A Multi-objective Model for Location of Transfer Stations: Case Study in Waste Management System of Tehran

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1 Journal of Industrial and Systems Engineering Vol. 9, No. 1, pp Winter (January) 2016 A Multi-objective Model for Location of Transfer Stations: Case Study in Waste Management System of Teran Armin Jabbarzade 1*1, FarzaneDarbaniyan 2, M.Saeed Jabalameli 3 1,2,3 Scool of Industrial Engineering, Iran University of Science and Tecnology, Teran, Iran. arminj@iust.ac.ir, f.darbaniyan@gmail.com, jabal@iust.ac.ir Abstract Tis paper presents a multi-objective optimization model for te design of a waste management system consisting of customers, transfer stations, landfills and collection veicles. Te developed model aims to simultaneously minimize te total costs, greenouse gas emissions and te rates of energy consumption. To tackle te multiple objectives in te problem, an interactive fuzzy programming solution approac is utilized. Te model is capable of determining te location and allocation of transfer stations as well as te selection of te waste processing tecnologies. Te proposed model is applied to a case problem were real data is used for long-term planning of solid waste of Teran city. Keywords: Waste management systems, Facility location, Transfer stations, Multiobjective optimization 1- Introduction Global waste generation rates are rising fast due to population explosion and economic development. Terefore, an effective approac for te design and planning of waste management system is indispensable (Sujing, 2010).Te planning and design of a regional solid waste management system involves selection of treatment and disposal facilities, allocation of solid wastes and waste residues to treatment and disposal sites, and determination of transportation routes (Sujing, 2010). Design of a regional solid waste management system typically requires consideration of several criteria suc as te distances from residential areas and main roads, investment costs, climate conditions, availability of solid wasted, and land slope (Önüt & Soner, 2008). *Corresponding autor ISSN: , Copyrigt c 2016 JISE. All rigts reserved 109

2 Waste transfer stations play an important role in a community waste management system by serving as links between community solid waste collection facilities and waste disposal centers. Te waste transfer stations aim to consolidate waste from multiple collection veicles into iger volume transfer veicles for more economical sipment to distant disposal sites. In oter words, a transfer station is a facility wit a designated receiving area were waste collection veicles discarge teir loads. Te waste is often compacted, and ten loaded into larger veicles for long-aul sipment to a final disposal site. No longterm storage of waste occurs at a transfer station. Tus, waste is quickly consolidated and loaded into a larger veicle and moved off site witin few ours (Anon, 2002). Te primary reason for using a transfer station is to reduce te cost of transporting waste to disposal facilities. Consolidating smaller loads from collection veicles into larger transfer veicles, reduces auling costs by enabling collection crews to spend less time traveling to and from distant disposal sites and more time collecting waste. According to Antunes (1999), sipment costs on transportation trailers are estimated to be only about 30% of te costs incurred by te same quantity auled by te collection veicles. Utilizing transfer stations, furtermore, reduces fuel consumption and collection veicle maintenance costs, and produces less overall traffic, air emissions, and road wear. Waste transfer stations also provide more flexibility in terms of disposal options. Decision makers ave te opportunity to select te most cost-effective and/or environmentally protective disposal sites, even if tey are more distant. Tey can consider multiple disposal facilities, secure competitive disposal fees, and coose a desired metod of disposal (e.g. land filling or incineration)(anon, 2002). Selecting suitable locations for transfer stations is a complex problem and calls for a detailed evaluation process accounting for te requirements of municipal, governmental and environmental regulations (Önüt & Soner, 2008). For example, in many communities, citizens ave voiced concerns about solid waste transfer stations tat are poorly sited, designed, or operated. In addition, some citizens migt feel tat transfer stations are disproportionately concentrated in or near teir communities. Yet transfer stations play an important role in a community s waste management system (Barcena-Ruiz & Casado-Izaga, 2015).Te rise in te popularity of environmental considerations in municipal planning also as increased te need to fully identify te environmental principles to determine te best location of te solid wastes to be collected (Önüt & Soner, 2008). In tis context, multi-criteria decision making approaces and optimization models ave been popular tools to tackle facility location problem witin waste management systems. Kao and Lin (1996) developed a facility location model to obtain optimal landfill sites utilizing a mixed-integer programming model. Siddiqui et al. (1996) were among te first scolars to use a combined geograpical information system and analytical ierarcy process procedure to aid in site selection. Later, Cang (1997) formulated an operational solid waste management model troug a ierarcical approac, in wic te site finding problem of transfer stations in a large scale metropolitan region decomposed into two different levels. Tis analytical metod contained a preliminary screening procedure using te geograpical information system and an optimization analysis by a mixed integer programming model. Kirca and Erkip (1988) proposed a static model to minimize te total transportation cost for transfer station location. Teir model selects te loading unloading facilities tecnology and number of transfer veicles. Antunes (1999) formulates a single objective mixed-integer optimization model to determine te location and size of te transfer stations and sanitary landfills, wile minimizing total transportation and opening costs. In anoter work, Cang and Wie (2000) presented a fuzzy multi-objective nonlinear integer programming model to optimize site aspects in te solid waste collection network. To select te best municipal solid waste management strategy, Cambal et al. (2003) developed a multiple-objective decision analysis model. Eiselt (2007) examined te site finding of landfills and waste transfer stations in 110

3 New Brunswick and compared te results wit te locations of existing facilities. Te developed optimization formulation was similar to te models used in te analysis of standard ub location problems. Xi et al. (2010) addressed a long-term planning of solid waste management in te City of Beijing, Cina using an inexact cance-constrained mixed-integer linear programming model. Samanlioglu (2013) presents a novel multi-objective location-routing model to decide on locations of treatment centers, routing different types of industrial azardous wastes to treatment centers, locations of recycling centers and routing azardous waste and waste residues to tose centers, and locations of disposal centers and routing waste residues tere. More recently, Eiselt and Marianov (2015) discussed different classes of decision-making models and formulate a generic cost-minimization model for landfill site problem. Tey also surveyed landfill location models tat ad appeared in te literature during te last forty years. Beskese et al. (2014) present a ybrid metod based on analytical ierarcy process to coose te proper landfill location among tree possible landfill sites for te city of Istanbul. Kinob et al. (2015) used geograpical information system tools to optimize travel distances, trips and collection time to maximize total waste collection, and as a result large savings and keeping te environment clean. For a compreensive review of te existing literature on solid waste management a reader can refer to Giania et al. (2014). Te above literature review reveals tat te main focus of existing studies as been placed on undesirable facility location, primarily on landfill site problems. However, tere are a limited number of models optimizing te locations and tecnologies of transfer stations. Moreover, most models in te literature of te urban waste management overlook te sustainability issues entailing te impacts of transporting wastes on environment. Motivated by a real-world case of designing te waste management system in Teran, tis paper presents a multi-objective model tat aims to address tese researc gaps. Teran is te most populated and is an industrial region of Iran. As a result, waste materials produced by te industrialization and urbanization cause various environmental problems. Te waste management system is comprised of customers, transfer stations and landfills. Te transfer stations are responsible for compacting te wastes collected from customers and loading tem into semi-trailers to transfer to landfills. Te proposed model determines te location and allocation of transfer stations and selects te waste processing tecnologies in facilities to compact te wastes. Te objective is to simultaneously minimize te greenouse gas emissions and te rates of energy consumption witin te waste management system at te lowest cost. To tackle te multiple objectives in te problem, an interactive fuzzy programming solution approac is used. Te remainder of tis paper is organized as follows. Section 2 states te problem and presents te multiobjective model. Te solution approac for te developed model is presented in Section 3. Te application of te multi-objective model in te real world case of Teran is presented in Section 4. Finally, Section 5 concludes te article and provides directions for future researc in te area. 2- Model Formulation An optimization model for designing a waste management system consisting of customers (waste generators), transfer stations and landfills is formulated in tis section. In tis system, te collection veicles collect te waste generated by customers at eac region and aul tem eiter to a landfill site directly, or to a transfer station. Te transfer stations compact te waste and transport it to a landfill by semi-trailers. Compacting te waste leads to decrease in te volume of te garbage and te amount of greenouse gas emission. Likewise, semi-trailers and collection veicles ave different capacities and 111

4 greenouse emissions. At eac transfer station, different tecnology types wit different costs and energy consumption rates can be acquired. Figure 1 sows te structure of tis waste management system. customers Transfer stations landfills Figure 1.Te structure of waste transportation system Te problem lies in determining te following decisions at once: 1. Te number of transfer stations to be located, 2. Te location of transfer stations, 3. Te tecnology adopted at eac transfer station, 4. Te number of semi-trailers at eac transfer station, 5. Te quantity of waste to transported from eac transfer station to landfills, 6. Te number of collection veicles at eac customer region 7. Te quantities of waste transported from eac customer region to transfer stations and landfills. To determine te above decisions, a multi-objective model is developed wic aims at minimizing te total cost as well as minimizing greenouse gas emissions and te rates of energy consumption witin te waste management system Notations In order to formulate te model, te following notations are used. Indices: i :Index of customers j : Index of transfer stations k : Index of landfills 112

5 Parameters: l : Index of tecnology levels at transfer stations Tc : Sipment cost by a collection veicle, per kilometer Sc l :Sipment cost by a semi-trailer wit tecnology level l, per kilometer Fc lj : Fixed cost of establising transfer station jj wit tecnology level l Vc lj : Variable cost of compacting waste at station j wit tecnology level l drt ij : Distance between customer region i and transfer station j dtl jk drl ik : Distance between transfer station j and landfill k : Distance between customer regioni and landfill k TSn : Maximum number of transfer stations Ca lj : Capacity of transfer station j wit tecnology level l Tp : Greenouse gas emission from a collection veicle, per kilometer Sp l : Greenouse gas emission from a semi-trailer wit tecnology level l, per kilometer Wp : Greenouse gas emission from waste, per cubic meter of waste and per kilometer Wcp l : Greenouse gas emission from te waste compacted wit tecnology level l, per cubic meter of waste and per kilometer β l : Compaction factor of tecnology l for reducing te volume of te waste (tis parameter sows ow muc te volume of waste will be after te compaction be reduced.) α l : Discount factor for a transfer station wit te tecnology level l (Tis factor sows ow muc te cost of sipping waste from a transfer station wit te tecnology level ll is lower tan directly sipping it from a customer.) 113

6 ε lj : Energy consumption rate of transfer station jj wit te tecnology level l ww i : Total amount of waste generated by customer regioni Tca : Capacity of a collection veicle Sca l : Capacity of semi-trailer wit tecnology level l Mca lj : Minimum percentage of te capacity of a transfer station wic needs to be used if tecnology level l is adopted at location j Decision variables: X ijl : Volume of waste sipped from customer region i to te transfer station j wit tecnology level ll(in cube meter) Y jkl : Volume of waste sipped from transfer station j wit tecnology level l to te landfill k (in cube meter) U ik : Volume of waste sipped from regioni to te landfill k (in cube meter) Z lj : Equal to 1 if a transfer station wit tecnology level l is establised at location j, 0 oterwise Tnt ij : Number of collection veicles for sipping waste from region i to transfer station j Tnl ik : Number of collection veicles for sipping waste from region i to landfill k Sn jkl : Number of semi-trailers wit tecnology level l for sipping waste from transfer station j to landfill k 2-2- Objectives In tis problem, tree objectives are taken into account: Minimizing te total cost Minimizing te total emission of greenouse gas Minimizing te total rate of energy consumption 114

7 Equations (1)-(3) present tese objectives respectively. Min ϖ = Fc z + vc x + Tc drl Tnl 1 lj lj lj ijl. ik ik j l i j l i k + Tc. drt Tnt + α Sc dtl Sn ij ij l l jk jkl i j j k l Min ϖ 2 = Tp. drt Tnt + Tp. dtl Tnl + Sp dtl Sn Min ϖ ij ij jk jk l jk jkl i j j k j k l + Wp. drt x + Wcp dtl y + Wp. drl u ij ijl l jk jkl ik ik l i j l j k i k = ε x 3 lj ijl i j l 1) (2) (3) Te cost components in Equation (1) include te fixed cost of establising transfer stations, te sipment from customers to transfer stations landfills, te cost of compacting waste at transfer stations, and te sipment cost from transfer stations to landfills. Equation (2) sums te amounts of greenouse gas emitted from collection veicles, semi-trailers, and compacted and uncompacted wastes. Equation (3) minimizes te total rates of energy consumptions considering different tecnologies of transfer stations Constraints j 1 Z lj TSn x + u = ww i ijl ik i j l k β x = y j, l l ijl jkl i k i l i l x Ca z j, l z ijl lj lj l lj 1 j x Mca Ca Z j, l ijl lj lj lj x Tnt T ca i, j ijl ij u Tnl T ca i, k ik ik y Sn Sca i, j, l jkl jkl l Tntij, Sn jk, Tnlik 0 x ijl, y jkl, uik 0 Z lj { 0,1} (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) 115

8 Constraint (4) enforces te maximum number of transfer stations wic can be located. Constraint (5) ensures tat te total amount of waste sipped to landfills is equal to te sum of te waste quantities sipped from transfer stations and customers to tem. Constraint (6) represents te flow balance constraint in transfer stations. Constraint (7) enforces te capacity limitation of transfer stations. Constraint (8) requires only a single tecnology level tat can be adopted at eac transfer station. Constraint (9) ensures te minimum percentage of capacity wic must be used at eac transfer station. Constraints (10)-(13) guarantee tat te amounts of te waste sipped by collection veicles and semitrailers do not exceed teir capacities in different routes. Finally, constraints (14)-(15) define te domain of decision variables. 3- Solution Approac Numerous tecniques ave been developed to solve multi-objective linear programming models. Weigted sum metods, goal programming, compromise programming, and ε-constraint are amongst te simplest and most popular tecniques. However, te primary difficulty wit tese metods is determining te weigt or te goal of eac objective (Jadidi et al., 2014; Selim & Ozkaraan, 2008). To cope wit tis difficulty, fuzzy approaces can be applied for solving te multi-objective models (Eydi & Javazi, 2012).Fuzzy approaces is capable of measuring te satisfaction degree of eac objective function explicitly. Tis issue can assist decision makers in making teir final decisions by selecting a preferred efficient solution according to te preference of eac objective function (Seifbargy, et al., 2011;Moammadi et al., 2011). In tis paper, te interactive fuzzy programming solution approac developed by Torabi and Hassini, (2008) is used to solve te model. Te primary reason wy we ave used tis metod is tat unlike classical multi objective programming tecniques wic may arrive at weakly efficient solutions, it can guaranty to find just efficient solutions. Also, te fuzzy programming solution approac can obviate te need for setting te precise weigt for eac objective function in advance (Magool & Razmi, 2010; Torabi and Hassini, 2008). Te fuzzy programming solution approac for our multi-objective model (1)-(15) includes te following steps: Step 1. Determine te positive ideal solution (PIS) and negative ideal solution (NIS) for eac objective function. To reac te positive ideal solutions, we just need to solve eac objective function separately as follows: ϖ PIS = minϖ s. t. Constraints (4)-(15) (16) Te negative ideal solution can be also obtained by solving te following model: ϖ NIS = maxϖ s. t. Constraints (4)-(15) (17) Were ϖ denotes te t objective value (see (1)-(3)). Step 2. Determine a linear membersip function for eac objective function using Equation (18): 116

9 NIS 1 ϖ < ϖ NIS ϖ ϖ PIS µ = ϖ NIS PIS ϖ ϖ ϖ ϖ PIS 0 ϖ > ϖ NIS (18) We can interpret µ as te satisfaction degree for te t objective function for te given solution vector v. Figure 3 illustrates te grap of tis membersip function. Figure 2.Te membersip function Step 3.Convert te multi-objective model (1)-(15) into an equivalent single-objective using te following formulation. Max λ( ν ) = γλ + (1 γ ) θ µ s.t. λ µ = 1,2,3 λ 0 0 Constraints (4)-(15) 0 γ [0,1] (19) Were µ and λ 0 = min { µ } indicate te satisfaction degree of t objective function and te minimum satisfaction degree of objectives, respectively. Equation (19) as a new acievement function defined as a convex combination of te lower bound for satisfaction degree of objectives ( λ 0 ), and te weigted sum of tese acievement degrees ( µ )to 117

10 guarantee arriving at an adjustable balanced compromise solution. Furtermore, θ andγ represent te relative importance for te t objective function and te coefficient of compensation, respectively. Te θ is selected by decision makers based on teir preferences, wile it is required tat θ = 1 θ > value of and 0. In addition, γ controls te minimum satisfaction level of objectives as well as te compromise degree among te objectives implicitly. In oter words, te developed formulation enables decision makers to yield bot unbalanced and balanced compromised solutions based on teir preferences troug adjusting te value of parameterγ. Evidently, a iger value for γ means tat more attention is paid to gain a larger lower bound for te satisfaction degree of objectives ( λ 0 ) and consequently more balanced compromise solutions. Conversely, a lower value for γ results a solution wit a iger satisfaction degrees for some objectives and lower satisfaction degrees for te oter ones (leading to unbalanced compromise solutions). Step 4. Having te coefficient of compensation (γ ) and relative importance of te fuzzy goals (θ vector), solve te model (19). If te decision maker is satisfied wit tis current efficient compromise solution, stop. Oterwise, provide anoter efficient solution by canging te value of controllable parameters and go to step Case Study Municipal solid waste as been one of te most major concerns in Teran over te past few years. Te main difficulty wit solid waste management in Teran is te large amount of waste per day wic is estimated to be 7.641million ton in average. Figure 3 illustrates te total amount of waste generated in Teran from 1997 to 2013, as reported by Teran waste management organization. Waste Generation (Million Tons) Year Figure 3. Total solid waste generation in Teran from 1997 to 2013 based on data provided by Teran waste management organization 118

11 As can be seen in Figure 3, te yearly generated waste in Teran as ad an increasing trend from 1997 to Tus, we expect even more quantities of waste in near future wic can lead to undesirable impacts suc as pollution, diseases, vermin animals, etc. Tis igligts te need for establising more infrastructures including transfer stations, landfills, and transportation veicles as well as utilizing iger tecnologies for managing suc a large amount of waste. Te experts of Teran waste management organization ave found tat te utilization of compacting tecnologies can be elpful for tis purpose. Compacting tecnologies can considerably reduce te volumes of wastes (up to 40%) and rates of energy at transfer stations witout any need for vast spaces. Tree tecnology levels can be adopted at transfer stations: 1. Tecnology level 1: Following tis approac, traditional tecnologies are selected. 2. Tecnology level 2: Tis tecnology level corresponds wit adopting compacting tecnologies and resuming te existing semi-trailers. Using tis approac, te quantity of compacted wastes are loaded in existing semi-trailers and auled to landfills. Tis tecnology is less expensive, but it leads to consuming more amounts of energy in comparison wit tecnology level Tecnology level 3: Tis tecnology level is equivalent to acquiring compacting tecnologies as well as purcasing modern trucks equipped wit compacting tecnologies. Tis tecnology level is te most expensive strategy due to te large costs of purcasing new trucks. However, it can result in lower rates of energy, fuel and pollution. Wile tere were 11 active transfer stations in Teran, five locations were identified as potential sites for establising new transfer stations. Table 1 provides te distances of tese locations from te 22 districts of Teran and te two landfills located in Abali and Karizak region. Te fixed costs of establising transfer stations wit different tecnology levels along wit teir capacities are presented in Table 2. Also, Table3 includes te distances between districts of Teran and landfills as well as te amounts of waste generated in tese sites. 119

12 Table 1. Distances between potential locations for establising transfer stations and te oter sites Transfer Station 1 Transfer Station 2 Transfer Station 3 Transfer Station 4 Transfer Station 5 District District District District District District District District District District District District District District District District District District District District District District Landfill Landfill Table 2. Capacity and cost of establising transfer stations wit different tecnology levels Cost of Adopting Cost of Adopting Tecnology Level 1 Tecnology Level 2 Capacity Transfer Station 1 120,000, ,000, Transfer Station 2 150,000, ,000, Transfer Station 3 150,000, ,000, Transfer Station 4 120,000, ,000, Transfer Station 5 60,000, ,000,

13 Table 3. Amounts of waste generated in districts of Teran and teir distances to landfills Quantity of Waste Distance to Landfill 1 Distance to Landfill 2 District District District District District District District District District District District District District District District District District District District District District District Te proposed model is implemented in tis study to redesign te waste management network of Teran. To solve tis model, te decision maker provides te relative importance of objectives linguistically as θ1 > θ2 > θ3, and based on tis relationsips we set te objectives weigt vector as: θ = (0.5,0.3,0.2). In tis respect, our initial experiments sow tat any value ofγ between 0.3 and 0.8 could be appropriate for obtaining a compromise solution. Figure 3 demonstrates te results of solving te model at θ = (0.5, 0.3, 0.2) andγ = 0.4. Table 4 and Table 5 moreover present sensitivity analyses on te values of γ andθ, respectively, wic can be used for exploring tradeoffs between te tree objectives of te problem. An important managerial insigt from te obtained results is tat te optimal solution requires adopting te tecnology level 3at all te transfer stations wic corresponds to acquiring compacting tecnologies as well as purcasing modern trucks. In oter words, despite te large costs of adopting compacting tecnologies and purcasing equipped trucks, tis tecnology level is te most effective strategy wen one aims to simultaneously minimize te total cost, rate of energy consumption, and air pollution in Teran. 121

14 Region 19 Landfill 5 20 Transfer station km 1 1 Figure3. Optimal decisions for locations and allocation of transfer stations in Teran Table4.Sensitivity analysis on γ value for exploring balanced compromise solutions γ Total Emission of Total Rate of Energy Total Cost ( ϖ 1 ) λ 0 Greenouse ( ϖ 2 ) Consumption ( ϖ 3 )

15 Table 5. Sensitivity analysis on θθ values for exploring tradeoffs between te tree objectives θθ 1 θθ 2 θθ 3 Total Emission of Total Rate of Energy Total Cost ( ϖ 1 ) Greenouse ( ϖ 2 ) Consumption ( ϖ 3 ) Conclusions In tis study, a multi-objective optimization model is presented for te design of solid waste management system. Te objective of te problem is to simultaneously minimize te greenouse gas emissions and te rates of energy consumption witin te waste management system at te lowest cost. An interactive fuzzy programming solution approac was utilized to solve te multi-objective model. Te proposed approac in tis study is used to redesign te waste management network of Teran using real data. Te obtained results revealed tat te optimal solution requires adopting ig tecnologies for transfer stations of Teran, albeit teir large costs. Future researc can study inerent uncertainty of input data suc as amounts of waste generated at eac region. Stocastic programming or robust optimization approac can be promising tools for tis purpose. Anoter direction for future researc can be te incorporation of veicle routing decisions into te model. In tis case, considering time windows may take a great importance in te problem. In addition, dealing wit larger network design problems, compared to tose investigated in our real case study, may need te development of solution metods tat can reac optimal solutions witin reasonable lengt of time. References Barcena-Ruiz, J. C. & Javier Casado-Izaga, F., Regulation of waste management under spatial competition. Journal of Cleaner Production, pp Selim, H. & Ozkaraan, I., A supply cain distribution network design model: An interactive fuzzy goal programming-based solution approac. Int J Adv Manuf Tecnol, 36(3-4), pp Abduli, M. & Azimi, E., Municipal waste reduction potential and related strategies in Teran. International Journal of Environmental Researc, 4(4), pp Anon., A., A manual for decision-making. United States Environmental Protection Agency. s.l.:s.n. 123

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