Waste Management 33 (2013) 2607–2622

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Waste Management

journal homepage: www.elsevier .com/locate /wasman

Optimal planning for the sustainable utilization of municipal solid waste

0956-053X/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.wasman.2013.08.010

⇑ Corresponding author. Tel./fax: +52 443 3273584.E-mail address: jmponce@umich.mx (J.M. Ponce-Ortega).

José Ezequiel Santibañez-Aguilar a, José María Ponce-Ortega a,⇑, J. Betzabe González-Campos b,Medardo Serna-González a, Mahmoud M. El-Halwagi c,d

a Chemical Engineering Department, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán 58060, Mexicob Institute of Chemical and Biological Researches, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán 58060, Mexicoc Chemical Engineering Department, Texas A&M University, College Station, TX 77843, USAd Adjunct Faculty at the Chemical and Materials Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia

a r t i c l e i n f o

Article history:Received 30 May 2013Accepted 3 August 2013Available online 10 September 2013

Keywords:Supply chainSustainable developmentMunicipal solid wasteOptimizationDistributed systemSuperstructureWaste management

a b s t r a c t

The increasing generation of municipal solid waste (MSW) is a major problem particularly for large urbanareas with insufficient landfill capacities and inefficient waste management systems. Several optionsassociated to the supply chain for implementing a MSW management system are available, howeverto determine the optimal solution several technical, economic, environmental and social aspects mustbe considered. Therefore, this paper proposes a mathematical programming model for the optimal plan-ning of the supply chain associated to the MSW management system to maximize the economic benefitwhile accounting for technical and environmental issues. The optimization model simultaneously selectsthe processing technologies and their location, the distribution of wastes from cities as well as the distri-bution of products to markets. The problem was formulated as a multi-objective mixed-integer linearprograming problem to maximize the profit of the supply chain and the amount of recycled wastes,where the results are showed through Pareto curves that tradeoff economic and environmental aspects.The proposed approach is applied to a case study for the west-central part of Mexico to consider the inte-gration of MSW from several cities to yield useful products. The results show that an integrated utiliza-tion of MSW can provide economic, environmental and social benefits.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Waste is defined as any residual material from industrial andhuman activities that has no residual value (Ortiz et al., 2010).Nowadays, there is much interest in waste production, manage-ment and disposal. This is attributed to the observation that wastegeneration is a side effect of consumption and production and ittends to increase with the economic development of the society(Beolchini et al., 2012). Furthermore, there is an increasing aware-ness of the environmental, health, economic, and social problemsassociated with waste disposal. Particular attention should be gi-ven to the treatment and management of municipal solid wastebecause of its abundance and impact on the environment (Vasud-evan et al., 2012).

In Malaysia the average amount of municipal solid waste gener-ated is about 0.5 kg/person/day; but it can be up to 1.7 kg/person/day in other cities of the world (Ramayah et al., 2012). This createsproblems in some countries because of the lack of sufficient land-fills and an adequate MSW management system. For example, inseveral countries of Central and South American (like the specific

case of Mexico), the waste management is not adequate; also,one important problem is that the MSW is mixed (i.e. differenttypes of materials are mixed and they require to be separated forfurther treatment), which increases the separation costs, makesmore difficult and expensive the treatment process and even yieldsinsalubrious conditions. This is very common in Mexico, wheremost of the people do not separate the solid wastes, which resultsin a very significant increase of total wastes volume and weight,besides the fact that the facilities are not adequate to store theseresidues. In these cases the application of proper environmental,institutional, financial, economic and social tools to guarantee asustainable waste management is required (Ghinea et al., 2012).There are also negative impacts on water, land, and air resultingfrom inadequate treatment and management of the municipal so-lid waste (Krüger et al., 2012).

It is important to note that the actions that have been imple-mented to solve this problem are focused only on one particulartype of waste, without taking into account the interaction betweenthe waste composition and distribution, and without consideringthe entire supply chain optimization as well as the economies ofscale. The distribution of wastes, products and the design andselection of the processing facilities are crucial in yielding anadequate solution for the entire problem. Therefore, this paper

2608 J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622

proposes a general methodology for the optimal planning of a dis-tributed system of processing facilities based on municipal solidwaste. The proposed methodology is based on a mathematical pro-gramming formulation for the optimal planning of the reuse of mu-nicipal solid waste to maximize the economic benefits whileaccounting for social and environmental aspects. The optimizationmodel is capable of selecting the processing technologies, consum-ers, cities producing wastes, amount of recycled waste, productsand location of processing facilities.

1.1. Different types of MSW

Since waste characteristics vary over time and location, there isa need to account for such variability. Plastic materials are exten-sively used (Passamonti and Sedran, 2012); nonetheless, plasticwastes have a great impact on the environment because they aremostly non-biodegradable and they occupy an enormous volume(see Table 1). Another important waste is paper, which represents30–40% of the total municipal solid waste. Metals are other impor-tant constituents of MSW, which are recyclable materials used toobtain high value products (Plunkert, 2006). Glass is another mate-rial that can be readily recycled. For glass recycling, it has to berecovered and separated from other wastes as well as differenti-ated between the different types of glass (clear, amber and green).A particular advantage for recycling glass is the reduction in energyconsumption compared to the use of silica feedstock. In addition,the food and garden wastes are important since they representaround 40% of the wastes generated in Mexico and 27% of thewastes generated in USA (see Table 1); their composition is very di-verse depending on the considered city, and the characterization touse this waste for the production of several valuable products iscomplicated since commonly there is not enough reported infor-mation for this purpose. However, these wastes are very importantand they have a high potential to be reused; in this paper, thesewastes are considered as a mixture, which is obtained after theseparation of the recyclable materials as plastics, metals, paperand glass (this is based on the proposed work by Young, 2010).

1.2. Processing routes to treat MSW

Effective methods need to be implemented to recycle the plasticmaterials (Kalantar et al., 2012). In this context, physical, thermal,and chemical recycling technologies are the most widely used (Huret al., 2003). Gasification provides a promising alternative to ther-mal recycling of plastic waste to produce a synthesis gas (syngas).Additionally, the plastic waste can be transformed into carbonnanotubes (Alireza and Gordon, 2012; Wu et al., 2012).

For recycling and utilizing paper wastes, there are several pro-cessing routes, including thermal processing and landfilling, whichdo not typically require sorting, while many other routes entail the

Table 1Composition of municipal solid waste for several countries.

Type of waste USAa

2010Mexicob

2009France2009

Paper and cardboard 28.5 14.2 35Plastic 12.4 5.8 7Metals 9 3.1 5Textiles 5.3 1.2 5Glass 4.6 6.6 12Food wastes 13.9 31.6 21Yard trimmings 13.4 9.8 –Others 12.9 27.7 15

a Environmental Protection Agency Office of Resource Conservation and Recovery (20b Mexican National Institute of Ecology (2012).c Rogoff and Screve (2011).

separation of paper, for example, paper digestion can be used forpapermaking (Hanan et al., 2012) and fermentation to yield bioeth-anol (Wang et al., 2012), mixed alcohols, acids, ketones, or fuel(Pham et al., 2010).

The biowastes (food and garden wastes) can be used to obtainseveral bioproducts through composting, anaerobic digestion or an-other processing technology; or even to obtain biofuels like biogasor bioethanol, however, their composition can be very different andvariable and the determination of production factors can be compli-cated, although these wastes could be included in the model as an-other type of waste separately if necessary data are available, thistype of wastes are taken into account with the mix of the remainwaste after the separation of plastics, glasses, paper and metal.

In addition, thermal pathways as incineration, gasification andpyrolysis have been proposed to treat the wastes as a mixture ofdifferent wastes (Grieco and Baldi, 2012). Incineration is a combus-tion process that uses an excess of oxygen to burn the municipalsolid waste. Pyrolysis is a thermal decomposition of carbon-basedmaterials in an atmosphere without oxygen using heat to producesyngas, the process is endothermic. For the pyrolysis process thereare several variations; for example, there is pyrolysis–gasification,where another reactor is added to gasify the produced liquids fromthe first step of pyrolysis. On the other hand, conventional gasifica-tion is a thermal process, which converts carbonaceous materialsin syngas using a limited quantity of oxygen, where steam maybe injected to promote CO and hydrogen production. Finally thereis another variation of the gasification process which is known asplasma arc gasification, and this processing route is a high temper-ature pyrolysis process, where organic compounds and solidwastes are converted into syngas and inorganic materials and min-erals (Young, 2010).

1.3. Assessment of processing routes to treat MSW

Several papers have addressed the processing technologies totreat the different types of MSW, these evaluations have consid-ered the human, environmental and economic aspects; in this re-gard, Young (2010) evaluated and compared the economicaspects of five thermal routes to treat the MSW. Ramayah et al.(2012) examined the human behavior for the recycling process.Also, Ghinea et al. (2012) investigated some waste managementalternatives in the city of Iasi in Romania from the environmentalpoint of view based on the life cycle assessment. Furthermore, thecosts and benefits of waste recycling in Portugal were presented byCruz et al. (2012), where the analysis included the return of thecapital employed and the landfilling activities. On the other hand,Ling and Poon (2012) presented a study to compare the feasibilityfor using recycled glass. Finally, the assessment to obtain energyfrom wastes has been studied too, for example Iakovou et al.(2010) concluded that biomass from wastes to energy production

b Colombiab

2009Americanc Samoa2009

Chinac

1993

22 26.4 3.15 12.8 4.91 7.9 0.74 4.2 2.12 3.4 2.2

56 3.78 46.910 11.30 –– 30.22 40.1

11).

J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622 2609

is an attractive solution; however, very few studies have addressedcritical supply chain management issues.

1.4. Performance for the waste management

Municipal solid waste management has been addressed by dif-ferent ways; for example Wan-Alwi et al. (2009) presented a gen-eric graphical approach for simultaneous targeting and design of autility gas network. Also, Chang and Chang (1998) developed anon-linear model taking into account waste streams from facilities,landfills, transfer stations and incinerators, where the non-linearityis provided by the presence of pre-treatment plants and technicalspecifications of the incinerator. In addition, Costi et al. (2004) pre-sented the structure and the application of a decision support sys-tem designed to help decision makers of a municipality in thedevelopment of incineration, disposal, treatment and recyclingintegrated programs. Recently, the municipal solid waste manage-ment has been treated in other ways, for example a multi-objectiveoptimization program was proposed by Minciardi et al. (2008),where the model was formulated as a non-linear multi-objectiveformulation for a case study in Genova, Italy. In addition, thewastes management has been applied to other countries; in thisway, Galante et al. (2010) proposed an effective decision supportsystem for wastes management through a multi-objective optimi-zation program, these authors addressed an incineration plant inSicily, Italy. Also, the optimization of a solid waste managementsystem in Port Said, Egypt was presented by Badran and El-Haggar(2006). Su et al. (2008) proposed a multi-objective optimizationmodel for the management of MSW via an uncertainty approach;which considered economic and environmental aspects appliedto the city of Fo San China. Finally, Kanat (2010) studied the situa-tion of MSW management in Istanbul, Turkey.

1.5. Optimization for the supply chain associated to the wastemanagement

Several works have been focused on the supply chain optimiza-tion for the specific case of biorefineries accounting for differentcriteria (i.e. Bowling et al., 2011; Santibañez-Aguilar et al., 2011,2013; El-Halwagi et al., 2013). In this context, Sammons et al.(2008) and Van Dyken et al. (2010) proposed mixed-integer linearprogramming (MILP) models for optimizing supply chains basedon biomass as feedstock. Recently, You et al. (2012) proposed anapproach for the optimal planning of biofuels supply chains con-sidering economic, environmental and social objectives and Paksoyet al. (2013) proposed a MILP model for the optimal planning ofsupply chain networks in biorefineries.

For the specific case of the supply chains based on waste man-agement, Hung et al. (2007) presented a review for several modelsdeveloped to support decision making in municipal solid wastemanagement and they developed a sustainable decision makingmodel for MSW management, which considered a multi-criteriadecision approach. Furthermore, the work by Morrissey andBrowne (2004) and Karmperis et al. (2013) classified the modelscurrently being used in the area of municipal waste managementinto three categories: cost benefit analysis, based on life cycleassessment and based on multi-criteria decision making.

2. Problem statement

Fig. 1 shows a schematic representation of the addressed prob-lem, which considers a set of cities C. These cities have a specificproduction rate of wastes that include different constituents suchas plastics, metals, papers, and food. The wastes from cities canbe separated into different subtypes (e.g., polyethylene and polyvi-

nyl chloride for plastics, green and amber for glass). After thewastes are separated, they may be transported to processing plantslocated in the set of cities (C) to treat the waste and yield severalproducts based on the used technologies and raw materials. A setof candidate technologies is considered for each class of waste.The products are transported to the consumers in the set of cities(C). Each city has a specific availability of generated waste and de-mand for products. The processing plants are located in differentgeographical locations. Each processing plant can treat the wastesusing several technologies. Given also are the capital and operatingcosts for the processing technologies and the transportation costsfor raw materials and products.

The optimization task seeks to determine the optimal supplychain network for the waste utilization including the transporta-tion of wastes, the location of the processing facilities, the selectionof technologies used in each place, and the distribution of products.

3. Model formulation

Prior to developing the model formulation, the used indices inthe mathematical model are defined. The index c represents thecities that generate wastes and consume useful products. Since dif-ferent types wastes may be generated (e.g., plastics, metals, glass,organics, papers), these wastes are defined with the index wn.The model considers several processing facilities distributed in aspecific region. There are several groups of processing facilitiesand each processing facility is specialized in a type of waste wn.To identify each group of processing facilities, it is necessary touse a coupled index: pp-wn where pp represents a group of pro-cessing facilities and wn indicates that group of processing plantsfor the specific waste type. In each processing facility there is aset of candidate processing technologies for each waste. The indexto describe these sets is n-wn, where n is used for the technologiesand wn is used to specify the set of processing technologies. Fur-thermore, the nomenclature used is presented in Table 2. Next,the model formulation is presented as follows.

3.1. Constraints for sources in the cities

Each city has a specific production of wastes and these wastescan be separated. Since not all the waste may be utilized, the usefulwaste is a portion of the total production of wastes in each city. Theused waste wn of the type p-wn in the city c (Fwn,c,p-wn) must belower than the useful waste type p-wn in the city cðasep

wn;c;p-wnFtotalc;p-wnÞ, the useful waste wn is equal to the total waste

type p-wn in the city c ðFtotalwn;c;p-wnÞ multiplied by a separation factor

ðasepwn:c;p-wnÞ. This is stated as follows:

Fwn;c;p-wn 6 asepwn;c;p-wnFtotal

c;p-wn; 8 wn 2W; c 2 C; p-wn 2 S ð1Þ

3.2. Waste distribution from cities to processing plants

When a waste is selected, it is distributed to different process-ing plants, which are located in different regions. The processingplants are specialized in a type of waste, this is, plastic, metal, glassor organic waste. Each processing facility has a set of processingroutes depending on the treated waste. The proposed mass balancefor a specific waste is stated as follows: The selected waste in thecity c (Fwn,c,r) is equal to the delivered waste from the city c tothe specific processing plant pp-wn (for example, Fplant

wn;c;pp-wn;p-wn forplastic) for all the types of considered wastes:

Fwn;c;p-wn ¼X

pp-wn2PH

Fplantwn;c;pp-wn;p-wn; 8 wn 2W; c 2 C; p-wn 2 S

ð2Þ

PLANT 1 FOR WASTE 1

Tech 1

Tech n1

Tech 1

Tech n2

Tech 1

Tech n3

Tech 1

Tech nwn

Product 1

Product p1

Product 1

Product p2

Product 1

Product p3

Product 1

Product pwn

City 1

Waste 1(Plastic)

Waste 2(Metal)

Waste 3(Glass)

Waste wn(Organic)

Tech 1

Tech n1

Product 1

Product p1

Waste 1(Plastic)

Waste 2(Metal)

Waste 3(Glass)

Waste wn(Organic)

Tech 1

Tech n2

Product 1

Product p2

Tech 1

Tech n3

Product 1

Product p3

Tech 1

Tech nwn

Product 1

Product pwn

City C

City 1

City C

Raw Material

Raw Material

Separationof waste

Separationof waste

Processing of raw material

PLANT PP1 FOR WASTE 1

PLANT 1 FOR WASTE 2

PLANT PP2 FOR WASTE 2

PLANT 1 FOR WASTE 3

PLANT PP3 FOR WASTE 3

PLANT 1 FOR WASTE WN

PLANT PPN FOR WASTE WN

Fig. 1. Superstructure for a supply chain of a distributed system of facilities based on waste.

2610 J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622

Notice that there are a lot of types of processing facilities, andeach processing plant has a set of processing technologies depend-ing on the waste. For example, each plastic plant has its set of tech-nologies to treat plastic wastes; in this regard, for each waste wn,there is a set of technologies to treat all subtypes of wastes p-wn,these technologies are defined with the script n-wn.

3.3. Waste distribution into the processing plants to be treated withdifferent technologies

The wastes in the processing plants are distributed to differentprocessing technologies, and depending on the selected technologyit is possible to produce several products. The sum of raw materialsfrom the cities c ðFplant

wn;c;pp-wn;p-wnÞ is equal to the sum of the distrib-uted raw materials to different technologies ðFtech

wn;pp-wn;n-wn;p-wnÞ:

Xc2C

Fplantwn;c;pp-wn;p-wn ¼

Xn-wn2T

Ftechwn;pp-wn;n-wn;p-wn; 8wn

2W; pp-wn 2 P; p-wn 2 S ð3Þ

There is not any index for products because from each technol-ogy can be produced only one product, since the technologies arespecific.

3.4. Mass balances in the processing plants

The model considers the transformation of raw materials toproducts through the processing plants. The conversion processesusually are modeled through nonlinear relationships; however, inthis paper the use of an efficiency factor for each technology andtype of feedstock ðaprod

wn;n-wn;p-wnÞ is proposed, this factor helps to

Table 2List of symbols used in the model.

Parameters Description

Ftotalc;p-wn

Maximum available waste type p-wn in the city c

asepwn;c;p-wn Factor used to determine the amount of useful waste type p-wn in the city c

aprodwn;n-wn;p-wn

Efficiency factor for each processing technology to obtain products from wastes

PDcitywn;n-wn;c;p-wn

Demand for each product in a given city

Csepwn;c;p-wn Unitary separation cost of wastes

Cno�sepwn;c;p-wn Unitary no separation cost that is paid by the government for use landfills

Cunit�transpwn;p-wn

Unitary transportation cost of waste per amount of material and distance

dc,pp-wn Distance between the city c and the processing facility pp-wn

C

unit � transpprod

wn;n-wn;p-wn

Unitary transportation cost of products per amount of material and distance

Cproductwn;n-wn;c

Unitary cost for products

Variables Description

Fwn,c,p-wn Used waste wn type p-wn in the city c

Fplantwn;c;pp-wn;p-wn

Distributed waste from city c to processing plants type pp-wn

Ftechwn;pp-wn;n-wn;p-wn

Distributed waste to each processing technology into each processing facility

Pwn,pp-wn,n-wn,p-wn Obtained product from each type of waste into processing facilities

Pcitywn;pp-wn;c;n-wn;p-wn

Delivered product to consumers

PTcitywn;c;n-wn;p-wn

Total product from all processing facilities in a given consumer

CostSepwn Individual separation cost for each type of waste wnCostSeptotal Total separation costCostNSeptotal Total no separation cost

CostTransp

cityprocessingplant

Transportation cost from cities to processing facilities

CostTransp

processingplantcity

Transportation cost from processing facilities to cities

Cprocessingwn;pp-wn;n-wn;p-wn

Unitary operational cost for processing plants

CostOpprocessing Total operational cost

Aprocessingwn;pp-wn;n-wn;p-wn

Fixed part of the capital cost for processing facilities

Bcapwn;pp-wn;n-wn;p-wn Part of the capital cost that depends on the capacity of the processing facilities

CostCaptotal Total capital costCsales Profit for selling of productsNetProfit Annual net profitConsumewaste Percentage of consumed waste

Binary variables Description

yprocessingwn;pp-wn;n-wn;p-wn;q

Binary variable used to define the existence of the processing plants and allows calculating the capital cost of the processing facility

J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622 2611

obtain the amount of produced product (Pwn,pp-wn,n-wn,p-wn) from anamount of given feedstock ðFtech

wn;pp-wn;n-wn;p-wnÞ:

Pwn;pp-wn;n-wn;p-wn ¼ aprodwn;n-wn;p-wnFtech

wn;pp-wn;n-wn;p-wn; 8 wn

2W; pp-wn 2 P; n-wn 2 T; p-wn 2 S ð4Þ

The efficiency factors are determined prior to the optimizationprocess and they are determined from simulation and/or previ-ously reported data.

3.5. Balances in splitters after the processing plants

When the raw materials are converted, the products are distrib-uted from the processing plants to product consumers located inthe different cities c. Then, the sum of amounts of delivered prod-ucts to all cities ðPcity

wn;pp-wn;c;n-wn;p-wnÞ is equal to the produced productin each processing facility (Pwn,pp-wn,n-wn,p-wn):

Pwn;pp-wn;n-wn;p-wn ¼Xc2C

Pcitywn;pp-wn;c;n-wn;p-wn; 8 wn 2W; pp-wn

2 P; n-wn 2 T ; p-wn 2 S ð5Þ

3.6. Balances in product distribution points before the cities

Before each city c, there is a product distribution point for eachproduct, where the amounts of the same product are mixed to ob-tain the total amount of product for a specific city. In this equation,

the sum of the amount of products arrived to the city from the pro-cessing facilities is equal to the total product in the city:Xpp-wn2PROCPLANT

Pcitywn;pp-wn;c;n-wn;p-wn ¼ PTcity

wn;c;n-wn;p-wn; 8 wn 2W;

n-wn 2 T; c 2 C; p-wn 2 S ð6Þ

3.7. Constraints for the demand of products in the cities

The total product in a city ðPTcitywn;c;n-wn;p-wnÞ must be lower than

the product demand ðPDcitywn;n-wn;c;p-wnÞ. This limits the production be-

cause it may cause an unbounded problem:

PTcitywn;c;n-wn;p-wn 6 PDcity

wn;n-wn;c;p-wn; 8 wn 2W; n-wn 2 T; c

2 C; p-wn 2 S ð7Þ

3.8. Wastes separation cost

The separation of wastes is one of the most expensive activitiesin this process; however, this activity is necessary because theMSW is a mixture of wastes. In countries like USA and theEuropean Union, the separation process is very efficient comparedwith countries like the ones of Central and South American likeMexico; since in USA the separation cost is linked to the collectionstage. In Mexico, most of the people do not separate the wastes andfurthermore there is not an efficient municipal collection system.

2612 J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622

For this reason, in this case the separation cost must be taken intoaccount, in addition to the transportation from houses to landfills.This approximation is given by a separation unitary cost ðCsep

wn;c;p-wnÞ,which depends on the type of waste and the place.

The separation is given in two steps: first the separation of thegeneric wastes (plastics, metals, glasses or organic compounds),and second the separation in different sub-wastes.

CostSepwn ¼Xc2C

Xp-wn2S

Csepwn;c;p-wnFwn;c;p-wn; 8 wn 2W ð8Þ

Also, the model takes into account a total separation cost, whichconsiders all individual separation costs:

CostSeptotal ¼X

wn2W

CostSepwn ð9Þ

3.9. No separation cost associated to the MSW

An important factor to consider is when the MSW is not sepa-rated, since this inaction has an associated cost. This cost is nor-mally absorbed by the government through landfills; however,this inaction must be considered to obtain a more integral solution.This cost is formed by a unitary cost to not separate multiplied bythe amount of MSW that is not separated. The unitary cost to donot separate is lower than the unitary cost to separate; however,the amount of MSW that is not separated is normally greater thanthe amount of separated MSW.

CostNSeptotal ¼X

wn2W

Xc2C

Xp-wn2S

Cno�sepwn;c;p-wnðF

totalwn;c;p-wn � Fwn;c;p-wnÞ ð10Þ

3.10. Total transportation cost of wastes from cities to processingplants

An important activity is the transportation of wastes from citiesto the processing facilities; this activity has an associated cost,which considers the unitary transportation cost of any type ofwaste ðCunit�transp

wn;p-wn Þ, also the distance between cities and processingfacilities (dc,pp-wn), as well as the transported wastes from citiesto processing plants ðFplant

wn;c;pp-wn;p-wnÞ. The unitary transportation costhas units of money per mass and distance. The equation to calcu-late the total transportation cost of wastes from cities to processingplants is given as follows:

CostTransp

cityprocessing plant

¼X

wn2W

Xc2C

Xpp-wn2P

Xp-wn2S

Cunit-transpwn;p-wn dc;pp-wnFplant

wn;c;pp-wn;p-wn ð11Þ

3.11. Total transportation cost of products from processing plants toconsumer cities

Another transportation activity is the transportation of productsfrom the processing plants to markets or cities, in this case the uni-

tary transportation cost C

unit-transpprod

wn;n-wn;p-wn

0BB@

1CCA depends on the type of

_q

Yprocessingwn;pp-wn;n-wn;p-wn;

Aprocessingwn;pp-wn;n-wn;p-wn ¼ aprocessing

wn;pp-wn;n-wn;p-wn;q

Bcapwn;pp-wn;n-wn;p-wn ¼ bcap

wn;pp-wn;n-wn;p-wn;qFtechwn;pp-wn;n-wn;p-wn

Fminprocessingwn;pp-wn;n-wn;p-wn;q 6 Ftech

wn;pp-wn;n-wn;p-wn 6 Fmaxprocessingwn;pp-wn;n-wn;p-wn;q

2666664

3777775;

wastes and the produced products. Remember that the index forthe products is equal to the index for processing technology n-wn. Furthermore, the total transportation cost considers the dis-tance between the cities and the processing plants, also the

amount of transported product ðPcitywn;pp-wn;c;n-wn;p-wnÞ:

CostTransp

processing plantcity

¼X

wn2W

Xn-wn2T

Xc2C

Xpp-wn2P

Xp-wn2S

C

unit � transpprod

wn;n-wn;p-wn dc;pp-wnPcitywn;pp-wn;c;n-wn;p-wn

ð12Þ

3.12. Processing cost in the processing facilities

For each technology is taken into account the processing cost,which is divided in two sections. The first one is the operationalcost that considers a unitary cost ðCprocessing

wn;pp-wn;n-wn;p-wnÞ, which dependson the processing plant pp-wn, type of used technology n-wn andtype of wastes wn and p-wn. The total operational cost also de-pends on the amount of processed feedstock in each processingfacility ðFtech

wn;pp-wn;n-wn;p-wnÞ. Finally, the equation for the total opera-tional cost is defined as follows:

CostOpprocessing ¼X

wn2W

Xpp-wn2P

Xn-wn2T

Xp-wn2S

Cprocessingwn;pp-wn;n-wn;p-wnFtech

wn;pp-wn;n-wn;p-wn

ð13Þ

On the other hand, also there is required to consider the capitalcosts for the processing facilities to obtain proper solutions. To cal-culate the total capital cost, the individual capital costs for the unitsconsidered are obtained. The capital cost is normally a function ofthe type: Aprocessing

wn;pp-wn;n-wn;p-wn þ B1capwn;pp-wn;n-wn;p-wn Ftech

wn;pp-wn;n-wn;p-wn

� �a,

the superscript a is used to consider the economies of scale; in thiscontext, the function is nonlinear and can generate problems duringthe solution approach; so, the function can be modified to produce alinear function of the type: Aprocessing

wn;pp-wn;n-wn;p-wn þ Bcapwn;pp-wn;n-wn;p-wn,

where Bcapwn;pp-wn;n-wn;p-wn is the unit variable capital cost. The capital

cost for each processing facility is given as follows:

CostCapprocessingwn;pp-wn;n-wn;p-wn

¼ Aprocessingwn;pp-wn;n-wn;p-wn þ Bcap

wn;pp-wn;n-wn;p-wn; 8 wn 2W;

pp-wn 2 P; n-wn 2 T; p-wn 2 S ð14Þ

Once the individual capital cost is obtained, is possible to obtainthe total annual capital cost, which is the sum of all individual cap-ital costs ðCostCapprocessing

wn;pp-wn;n-wn;p-wnÞ for each type of waste, processingplant, and processing technology:

CostCaptotal ¼X

wn2W

Xpp-wn2P

Xn-wn2T

Xp-wn2S

CostCapprocessingwn;pp-wn;n-wn;p-wn ð15Þ

The terms in the capital cost of the processing plants depend onthe capacity of the plants; these are defined for the following dis-junctions, which are activated when the processed feedstock is be-tween the lower and upper limits ðFminprocessing

wn;pp-wn;n-wn;p-wn;q andFmaxprocessing

wn;pp-wn;n-wn;p-wn;q, respectively):

8wn 2W; pp-wn 2 P;

n-wn 2 T;p-wn 2 S; q 2 I

Fig. 2. General representation of the addressed case study.

Table 3Efficiency factors for the processing technologies to treat the municipal solid waste.

Waste Sub-waste Technology Product Production factor kg product/kg waste

Plastic PP Technology 1 for nanotubes Nanotubes of 140 lm diameter 0.11a

Plastic PE Technology 1 for nanotubes Nanotubes of 140 lm diameter 0.16a

Plastic PET Technology 1 for nanotubes Nanotubes of 140 lm diameter 0.19a

Plastic PE Technology 2 for nanotubes Nanotubes of 252 lm diameter 0.32a

Plastic PP Technology 2 for nanotubes Nanotubes of 252 lm diameter 0.51a

Plastic PE Material recycling 1 Pellet 0.672b

Plastic PS Material recycling 1 Pellet 0.672b

Plastic PP Material recycling 1 Pellet 0.672b

Plastic PE Thermal Recycling Gasoline 0.299b

Plastic PE Thermal recycling Diesel 0.089b

Plastic PE Thermal recycling Heavy oil 0.068b

Plastic PE Chemical recycling Heat energy 19.44A,b

Plastic HDPE Pyrolyis n-Parafines 0.432b

Plastic HDPE Pyrolyis n-Olefines 0.446b

Plastic PP Pyrolysis Branched parafines 0.304b

Plastic PP Pyrolysis Branched parafines 0.333b

Paper Paper Material recycling 2 New paper 0.84c

Metal Aluminum Material recycling 3 Useful aluminum 1d

Glass Clear glass Material Recycling 4 New Glass 1e

Glass Green glass Material recycling 4 New Glass 1e

Glass Brown glass Material recycling 4 New glass 1e

MSW MSW Mass burn (incineration) Electricity 1.9584A,f

MSW MSW Pyrolysis Electricity 2.0556A,f

MSW MSW Pyrolysis/gasification Electricity 2.466A,f

MSW MSW Plasma arc gasification Electricity 2.9376A,f

MSW MSW Conventional gasification Electricity 2.466A,f

A This factor has units of MJ Energy/kg Waste.a Alireza and Gordon (2012).b Hur et al. (2003).c Environmental Protection Agency Office of Resource Conservation and Recovery (2011).d Plunkert (2006).e http://elreciclaje.org/content/reciclaje-de-vidrio. Accessed (09/29/2012).f Young (2010).

J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622 2613

Previous disjunction is algebraically reformulated as follows:

Aprocessingwn;pp-wn;n-wn;p-wn ¼

Xq2I

aprocessingwn;pp-wn;n-wn;p-wn;qyprocessing

wn;pp-wn;n-wn;p-wn;q; 8 wn

2W; pp-wn 2 P; n-wn 2 T; p-wn 2 S

ð16Þ

Bcapwn;pp-wn;n-wn;p-wn ¼

Xq2I

bcapwn;pp-wn;n-wn;p-wn;qdFtech

wn;pp-wn;n-wn;p-wn;q; 8 wn

2W; pp-wn 2 P; n-wn 2 T; p-wn 2 S

ð17Þ

Table 5Unit price for the considered products in the cities.

Product Price ($US/kg)

Nanotubes of 140 lm 100d

Nanotubes of 252 lm 70d

Pellet 0.3645a

Fuel 0.332a

ElectricityA 0.052632b

Olefines 0.18a

Aluminum 1.3c

Clear glass 0.039057d

Green glass 0.01171d

Brown glass 0.02994d

Paper 0.2109d

A $US/MJ.a Hur et al. (2003).b Young (2010).c Plunkert (2006).d Mexican National Institute of Ecology (2012).

2614 J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622

Ftechwn;pp-wn;n-wn;p-wn ¼

Xq2I

dFtechwn;pp-wn;n-wn;p-wn;q 8 wn 2W; pp-wn

2 P; n-wn 2 T; p-wn 2 S ð18Þ

Fminprocessingwn;pp-wn;n-wn;p-wn;qyprocessing

wn;pp-wn;n-wn;p-wn;q

6 dFtechwn;pp-wn;n-wn;p-wn; 8 wn 2W; pp-wn 2 P; n-wn

2 T; p-wn 2 S; q 2 I ð19Þ

Fmaxprocessingwn;pp-wn;n-wn;p-wn;qyprocessing

wn;pp-wn;n-wn;p-wn;q

P dFtechwn;pp-wn;n-wn;p-wn; 8 wn 2W; pp-wn 2 P; n-wn

2 T; p-wn 2 S; q 2 I ð20ÞXq2I

yprocessingwn;pp-wn;n-wn;p-wn;q ¼ 1; 8 wn 2W; pp-wn 2 P; n-wn

2 T; p-wn 2 S ð21Þ

Eq. (17) is used to define the fixed capital cost ðAprocessingwn;pp-wn;n-wn;p-wnÞ,

which depends on the processing plant, processing technology andtype of waste. In this context, the unitary variable capital costðBcap

wn;pp-wn;n-wn;p-wnÞ is defined in Eq. (18). Also, the value of the

amount of waste in the processing plants ðFtechwn;pp-wn;n-wn;p-wnÞ is as-

signed through Eq. (19) and this amounts are limited for Eqs.(20) and (21). Besides, Eq. (22) is used to limit to one the numberof defined intervals, which are based on the economies of scale.

3.13. Profit for selling of products

Produced products can be sold in different markets, in this casethe markets are located around the cities; each product has a uni-tary price, which depends on the type of product and the citywhere it is sold. The price changes respect to the city because eachcity has product demands. The profit from the sold products (Csales)is the sum of the amount of products distributed to the different

markets ðPcitywn;pp-wn;c;n-wn;p-wnÞ multiplied by the corresponding uni-

tary cost ðCproductwn;n-wn;cÞ:

Csales ¼X

wn2W

Xpp-wn2P

Xn-wn2T

Xc2C

Xp-wn2S

Pcitywn;pp-wn;c;n-wn;p-wnCproduct

wn;n-wn;c ð22Þ

Table 4Generated wastes and sub-wastes for each city and efficiency for recollection (kg).

Moreliaa Celayaa Apat

MSW Total production 4.35 � 1008 2.00 � 1008 5.46Non-recyclables (70.3% MSW) 3.06 � 1008 1.41 � 1008 3.84

Plastics Total production (5.8% MSW) 2.52 � 1007 1.16 � 1007 3.16PP (Tonnes) 9.37 � 1006 4.32 � 1006 1.18PE (Tonnes) 6.30 � 1006 2.91 � 1006 7.91PET (Tonnes) 3.68 � 1005 1.70 � 1005 4.62PS (Tonnes) 1.33 � 1006 6.15 � 1005 1.67HDPE (Tonnes) 2.69 � 1006 1.24 � 1006 3.38

Metals Total production (3.1% MSW) 1.35 � 1007 6.21 � 1006 1.69Aluminum (Tonnes) 8.24 � 1005 3.80 � 1005 1.03

Glasses Total production (6.6% MSW) 2.87 � 1007 1.32 � 1007 3.60Clear glass (Tonnes) 5.21 � 1006 2.40 � 1006 6.54Green glass (Tonnes) 6.10 � 1006 2.81 � 1006 7.66Brown glass (Tonnes) 1.74 � 1007 8.01 � 1006 2.18

Paper Total production (14.2% MSW) 6.17 � 1007 2.85 � 1007 7.75Paper useful 2.58 � 1007 1.19 � 1007 3.23

a Mexican National Institute of Ecology (2012).b Environmental Protection Agency Office of Resource Conservation and Recovery (20

3.14. Economic objective function

The economic objective function is the maximization of the to-tal net annual profit (NetProfit), which takes into account the profitfor the selling of products (Csales) minus the total separation cost(CostSeptotal), the total capital cost (CostCaptotal), the total opera-tional cost (CostOpprocessing), the transportation cost

ðCostTransp

processing plantcity and CostTransp

cityprocessing plantÞ the no

separation cost (CostNSeptotal). This economic objective function isstated as follows:

Max NetProfit ¼ Csales � CostSeptotal � CostCaptotal

� CostOpprocessing

� CostTransp

processing plantcity

� CostTransp

cityprocessing plant

� CostNSeptotal ð23Þ

zingana Lazaroa Cardenas Leona Efficiency for recollectionb (%)

� 1007 9.72 � 1007 5.23 � 1008

� 1007 6.83 � 1007 3.68 � 1008 10

� 1006 5.64 � 1006 3.03 � 1007

� 1006 2.09 � 1006 1.13 � 1007 6.40� 1005 1.41 � 1006 7.59 � 1006 6.40� 1004 8.23 � 1004 4.43 � 1005 6.40� 1005 2.98 � 1005 1.61 � 1006 6.40� 1005 6.02 � 1005 3.24 � 1006 6.40

� 1006 3.01 � 1006 1.62 � 1007

� 1005 1.84 � 1005 9.91 � 1005 35.80

� 1006 6.42 � 1006 3.45 � 1007

� 1005 1.17 � 1006 6.27 � 1006 24.70� 1005 1.36 � 1006 7.34 � 1006 41.40� 1006 3.89 � 1006 2.09 � 1007 18.10

� 1006 1.38 � 1007 7.43 � 1007

� 1006 5.76 � 1006 3.10 � 1007 71.60

11).

Table 6Distance from cities to processing facilities and unit transportation costs.a

Cities Distance to processing facilities located in cities (km)

Morelia Celaya Apatzingan Lazaro Cardenas Leon

Morelia 1 147 192 144 207Celaya 147 1 326 447 135Apatzingan 192 326 1 186 393Lazaro Cardenas 144 447 186 1 514Leon 207 135 393 514 1Unit transportation cost ($US/kg km) 1.65 � 10�5A 4 � 10�5B

A For plastic, MSW, paper.B Metal and glass.a Mexican Ministry of Transportation and Communications (2012).

J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622 2615

3.15. Reused wastes

The reused waste represents environmental and social objectivefunction. This is because for a greater reuse of the produced MSW,the waste discharged in the landfills decreases. This way, the envi-ronmental problems associated to the land and water pollution de-crease. In the same way, the reuse of MSW represents a positiveimpact to society, this is because the generated jobs required forthe different stages involved in the reusing process as well as thelife quality improvement. Therefore, the percentage of the con-sumed waste (Consumewaste) is considered in this work as a mea-sure of the social impact, and this objective function is stated asfollows:

Table 7Estimated separation cost in Mexico.

Type of wastes Separationcost ($US/kg)

Reference and consideration

Plastic 0.235 Manual separation. Mexican NationalInstitute of Ecology (2012)Paper 0.235

Glass 0.235Aluminium 0.235Mixture of wastes 0.235

Fig. 3. Pareto curve for a system of processing

Max Consumewaste ¼ 100

�P

wn2W

Pc2C

Pp-wn2SFwn;c;p-wnP

wn2W

Pc2C

Pp-wn2Sa

sepwn;c;p-wnFtotal

c;p-wn

ð24Þ

3.16. Remarks for the proposed model

� The optimization formulation is a multi-objective mixed integerlinear programming problem, and this involves the simulta-neous maximization of the net profit and the percentage ofwaste consumption. Then, this multi-objective optimizationproblem can be reformulated using the constraint method todetermine the tradeoffs between these two objectives. Thisway, the problem is reformulated to maximize the total annualnet profit (Eq. (23)) subject to relationships (1)–(22), and thisproblem is solved for different levels of the total consumedwaste to yield a Pareto curve, where the tradeoffs betweenthe contradicting objectives are presented.� The proposed model considers simultaneously the supply chain

optimization, facility location, markets, cities, waste to reuse,technology selection and accounting for the economies of scalefor the optimal design of a distributed facility system based onthe use of municipal solid wastes.� The proposed model accounts simultaneously for two objec-

tives, the maximization of the net profit and the maximization

facilities based on municipal solid waste.

2616 J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622

of the percentage of wastes consumed. The maximization of thenet profit is considered as an economic objective function;whereas the maximization of the percentage of the wastes con-sumed is considered as an objective function that simulta-neously impacts the environmental and social aspects.� The model can be applied to cases in which the waste manage-

ment infrastructure is not developed and the waste generationis a serious problem.� It is necessary that the decision makers have available data for

composition and amount of generated wastes, costs of transpor-tation, separation and processing, as well as products that couldbe obtained from these wastes.� Accurate data for the processing technologies are needed to

ensure proper solutions.

Fig. 4. Percentage of consumed plas

Fig. 5. Percentage of consumed pap

� The model can be applied without problems in regions in which,the waste management is inadequate but there is interest toimplement a proper system for the waste management.

4. Case study

A case study is presented to show the applicability of the pro-posed methodology. This case study corresponds to the optimalmanagement of the municipal solid waste for the region locatedat the central-west part of Mexico respect to the profit as economicobjective and the percentage of utilized waste as environmentalobjective, where several cities and markets have been consideredas can be seen in Fig. 2. Five cities are considered as sources and

tic respect to the Pareto curve.

er respect to the Pareto curve.

J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622 2617

consumer locations for the considered system; in addition, fifteentechnologies to treat different wastes are taken into account.

The data for the considered conversion technologies (see Table 3)were taken from EPA (2011), Alireza and Gordon (2012), Plunkert(2006), Hur et al. (2003) and Young (2010). Although, each cityhas a given waste production rate, this production depends onthe amount of people living there and the economic activitiesdeveloped in such city; moreover, the composition (i.e. the typesof MSW) is different for each considered city. The amount of the dif-ferent wastes as well as the efficiency factors for recollection ofwastes are presented in Table 4, which were estimated from aver-age quantities reported by INE (2012) and EPA (2011). Data forthe unit production costs are presented in Table 5. The transporta-tion costs for products and wastes as well as the distances betweenthe considered places are shown in Table 6. Finally Table 7 showsthe separation costs for the different wastes and their assumptions.

Fig. 6. Percentage of consumed gla

Fig. 7. Percentage of consumed no recyclab

5. Results

The mathematical model formulation associated to the casestudy considered consists of 800 binary variables, 6426 continuousvariables and 5442 constraints. It was coded in the software GAMS(General Algebraic Modeling System, which is a high-level model-ing system for mathematical modeling and optimization), takingan average of 0.08 s of CPU time in a processor i7-3720QM at2.60 GHz with 16 GB of RAM for the solution of each point of thePareto curve using the solver CPLEX, which is a GAMS solver thatis able to efficiently solve large optimization problems (Brookeet al., 2013).

Pareto solutions that compensate the two objective functionsconsidered (net profit and percentage of reused MSW) arepresented. First, Fig. 3 shown the generated Pareto curve whenthe net annual profit is considered as the main objective, which

ss respect to the Pareto curve.

le wastes respect to the Pareto curve.

Fig. 8. Distribution for the costs of the supply chain based on solid waste.

Fig. 9. Solution of the distribution in the point A of Fig. 3.

2618 J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622

J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622 2619

is subject to the percentage of total available consumed waste; inthis case, the net annual profit decreases when the percentage ofwaste increases.

It is important to note that a Pareto front is a graphical repre-sentation formed by optimal points subject to different con-straints; normally this type of graphic is given in two dimensionsin which are two contradicting objectives. The points above thePareto front (see Fig. 3) are infeasible solutions; whereas the pointsbelow the Pareto front are sub-optimal solutions (for example,Point D of Fig. 3 where is possible to obtained a greater profit forthe same percentage of recycled waste until it touch the Paretofront). Therefore, from this Pareto front the decision maker can se-lect the solution that best satisfy specific requirements.

In the Pareto curve of Fig. 3 several regions that are obtained forthe selection of different configurations of the supply chain to sat-

Fig. 10. Solution of the distribut

isfy all the constraints are identified. Notice that the annual profitis always negative because the separation and no separation costsare high. It is also important to note that a consumption of the100% of the total available waste is not equal to the 100% of wastesreused, since each waste has a given percentage of separation andin most of cases this is not greater than 10%.

Figs. 4–7 show distribution of the wastes consumed in eachpoint of the Pareto curve, these figures allow understanding thebehavior of the Pareto curve, because for each point of the Paretocurve the number, type and distribution of the consumed wastesare different. In this context, metal is consumed in all the pointsof the Pareto curve, and it is totally used because this representsabout 0.5% of total available consumed waste, plastic is consumedin just a few points of the Pareto curve, because the operating andcapital costs associated to the conversion technologies to treat

ion in the point B of Fig. 3.

2620 J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622

plastics are very expensive. An important change in the behavior ofthe Pareto curve is observed in the point between 46% and 48% ofthe total available consumed waste, this behavior can be explainedas follows: Figs. 6 and 7 show that when the 46% of the total wasteis consumed, then glass is totally consumed but no-recyclablewastes are not consumed at all; however, when the 48% of the totalwastes are consumed, then glass is not consumed and around of30% of the no-recyclable wastes are consumed, also the percentageused of no recyclables increases in this point to 86% of total avail-able. Fig. 5 represents the amount of consumed paper, in this casepaper is consumed in almost all the points of the Pareto curve and

Fig. 11. Solution of the distribut

the percentage of recycled paper increases while the net profit in-creases, this suggests that the technologies to treat paper have avery positive effect in the net profit.

Fig. 8 shows the distribution of the costs through the supplychain for the case study analyzed. In this context, the separationcost is the highest cost above the point where around 36% of totalavailable waste is consumed, this is because the separation activityis the most important in the treatment of wastes; furthermore, thisactivity is the one that more jobs generates, this way, this can pro-mote tax credits or incentives from governments for the recyclingprocess due to the social benefit obtained. The disposal cost is the

ion in the point C of Fig. 3.

J.E. Santibañez-Aguilar et al. / Waste Management 33 (2013) 2607–2622 2621

highest cost from 0% to 34% of the total waste reused, this is be-cause the amount of trash without treatment is huge; this cost de-creases when the percentage of consumed waste increases, but thisdepletion is small because there is a high amount of wastes un-treated. The transportation cost is not representative in the totalcost because the cities are located in a small geographic regionwith only five considered cities as a result of the optimization ofthe supply chain. Since the separation and no separation costsare taken into account, the total cost is always greater than the rev-enue from sales; however, this is an area of opportunity to makethese processes more efficient.

In addition, three points were selected from Fig. 3 to show thedifferent wastes consumed in each point. First for point A, 32% oftotal consumed wastes is used, this represents the consumptionof two wastes: aluminum and paper, five cities and two processingfacilities (to treat aluminum and paper, respectively); both pro-cessing plants are located in Morelia, it is important to note thatthe city of Morelia is located in the center of the considered region.The products obtained from aluminum are distributed to the citiesof Morelia and Lazaro Cardenas; on the other hand, the productsobtained from paper are distributed to the considered cities exceptLeon, the selected technology in both cases was material recyclingand a schematic representation for this solution is presented inFig. 9.

Fig. 10 shows the results for point B, which represents almostthe 46% of the total consumed waste, at this point seven subtypesof wastes were selected (i.e., aluminum, paper, clear glass, greenglass, brown glass, polyethylene and polypropylene). The configu-ration for aluminum is the same than the one corresponding topoint A; for paper, the difference is that the products are distrib-uted to all considered cities. Two types of plastic are consideredin this case, polypropylene is distributed from all cities to Moreliato treat this plastic by thermal recycling to produce a fuel; on theother hand, polyethylene is transported to Leon to obtain olefinsthrough pyrolysis. Also, glass is delivered to two different plants,both located in Morelia; in the first one, clear and green glass areprocessed whereas in the second one, only brown glass is treated,in this case, all products are consumed in Morelia.

For Point C, plastic waste is obtained from two cities and thiswaste is processed by thermal recycling in a processing facility lo-cated in Leon. Also, no-recyclable wastes are processed in a pro-cessing plant located in Morelia through plasma arc gasificationto obtain energy which is used in Morelia; this configuration isshown in Fig. 11.

6. Conclusions

This paper proposes a mathematical model for the optimalplanning of a distributed system to treat MSW while consideringeconomic and environmental aspects. The problem has been math-ematically formulated as a multi-objective mixed integer linearprogramming problem. The model considers simultaneously thesupply chain optimization for the products obtained from the mu-nicipal solid waste. The application of the proposed methodologyhas been illustrated through a case study of a distributed systemfor treating MSW in a central-west region of Mexico. The resultsshow that it is possible to implement a distributed processing sys-tem to reuse MSW while maximizing the net profit of the supplychain. In addition, the obtained Pareto solutions can provide valu-able insights to decision makers in order to select the solution thatshows the best compromise among the considered objectives. Inthis regards, the model can be useful to consider the waste man-agement in regions where the waste management has not beendeveloped or there is not an established way to control wastes.Also, this work can be used as a starting point to add more objec-

tives for example social, safety, health, between others as well asthe scheduling of the waste management system. The model canalso be extended to consider the associated uncertainty.

Nomenclature

The nomenclature used in the mathematical model has beenseparated as parameters, continuous and binary variables.

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