OptimizationModel for IntegratedMunicipal SolidWaste System Using Stochastic Chance-Constraint Programming under Uncertainty: A Case Study in Qazvin, Iran

Municipal solid waste management (MSW) is a factor that affects environmental pollution and the spread of diseases in cities. )erefore, an efficient MSWmanagement system results in reducing the cost of environmental impact by tackling the processes of waste collection, recycling, and disposal. In this study, a biobjective optimization model is developed which aims to minimize the costs of facility location and transportation planning and the emission of environmental pollutants. Furthermore, to consider the uncertain nature of the problem, demand or the volume of the generated waste is considered as a random parameter. As a result, a stochastic mathematical programming model with probable constraints is developed. To solve and validate the model, the ε-constraint approach has been employed. Moreover, for a real-world application of the proposed model, a case study is implemented in Qazvin, Iran. Finally, various problems are solved for different levels of reliability and an efficient MSW system is designed for each of them. Results show that the proposedmethod was able to achieve Pareto solutions where managers can decide to choose one of them based on their priorities in comparison with the current status. Moreover, results revealed cost and emission would be reduced by increasing confidence level. Finally, a comparison is made between our proposed ε-constraint method and one of the recently used solution approaches.


Introduction
Municipal solid waste (MSW) is the generated solid waste in urban residential areas. MSW includes the generated waste by residential houses, commercial units, industrial sectors, and institutional units such as schools, hospitals, care centers, and public centers such as streets, markets, bus stops, and parks [1,2].
In this study, an integrated location-allocation problem for the municipal waste collection vehicles is studied [3]. For each level, including collection, recycling, and disposal, a set of facilities is selected and transportation planning is set among the different levels.
is study aims to develop an efficient planning system for the collection and transportation of municipal waste [4,5]. For this purpose, vehicle routing is one of the main components of the proposed mathematical model while considering the uncertain nature of the demand in the problem. As a result, the outcomes of the research can be implemented in municipal organizations with the least degree of deviation.
Routing the waste collection vehicles and their allocation and considering the various types of waste are the main challenges that municipalities usually face in planning for municipal waste collection. Using these concepts and analyzing the results, various policies can be easily evaluated and the optimal policy can be selected [6,7].
However, a high degree of uncertainty in the amount of generated waste in municipal areas is likely to result in the infeasibility and inefficiency of the problem in static and deterministic conditions [8]. Accordingly, in the next step, the problem is analyzed employing stochastic programming.
All in all, the purpose of this study is to do the following: (i) Increase the efficiency of the waste collection system (ii) Minimize the location and construction costs of required facilities for municipal waste processing (iii) Minimize the required number of vehicles, total transportation costs between facilities, and operating costs of the facility (iv) Minimize environmental pollution, specifically greenhouse gas emissions which are generated by various facilities and transportation systems In the following, the relevant literature of the research is reviewed. e deterministic problem and proposed modeling are presented in Section 3. Stochastic modeling of the problem using the probabilistic programming approach is presented in Section 4. Section 5 includes validation of the proposed model and computational results of the research based on the case study, and finally, conclusions and future suggestions are presented in Section 6.

Literature Review
In this section, the relevant literature on location problems and vehicle routing problems for municipal waste collection is reviewed.
Huang and Lin [9] proposed a vehicle planning for the municipal waste collection system with a specific "Removing waste from the ground"policy. In this policy, people are responsible for transporting household wastes into the collection vehicles. e purpose of their study was to cover all demand points and to employ an innovative method to optimize routes and the number of vehicles. Kinobe et al. [10] presented a novel and compound approach to optimize waste collection and disposal in the city of Kampala. eir methodology includes the use of Geographic Information System (GIS) tools to optimize total traveled distance, number of trips, and the total spent time on waste collection. is resulted in maximizing the total volume of collected waste, large savings, and environmental conservation. Finally, they were able to determine the appropriate fleet size with the required capacity, taking into account the reduction of fuel consumption and emissions from vehicles to collect waste using GIS tools. ere are some other studies that analyzed different aspects of waste management scenarios, such as Suja et al. [11] and Fei-Baffoe et al. [12], who investigated e-waste management scenarios in Malaysia and MSW in Ghana, respectively.
Inghels et al. [13] presented a multipurpose transportation model for designing a municipal solid waste transportation service network. In their research, they studied the possibility of using multipurpose trucks and inland water transport instead of using transport trucks to send bulk household waste from collection centers to waste processing facilities. e proposed model is a dynamic planning model at the tactical level that aims to minimize total transportation, environmental and social costs. By implementing their model in a case study, they proved that the proposed transportation system leads to cost savings.
Akhtar et al. [14] developed a backtracking search algorithm (BSA) to solve VRP models of municipal waste collection problems. e obtained results indicated the suitable performance of the proposed algorithm. Dotoli and Epicoco [15] studied the vehicle routing problem for collecting hazardous municipal waste. ey considered traveled distance constraints, time windows, and availability of vehicles in their model and solved a case study to evaluate the applicability of their model. Jun Zhao et al. [16] proposed a multiobjective continuous network flow model to locate various waste facilities for regional hazardous waste and find the transportation route among them.
eir goal was to minimize the total cost and risk. ey evaluated their model in a hypothetical case and a realistic one in the Sichuan province of China. López-Sánchez et al. [17] developed a multiobjective optimization algorithm based on the variable neighborhood descent (VND) method to solve the waste collection problem in a city in southern Spain. e goals were to minimize total travel costs and to balance the vehicle routes. ey solved the problem and presented the obtained computational results as Pareto front. Hannan et al. [18] developed a VRP model for waste collection by constructing the optimal routes. To solve their problem, they developed a metaheuristic algorithm to solve the examples of the literature. e special feature of this problem was the consideration of weekly planning. Tirkolaee et al. [6] developed a solid arc routing problem by considering the work shift of drivers and crew. To solve the proposed problem and validate their mathematical model, they designed random examples and solved them using the exact method and simulated annealing algorithm. Nowakowski et al. [19] studied a VRPTW problem for collecting mobile e-waste based on the demand records. In their proposed methodology, they considered the possibility of using a comprehensive online communication system for people to register the demand for electronic waste collection and data recording. ey solved the VRPTW problem by employing metaheuristic algorithms. eir goal was to determine the required number of collection vehicles, plan the routing of vehicles, collect household waste on time, and minimize collection costs.
Pablo A. Miranda et al. [20] formulated a waste collection problem for a set of nearby islands as a MIP model considering two strategies that were designed for a year.
ey evaluated the proposed model in a case study in the south of Chile. Rabbani et al. [21] developed a nondominated sorting genetic algorithm II (NSGA-II) and multiobjective PSO (MOPSO) to solve the multiobjective location-routing problem (LRP) of a hazardous waste considering all types of incompatible wastes. e objectives of their proposed model included minimizing the total cost, minimizing the transportation risks of hazardous waste, and minimizing the risk of landfills and waste processing in residential areas. Goli et al. [22] developed a hybrid artificial intelligence and metaheuristic algorithms for dairy products' demand prediction. Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Invasive Weed Optimization (IWO), and Cultural Algorithm (CA) are applied as well as 2 Journal of Advanced Transportation Adaptive-Neural-based Fuzzy Inference System (ANFIS), and Support Vector Regression (SVR). A triobjective MILP model was offered by Olapiriyakul et al. [23] to design a sustainable MSW network. ey considered sustainability issues such as land use and public health impacts and investigated a real case study in ailand. Asefi et al. [24] proposed a MILP formulation to solve the HFVRP problem considering the variable size of the fleet for integrated MSW collection. eir goal was to minimize the transportation costs and total deviation from the fair distribution of goods in the transportation stations. Finally, they employed lexicographic and ideal programming methods to solve the proposed model. Habib et al. [25] designed a large-scale natural disaster waste management system considering a sustainability index.
ey proposed a fuzzy multiobjective planning model to model the supply chain for the processing of waste generated after the disaster. Wei et al. [26] developed a hybrid algorithm based on an artificial bee colony algorithm to solve the waste collection problem in the form of a CVRP problem considering intermediary disposal. e achievement of their research was a 7.16% reduction in carbon emissions compared to the traditional collection model. More studies performed on the application of routing problems for MSW collection application can be found in Babaee Tirkolaee et al. [27]; Babaee Tirkolaee et al. [28]; Babaee Tirkolaee et al. [29] Aliahmadi et al. [30]. Goli et al. [31] applied a robust optimization approach for a multiobjective product portfolio problem. ey developed the multiobjective invasive weed optimization (MOIWO) algorithm to solve the proposed model. Goli and Malmir [32] developed an allocationrouting model for vehicles in a disaster area under uncertainty.
ey proposed a GRASP algorithm and a harmony search algorithm to find solutions. Goli et al. [33] developed an integrated approach to predict demand for dairy products. ey developed grey wolf optimization (GWO), invasive weed optimization (IWO), cultural algorithm (CA), and particle swarm optimization (PSO).
Recently, Tirkolaee et al. [34] presented a study to develop a robust optimization model to design a municipal waste management system taking into account economic and environmental indicators under uncertainty. ey evaluated and validated the proposed model employing a robust optimization approach and conducting a case study. In another study, Tirkolaee et al. [8] developed a sustainable routing location model for managing the collection and timely disposal of COVID-19-related hospital waste during the pandemic. ey also employed goal programming and a chance-constraints fuzzy approach to deal with the multiobjectiveness and uncertainty of the problem. Pourhejazy et al. [35] developed a two-index CGRP formulation model considering traditional (door-to-door) and on-call collection methods for electrical and electronic equipment wastes. ey aimed to maximize the profit with acceptable service quality. Goli et al. [36] developed a fuzzy programming model for the integrated cell formation and production scheduling problem. ey proposed a hybrid genetic algorithm and whale optimization algorithm to solve the problem considering automated guided vehicles and human factors. Pahlevan et al. [37] developed a multiobjective sustainable closed-loop supply chain using products' life cycle in the aluminum industry. Some metaheuristic algorithms including multiobjective grey wolf optimizer (MOGWO), the multiobjective red deer algorithm (MORDA), and augmented epsilon constraint (AEC) are used to obtain Pareto solutions.
On the other hand, there are some existing transportation planning models such as 'MyRouteOnline' software [38] and Route View ProTM software [39] which exclusively deal with routing decisions. Moreover, other types of routing decisions in the field of MSW management can be found in the literature addressing the application of Geographic Positioning System (GPS) in vehicles. In this regard, you may see Faccio et al. [40]. In this study, there is no routing decision practically, but the transportation planning is conducted along with locational and allocation decisions. In other words, in transportation planning models, the scheduling of vehicles and service sequence not considered. e only important point is the determination of appropriate vehicles and the number of products to be transported between two facilities. In fact, we tried to address the strategic and operational decisions in our proposed MSW system. Table 1 summarizes the current research and the most important studies in the literature.

Problem Definition
In this section, the proposed biobjective mathematical model for facility location and transportation planning of municipal waste management network is developed. e intended network consists of five levels which include different municipal waste generation centers, waste collection centers, recycling facilities, disposal centers, and shopping centers of recycled material. e model aims to minimize the total cost and minimize gas emissions and environmental pollutions. Moreover, the location of waste generation centers and shopping centers of recycled waste is fixed, and the goal is to locate collection, recycling, and disposal facilities due to capacity constraints. e proposed network is considered a dynamic (multiperiod) supply chain. To better understand the research problem, Figure 1 illustrates the network for the collection, transportation, disposal, and recycling of municipal solid waste. e main assumptions of the problem are as follows: (i) e model is multiperiod and decisions are made in a time horizon. (ii) e model contains five levels such as waste generators, collection centers, recycling centers, disposal centers, and shopping centers of recycled waste. But, the locations of the three levels are just determined by the model consisting of collection, disposal, and recycling centers. (iii) e capacities are limited. (iv) ere is a setup fee for the facilities.    Decision variables X wt : If collection center w is set up in period t, the value is 1, otherwise the value is zero. X dt : If recycling center d is set up in period t, the value is 1, otherwise the value is zero. X ct : If disposal center c is set up in period t, the value is 1. Otherwise, the value is zero.
x mwth : e amount of transported waste from waste generating center m to collection center w in period t by the transport system h w h m h x mwth ≤ ca wt , ∀w, t, w h x wdth ≤ ca dt , ∀d, t, d h x dcth ≤ ca ct , ∀c, t, d h x dkth ≤ ca kt , ∀t, k, m w x wdth ≤ MX dt , ∀w, d, t, h, x dcth ≤ MX ct , ∀d, h, t, c, h c h k  (1) is to minimize the costs, including fixed setup fees, variable costs of facilities, and waste transportation costs. e objective function (2) minimizes the gas emission in processing operations of different facilities and the emission of greenhouse gases due to the transportation between different levels. Constraint (3) guarantees that all of the demand must be fulfilled. In other words, the minimum amount of waste sent to collection centers must be equal to demand.

Journal of Advanced Transportation
Constraints (4)-(8) indicate the facility's capacity constraints for collection centers, recycling centers, disposal centers, shopping centers of recycled waste, and transportation systems, respectively. Constraints (9)-(11) represent the need to establish collection centers, recycling centers, and disposal centers. Constraint (12) shows the relationship between the amounts of incoming waste from recycling centers to disposal centers in each period. Constraint (13) indicates the relationship between the amounts of incoming waste from recycling centers to the shopping centers of recycled waste in each period. Constraint (14) indicates the relationship between the amount of waste entering the collection centers and the waste exiting from collection centers to disposal centers. Constraint (15) specifies the domain of variables.

Stochastic Chance-Constraint Programming.
To deal with the uncertainty of the parameter, stochastic chanceconstraint programming is investigated. is approach, as a noticeable approach, has been applied by many researchers, which was developed by Charnes and Cooper [41]. Consider dem mt parameter (∼ symbol represents the uncertainty). e probability of occurring a constraint is as follows:

m. (16)
A summary of the chance-constraint programming for maximization and minimization problems is as follows: Based on the constraints of the multiobjective chanceconstraint model at α% level (confidence level), constraint (3) is changed as follows:

Solution Method: ε-Constraint
In this study, a multiobjective mixed-integer mathematical programming model is proposed. Since the proposed model has two objectives, the solution approach should find the best answer while considering both objectives simultaneously. e ε-constraint method is one of the well-known approaches for dealing with multiobjective problems that solves the problem by transferring all but one of the objective functions to the constraints at each step [42]. e Pareto front can be created employing the ε-constraint method as follows: subject to x ∈ X, . . . 8 Journal of Advanced Transportation e steps of the ε-constraint method are as follows: (i) Select one of the objective functions (cost objective function) as the primary objective function. (ii) Solve the problem according to each of the objective functions and obtain the optimal values of each objective function separately. (iii) Divide the interval between two optimal values of the latter objective function (gas emission) into a predetermined number of divisions and obtain a table of values for ε 2 , . . ., ε n (iv) Solve the problem with the primary objective function for each of ε 2, . . ., ε n values (v) Report Pareto solutions. e ε-constraint approach is implemented in GAMS software. In this method, firstly, each of the objective functions is optimized separately. us, the first objective function, i.e., minimization of supply chain costs, is considered as the only objective function of the problem, and according to the existing constraints, the first model (M1) is changed as follows: Equations (4)- (15). (20) After solving the first model, the best value of the objective function (lowest cost) is stored as the optimal value of the first objective function. en the second model based on the second objective function, i.e., minimizing the amount of emitted gases, is considered as the only objective of the problem, and according to constraints of the problem, the second model (M2) is created as follows: Equations (4)- (15).

Journal of Advanced Transportation
Finally, the cost objective function is considered as the primary objective function, and the emitted pollutants objective function is considered as a subobjective within the constraints of the problem.

Case Study
In this section, the proposed solution method is validated by implementing a case study in one district of Qazvin, Iran. For this purpose, a densely populated area is considered, which is shown in Figure 2. e required data is estimated using the consultation of an expert team from the local office of Qazvin Municipality. Using these data, two sample problems are generated to fully investigate the proposed mathematical model. en, different levels of confidence are considered in the problem. e size of problems and values of the parameters are presented in Tables 2 and 3.

Computational Results
In this section, the case study is solved based on the proposed model. To solve the proposed model, the CPLEX solver of GAMS software is used as an efficient tool in optimal problem-solving. Regarding the proposed solution approach, firstly, the optimal values of two objective functions are obtained in different confidence levels and reported in Tables 4 and 5.  According to Tables 4 and 5, the optimal value of each objective function has been obtained for different confidence levels for two sample problems. en, according to the proposed solution approach, the interval between the minimum and maximum amounts of emitted pollutants is divided into a predetermined number of points (divisions). In this research, the number of points (divisions) is equal to 6. Tables 6 and 7 show the ε values for each breakpoint for the two sample problems, respectively.
Finally, the main problem is solved for each breakpoint. e best possible value of the first objective function for different values of emitted pollutants for the two problems is presented in Tables 8 and 9, respectively. e obtained Pareto solutions of the first sample problem in three confidence levels are shown in Figure 3. e obtained Pareto solutions of the second sample problem in three confidence levels are shown in Figure 4.
In order to evaluate the obtained Pareto solutions and to select the best solution, the reference point approach (RPA) has been used. Deb and Sunder [43] proposed this approach to determine the best point in the multiobjective problems.
e main idea of this method is to identify the solutions which are close to the reference point. Normal Euclidean distance (dev p ) between two nondominated solutions is obtained by the following equation:  Table 10.
As shown in Table 10, the two objective functions are of equal importance. Accordingly, the value of dev p for each sample problem is obtained and reported in Tables 11 and 12.  According to Tables 11 and 12, the best Pareto solution is obtained regarding the least value of dev p . Table 13 shows the best Pareto solutions for the two sample problems. e runtime values for sample problems 1 and 2 are 5.27 and 79.05 seconds, respectively.
Finally, a sensitivity analysis is performed on the values of the objective function for different confidence levels based on the results in Table 13. is analysis is highly important as it directly affects supply chain costs and emitted pollutants. Depending on the confidence level, the decision-maker can obtain the number of costs and emitted pollutants and choose the desired confidence level according to their      priority. As shown in Figure 5, by increasing the confidence level, the cost of the whole chain decreases. Furthermore, Figure 6 shows the changes of the emitted pollutants objective function for the various confidence levels for the two sample problems. It is observed that increasing the confidence level leads to the reduction of pollution.

Comparison with the Current Status.
In order to further assess the efficiency and applicability of our proposed methodology, we asked the experts of the given district in Qazvin Municipality to estimate the values of the objective functions in the first sample problem. Moreover, six days of a week starting from April 3, 2021, are regarded as the planning horizon. e confidence level of 1 is also     considered in order to attain the best reliable results. e comparison of the current and optimal status is represented by Table 14.
As can be seen in Table 14, our proposed methodology was able to provide a 5.13% decrease in the total cost and also a 6.20% decrease in the total pollution emission. It is expected that these savings will be higher in large-scale problems.

Comparison with WGP Approach.
In order to test the efficiency of our solution method, Weighted Goal Programming (WGP) is considered as a rival that was employed by Tirkolaee et al. [34] in a medical waste management system. For more information on the performance of this approach, please see Tirkolaee et al. [34]. e weights of 0.6 and 0.4 are assigned to the 1 st and 2 nd objective functions based on the experts' opinions. e obtained results from the comparison are shown in Table 15 for both samples.
According to Table 15, it is obvious that different solutions are proposed by εε-constraint and WGP methods. e main reason is that the output of WGP is an individual solution, but the εε-constraint method generates a Pareto front including Pareto optimal solutions, and finally, the best Pareto solution is obtained by RPA. e important point here is that none of the methods are superior in sample problems. For example, in sample problem 1, WGP obtained a better Z 2 value while the εε-constraint method offers a better Z 1 value. On the other hand, the average runtime     value of WGP is less than the average runtime of the εε-constraint method. However, the difference is not tangible and can be ignored. It is very important that the decision-maker applies the more desirable solution method based on its performance.

Conclusions and Future Suggestions
e management of municipal services is getting more challenging due to the production of solid waste and the occurrence of various social, economic, and environmental incompatibilities related to them. erefore, it has faced many problems in the collection, transportation, processing, and disposal of such waste.
As mentioned, municipal waste collection is one of the vital issues in the urban area that deals with individual and social health. If waste is not collected in time, it will cause pollution. erefore, the issue of waste collection planning is of great importance. is research has tried to provide a comprehensive model for the problem of location and use of facilities for waste collection with the aim of minimizing the total costs and pollution caused by the transportation system. Also, in order to evaluate the proposed model and express its feasibility, a case study in Qazvin city, including waste collection planning of an area of the city, has been considered. e obtained results indicate the proper performance of the proposed model so that it can be used for urban waste collection planning.
As a result, in this study, a biobjective mixed-integer planning model was developed considering the real-world assumptions to formulate the integrated location-allocation problem and transportation planning. Due to the uncertainty of demand (amount of generated waste), a stochastic planning approach based on chance constraints was used to deal with the problem of uncertainty. e objectives were to minimize supply chain costs and emitted pollutants by transportation. In order to solve the biobjective model, the εε-constraint approach was employed. Afterward, based on the real data, a case study in one district of Qazvin, Iran, was conducted. Finally, the results were analyzed by solving two problems in different sizes and for different confidence levels. Presenting various confidence levels makes decisionmakers obtain the solution with specific cost and emission based on their priority. Results show that increasing confidence level causes to decrease in the total cost and emission amount. Moreover, the comparison with the current status revealed that our proposed methodology can provide significant savings in the total cost and total pollution emission. Finally, a comparison was made between the εε-constraint method and WGP approach in order to show the performance of the εε-constraint in terms of the 1 st and 2 nd objective functions, and runtime value.
In this study, a stochastic programming model was used to control uncertainty while other approaches such as robust optimization or fuzzy programming can be applied to compare the results obtained. Furthermore, only beneficial    and environmental aspects were considered in this research; however, social aspects can be considered by maximizing citizen satisfaction and system reliability [44,45]. As mentioned, a real case study in small-and medium-size was studied while multiobjective optimization algorithms can be applied to solve highly large-sized problems. Apart from the optimization recommendations for future research, the application of online tools and Internet-ofings (IoT) can be studied in the problem to take care of the routing decisions exclusively in the problem. Furthermore, the existing routing software like MyRouteOnline software [38] can be employed to cope with real-time data of routing in an MSW system along with strategic and tactical decisions Data Availability e required data were estimated using the consultation of an expert team from the local office of Qazvin Municipality. e data used to support the findings of this study are included within the article in table format. e complete data source can be accessed for other researchers by author's mail, m_bavaghar@yahoo.com.

Conflicts of Interest
e authors declare that they have no conflicts of interest.