion of MSW flow from direct landfilling should bring positive economic, environmental, and social impacts. In general, construction of MSW treatment plants leads to generation of carbon credits as recommended by United Nations through the clean development mechanism. In order to give an estimate for the carbon avoidance (f ca ), the GWP LF from direct disposal of MSW mass in landfills is needed. We follow the IPCC guidelines for this estimation. 44 The carbon avoidance by adopting the MSW treatment network is expressed by Equation (11). rise the operating cost of combustion. 33,34,45 It is assumed that a biodrying process exists before the thermal MSW treatment technologies in order to reduce the moisture content to an acceptable level if it is necessary. This condition imposes additional modeling constraints.
We assume that several MSW constituents are allowed to pass through the biodrying process. An overall material balance is carried out for every MSW constituent around the biodrying process, and it is given by Equation (12). fin and fout represent the input and output material flow for a given MSW constituent, respectively. Orgloss and MSfout are continuous variables that describe the organic material loss, and the moisture output from MSW constituents as a result of the biodrying process operation. The organic material loss from these fractions is proportional to the input flow by a factor (e.g., OF % ) as given by Equation (13). Also, it is required to have moisture content balance around the biodrying process, and it is given by Equation (14).
inmo, and outmo are parameters which provide the input and output moisture content, respectively. In addition, Equation (15)

| Objective functions
The cost associated with the MSW network comprises capital cost, operation cost, and profit generated from the desired products, carbon credit, and tipping fee. These elements (e.g., cost and benefits) are optimized over the planning time horizon taking into consideration an annual interest rate (i). The NPV is maximized in case the objective under an economic target. The NPV involves several terms as given by Equation (16). The profit is generated from selling a set of products (p), carbon credit, and tipping fee on the MSW treatment as given by Equation (17). The capital cost and operation cost are given by Equations (18) and (19). It should be noticed that the economies of scale for the capital cost is assumed to be linear function. However, this assumption can be relaxed by introducing additional binary variables to approximate the concave capital cost function.
Another objective function considered in this study is the minimization of the environmental impact for the treatment network. We described previously that the environmental impact is due to GWP, AP, for the GWP, AP, DFP, and SSWG when we carry out the analysis under economic target (e.g., by considering only maximization of Equation (19)).
Therefore, the optimal results of minimizing Equation (20) shows how relatively the NEOF of the MSW treatment can be minimized with respect to the solutions from the economic target. There are many measures reflecting the social sustainability of engineered projects such as the creation of job opportunities, regional economic development, and work safety. The creation of job opportunities is a popular quantitative social indicator. 46 The social objective function is to simply maximize job creation as given by Equation (10).
The economic, NEOF, and social objective functions normally show conflicted results when these functions are treated in an isolated fashion. The decision makers may be interested in a compromised solution among several optimal solutions. The following section describes the MO approach adopted in this study.

| MO optimization
MO optimization methods can be classified in general as Pareto and scalar weighted methods. 47 Pareto-based MO optimization approach showed several advantages over the weighting approach. 48,49 Therefore, we adopt the augmented ε-constraint method, and it is shown to be effective in identifying the Pareto optimal solutions with an effective solution algorithm. 48,49 To explain this method, first let us consider the mathematical programming model below as MP1. For the sake of simplicity, we assume that we consider p objective functions that should be maximized subject to the feasible set of solutions S.   Figure 2 shows the expected growth of MSW for Abu Dhabi city during the considered planning time horizon 18 , and Table 1 shows

| Abu Dhabi Emirate initiatives
The center for waste management was setup in February 2008 by the government of Abu Dhabi to manage and coordinate waste Dhabi. 54 Other research projects are in progress which include for example the production of biodiesel from restaurants oil waste.
TAQA, an international energy company based in Abu Dhabi, is adopting the waste to energy initiatives in Abu Dhabi by considering an incineration plant. 55 TAQA plans to construct two waste to energy plants, and the company plans to convert 1 million ton/year of waste to power. 56 The plant is projected to eliminate the discharge of more than 1 million ton of CO 2 per year. Several conditions will be analyzed in the following sections.

| Case study structure
These conditions describe the following: • The first one shows that the decision makers focus is primarily on the economic impact.
• Under the second condition, the interest of decision makers is to examine the possibilities of reducing the environmental impact from the MSW treatment network over time.
• The third condition examines enhancing the social impact of the MSW treatment network.
• The fourth condition explores the tradeoff between the economic, environmental, and the social objectives.

| Economic objective condition
The NPV is around $8.67 billion as given in Figure 3, and the selected treatment technologies are LFGE, composting, AD, and pyrolysis for the treatment of nonrecycable MSW constituents. MRF is the accumulated treatment capacity for recycling the glass, and metals as given in Figure 4. LF without energy recovery is the ultimate disposable of SSWG from the treatment technologies. In Figure 3, the generated profit arises mainly from selling the compost and generating CO 2 credit, followed by the tipping fee, MRF sale, and power sale. The digestate represents minor profit which is around 0.14% from the generated profit. In addition, the capital and operation cost is relatively smaller than the generated profit. In Figure 4, it can be noticed   Table S11 in the supplementary section), and to enhance the material utilization. The total amount of MSW treatment is around 1.52 billion ton over the planning time horizon.
Around 92% of this flow is treated by the biological technologies, and the rest is treated by the pyrolysis technology.
The environmental and social impacts are given in Figure 6. In this figure, the MRF environmental and social impacts are excluded from the presentation since the technology shows fixed amount of environmental and social impacts over all the given conditions under this study which will be covered in the following sections. The GWP and AP for the selected technologies in Figure 6 Figure 6. This social impact is affected mainly by the pyrolysis and composting technologies with values around 50 and 31% of the total generated jobs, respectively. In

| Social objective condition
The optimal solution under the given condition gives 5359 jobs over the planning time horizon. Clearly, there is a great improvement for

| MO optimization
In order to properly apply the augmented ε-constraint method, one must have the ranges of at least two objective functions (e.g., the range between the maximum and minimum values for the NEOF and social objective function). Then, the economic objective function can be optimized over the obtained ranges for the normalized environmental and social objective functions. In order to apply the method, the payoff table should be constructed by the lexicographic optimization. The results of the lexicographic optimization are given in Table 3. Within these ranges of the objective functions, the Pareto optimal solutions exit. However, it is not guaranteed to find optimal values for all grid points within these ranges since infeasibilities may exist. 47,48 Five grid points were chosen for every range of the objective functions. Figure 8 shows     Figure 8). Furthermore, the economic indicator shows negative impact of around 3% loss of profit compared with the best economic value in Figure 8.  The environmental target showed that the optimal value for the NEOF is 2.9 units which is lower than the environmental impact under the economic target by 28%. In addition, the social target optimal results provide around 5359 jobs which is higher than the economic target by 329%.
The selected treatment technologies vary significantly under the economic, environmental, and social conditions.