815950
research-article2018
WMR0010.1177/0734242X18815950Waste Management & ResearchFarahbakhsh and Forghani
Original Article
Sustainable location and route
planning with GIS for waste sorting
centers, case study: Kerman, Iran
Amin Farahbakhsh1
Waste Management & Research
2019, Vol. 37(3) 287­–300
© The Author(s) 2018
Article reuse guidelines:
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https://doi.org/10.1177/0734242X18815950
DOI: 10.1177/0734242X18815950
journals.sagepub.com/home/wmr
and Mohammad Ali Forghani2
Abstract
One of the important issues in the world is the significant growth of waste production, including waste that is not biodegradable
in nature. According to the Kerman Municipality, 440 tonnes of municipal waste is collected daily in Kerman consisting of five
major parts of paper, plastic, metal, glass, and wet waste. The major problems of municipal solid waste disposal are soil erosion,
air pollution, and greenhouse gas emissions. The most important factors related to recycling are waste sorting and the relevant
environmental conditions. This study aims to create a sustainable approach by locating the optimal sites to reduce environmental
pollution, decrease costs, and improve the service system to the society. Optimal locations for establishing the collecting and sorting
centers in the city are specified by the use of geographic information system software, based on criteria consisting of population
density, road network, distance to health centers, distance to disposal center, waste sorting culture, land space, and land cost, which
were weighted by an analytical hierarchy process. It was noteworthy that the criterion “waste sorting culture”, which has a foundation
in human sciences and sociology, has been considered by experts in this study to be of the highest importance among other criteria
at locating sorting centers. Subsequently, using a symmetric capacitated vehicle routing problem, the number and capacity of each
vehicle are determined to serve the specified locations according to the economic, social, and environmental constraints.
Keywords
Location, waste sorting centers, sustainable approach, geographical information system, analytical hierarchy process, vehicle
routing problem
Received 24th May 2018, accepted 18th October 2018 by Editor in Chief Arne Ragossnig
Introduction
Today one of the most critical issues in the world is the excessive production of garbage, both urban and industrial, which has
grown significantly in recent decades. The emergence of economic problems, harmful pollution, and environmental degradation are the significant consequences of this issue. Meanwhile, a
considerable share of waste produced, including plastics, glass,
paper, and metals is not decomposable by nature or requires a
long time to decompose; however, it is recyclable. A critical
point in waste management in the form of collection, transfer,
processing, recycling, and landfill site of the waste produced is
the need to avoid its adverse effects on the environment and
community health. According to the Municipality of Kerman,
per capita production of waste per person per day is 670 grams.
The city of Kerman, as the capital of Kerman Province, is one of
the major cities in the southeast of Iran, with a population of
3,164,718 (according to the population census in 2016). It is the
ninth most populous province of the country. Kerman is the largest province in Iran and as the center of the southeast of the
country is the industrial, cultural, political, agricultural, and academic–scientific authority among the provinces of the southeast
of the country. Kerman Province has more than 660 nationally
registered heritage sites and six registered works on the United
Nations Educational, Scientific and Cultural Organization World
Heritage Site including the Bam Citadel, and in this respect
ranks first among all provinces of Iran. Kerman Province also
achieved the country’s highest rank for non-oil exports of pistachios and dates for several consecutive years. The province is
between 53 degrees 26 minutes to 59 degrees 29 minutes east
longitude and 25 degrees 55 minutes to 32 degrees north latitude. The city of Kerman which is 1,778 m above sea level is the
second highest city in Iran. In Kerman, about 440 tonnes of
waste is produced per day, 30% of which is made up of recyclable materials (according to figures from Kerman Municipality).
The main problems of municipal solid waste (MSW) disposal
can be soil erosion, air pollution, increased greenhouse gas
1Department
of Industrial Engineering, Faculty of Engineering,
Shahid Bahonar University of Kerman, Kerman, Iran
2Department of Industrial Engineering, Faculty of Engineering,
Shahid Bahonar University of Kerman, Kerman, Iran
Corresponding author:
Amin Farahbakhsh, Department of Industrial Engineering, Faculty of
Engineering, Shahid Bahonar University of Kerman, Kerman, Iran.
Email: A.farahbakhsh@eng.uk.ac.ir
288
emissions, and surface water pollution by leachate of organic
waste. Despite increasing environmental awareness, it is felt
necessary to define legal, economic, and social incentives to
support recycling and improve this procedure (Cruz-Rivera and
Ertel, 2009). Among waste topics such as waste reduction, recycling, waste management as a source of energy generation, etc.,
the use of industrial methods of waste collecting and sorting as
well as the establishment of industrial recovery units play an
essential role in economic development. Since one of the significant problems of state recycling management is to collect recyclable materials and to support sorting activities, it is an excellent
way to use the product lifecycle and sustainable reuse to achieve
urban waste management (Toso and Alem, 2014). Among the
factors related to selected collections, the most cost-effective
one is waste management in sorting centers (de Oliveira
Simonetto and Borenstein, 2005). The sorting method at the
source is considered as one of the best and least expensive waste
sorting methods due to the reduction of biological contamination, the cost of disinfection, and second washing. Another
important aspect of this issue is the social aspect that can refer
to the ways of culture-making in waste sorting at the source and
co-operative schemes (Toso and Alem, 2014). The allocation of
optimal points for the establishment of these waste sorting centers requires a comprehensive number of scientific and practical
studies that can cover all the subsectors related to the economic, social, and environmental aspects. Providing such optimal locations is one of the primary goals of the current study.
Transportation in economic systems, including services, production, and distribution has a special importance and it
accounts for the significant part of gross national product of
countries. Improvement in transportation systems means eliminating unnecessary distances and optimizing routes traveled in
each system. Considering the significance of the transportation
system and its particular impact on cost and pollution, the present study, after finding the optimal location of waste sorting
centers, seeks to identify the optimal route for servicing these
centers.
Literature review
Lin et al. (1996), using fuzzy logic and the Simple Additive
Weighting method in the geographic information system (GIS)
environment, presented a progressive weighting method for
locating landfill sites that specifies the final acceptance values
for the integration of different information layers. Shrivastava
and Nathawat (2003) in their study, using GIS and remote sensing, selected five different sites for landfill around Ranchi
City. Baldacci et al. (2004) solved the capacitated vehicle routing problem (CVRP) with accurate algorithms. A study by
Yesilnakar and Cetin (2005) selected the optimal location for
hazardous wastes landfill. Şener et al. (2006) first determined
the proper landfill locations by GIS, then weighed and prioritized them using the multi-criteria decision analysis (MCDA)
method. Pessoa et al. (2008) presented a strong branch and
Waste Management & Research 37(3)
bound algorithm for the asymmetric capacitated vehicle routing
problem. Chang et al. (2008), in a research using the analytical
hierarchy process (AHP) method and GIS software, located an
appropriate landfill site in Ramallah, Palestine, with the least
adverse environmental impacts. A paper by Karadimas and
Loumos (2008), proposed an innovative model for the estimation of MSW generation and collection. This model was part of
an extended solid waste management system and used a spatial
geodatabase, integrated with a GIS environment. Wang et al.
(2009), weighted and prioritized the locations specified using
the AHP method, after selecting the proposed landfill site.
Tralhão et al. (2010) presented a mixed integer multi-objective
programming model for locating and determining the capacity
of urban sorted municipal waste collection containers.
Kanchanabhan et al. (2011) proposed an innovative model for
the collection and transportation of MSW using a spatial geodatabase, integrated with a (GIS) environment. Research by
Shanmugasundaram et al. (2012) proposed an effective planning of a healthcare waste management system including components such as the treatment plant siting and an optimized
routing system for collection and transportation of waste, and
demonstrated the use of an inexpensive GIS modeling tool for
healthcare waste management in Lao People’s Democratic
Republic. Alumur et al. (2012) proposed a mathematical model
for multi-cycle reverse logistics network problems that take
into account various features such as facility capacity expansions, sample capacities, different operating costs, and an
objective function based on profit. Erdoğan and Miller-Hooks
(2012) have introduced the vehicle routing problem (VRP) considering gas emissions as an issue of the green vehicle routing
problem (GVRP). Alavi et al. (2013) used a combination of GIS
and AHP to determine the best sites for disposal of MSW in
Mahshahr County, Iran. An article by Yildirim (2012) described
a raster GIS-based landfill site selection (LSS) method. This
method utilized a raster-based spatial database in which the factors affect the landfill site selection. Furthermore, this GISbased LSS method was applied for the evaluation of two landfill
sites in Trabzon Province in Turkey, for which the traditional
evaluation method for site selection was used. A paper by Bing
et al. (2014) aimed for redesigning the collection routes and
compared the collection options of plastic waste using eco-efficiency as a performance indicator. Eco-efficiency concerns the
trade-off between environmental impacts, social issues, and
costs. The collection problem was modeled as a VRP and a
Tabu search heuristic was used to improve the routes. Boskovic
and Jovicic (2015) developed a methodology aimed at determining the optimal number of waste bins as well as optimizing
the location of collection points based on a GIS. Khan and
Samadder (2016) presented a suitable solid waste collection bin
allocation method at appropriate places using ArcGIS with uniform distance and easily accessible location so that the collection vehicle routes become minimum for the city of Dhanbad,
India. Bosompem et al. (2016) used a MCDA incorporated
into a GIS to determine potential waste transfer station sites.
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Farahbakhsh and Forghani
Torabi-Kaveh et al. (2016) developed an MCDA process, which
combined GIS analysis with a fuzzy analytical hierarchy process, to determine suitable sites for landfill construction in
Iranshahr County, Iran. Nguyen-Trong et al. (2017) proposed a
model for optimizing MSW collection. First, the optimized plan
was developed in a static context, and then it was integrated
into a dynamic context using multi-agent based modeling and
simulation. A case study related to Hagiang City, Vietnam, was
presented to show the efficiency of the proposed model. Erfani
et al. (2017) proposed an integrated model to optimize two
functional elements of MSW management (storage and collection systems) in the Ahmadabad neighborhood located in the
City of Mashhad – Iran. The integrated model was performed
by modeling and solving the location allocation problem and
CVRP through GIS. Harijani et al. (2017) proposed a systematic approach to build an integrated recycling and disposal network for MSW by explicitly considering the sustainability with
an objective to maximize the total profit with a budget constraint. A multi-period mixed integer linear programming model
was proposed to design the network optimally as well as to optimally operate the network. They also extended the developed
the social life cycle assessment methodology to model the
social impacts of the network. San Martin et al. (2017) developed an MCDA tool to help decision-makers (private or public
waste management bodies and companies) to implement food
waste valorization strategies. This tool implements the AHP
method and GIS to evaluate the main parameters involved in
the process. Zhao and Ke (2017) developed an optimization
model minimizing total cost and risk to simultaneously decide:
(1) where to locate the collection centers; (2) how to manage
the inventory level for each center; (3) how many vehicles need
to be purchased; (4) how to route explosive wastes from generation nodes to collection centers; and (5) how to route explosive
wastes from collection centers to recycling centers. A solution
procedure on the basis of the Technique for Order of Preference
by Similarity to Ideal Solution method was proposed to solve
the optimization model within reasonable computation time.
Lella et al. (2017) discussed possible collection methods for
solid waste management in India, and presented methods for
optimal collection and transportation of waste using GIS techniques through network analysis. In addition, they proposed
possible transfer station locations based on various design factors such as open land availability, ease of access from all the
composting units/dustbin locations, transfer means by tractor
trailers, and sanitation and environmental requirements. In an
article by Dao-Tuan et al. (2017), GIS analysis, integer linear
programming and mixed integer linear programming for
optimizing vehicle routing and carbon dioxide (CO2) emission
of MSW collection was proposed. A study by Chaerul and
Malananda (2018) aimed to minimize the total distance of a
waste transportation system by applying a transshipment model.
The problem related to the waste transportation was solved
using the VRP method. The shortest distance of route was determined by using meta-heuristic methods, namely Tabu search 2
phases. A study by Paz et al. (2018) planned a network for
municipal management of construction and demolition waste in
Brazil with the assistance of a GIS, using the city of Recife as a
case study.
By scrutinizing the articles listed in the literature review, it
became clear that the main focus of most articles is on landfill
sites and they have researched more about this topic; and very
few articles have worked on waste bins. But in this article, the
main focus is on waste sorting centers that have been dealt with
less so far. Most articles have followed the issue of location, but
most of them have sought discrete location, and there are few
articles on continuous location which can be done using GIS software and require layers that are detailed and updated. This article
uses this method to find the location of the waste sorting centers.
Routing problems are presented in the articles exclusively or in
combination using both GIS and modeling methods. In this
research, the related optimal routes have been identified using a
VRP model. Each of the intended articles that used GIS for
location, have considered some layers to get to the answer.
Among them, most layers are identical; in this research we have
tried to select layers that are very effective and relevant among
others and also a layer called ‘waste sorting culture’ in this
paper has not been used before. Another main topic in the literature review is the issue of sustainable approach. Almost all articles have benefited from the economic aspect, and many have
paid attention to the environmental aspect in addition to the
economic one. But a limited number of researches have investigated the social aspects. This paper has tried to use all three
aspects in both location and routing, in order to get to a more
accurate and realistic analysis.
Materials and methods
Locating or choosing the appropriate location for establishing a
facility should be such that it provides the specific requirements of
that use, which in fact are the locating criteria. Locating criteria
are the means for determining the capability of the intended site
based on the capabilities of each location according to the type of
activity which is considered. MCDA for choosing the best alternative with the least error and making the right decision provides
appropriate techniques that in addition to analyzing with a rational
basis includes unconscious factors (Ghodsi Pour, 2008). Among
these methods, AHP presented by Thomas L. Saaty (1987) and its
process is based on pair comparisons which takes into account
both the quantitative and qualitative criteria. Making a hierarchical tree is one of the most comprehensive systems designed for
this kind of decision-making (Saaty, 1987). A GIS is a method for
collecting, storing, controlling, integrating, processing, analyzing,
and displaying data, whose reference is the Earth’s surface (Dunne
and Halliday, 1987). The presence of both graphical information
(spatial), including visual information and maps that determine
the position of phenomena on the Earth’s surface, and non-graphical (descriptive) information that delivers the characteristics of
an event or phenomenon, turn GIS into a comprehensive database
290
that has actually created a simple model of reality (Azimi Hosseini
et al., 2011). The major areas in application of combined GIS–
MCDA methods are environmental management/planning, transportation, urban and regional planning, waste management,
hydrology and water resources, agriculture, and forestry; this
wide range of applications in different areas is one of the most
significant features of these methods (Malczewski, 2006).
Malczewski and Rinner (2016) presented the most effective
method in GIS history for the development of GIS–MCDA: casting the maps together to evaluate the suitability of the lands in
question so that each evaluation criterion is presented in the form
of a clear and conspicuous map, and the darker the map of each
criterion, the higher the value of that criterion is, and eventually to
find the most suitable place, all the maps are cast together. The
VRP is one of the most well-known optimization problems, with
the aim of designing the optimal set of routes for serving customers, such that it is compatible with the existing constraints. The
VRP goal is, in the most common case, minimizing the overall
cost of the trip based on maximum working hours and maximum
vehicle capacity limitations (Irnich et al., 2014). The VRP was
first introduced by Dantzig and Ramser (1959). Green intelligent
transportation systems are designed and implemented as part of a
gradual shift in industry focus on production and distribution networks. Sustainability challenges encourage an effective change
from a merely profit-oriented economy to a responsible and environmentally-friendly business (Sbihi and Eglese, 2010).
Implementing green logistics ideas in the VRPs and other types of
problems leads to GVRPs. These problems relate to finding routes
that are consistent with the increasing environmental concerns
and which are financially justifiable.
Locating criteria
Seven criteria have been selected based on the views of five
groups of experts from an environmental organization, waste
management organization, municipality, economics and finance
organization, and sociology, and their integration with related
articles. Choosing a location continuously should be such that it
is possible to construct a facility in terms of feasibility, type of
use, and area. Choosing the land size criterion can take these factors into account in locating (Samad et al., 2012). One of the most
critical issues in urban planning is the population density factor
which can be used in facility location in two desirable and undesirable ways (Mohamad et al., 2015). One of the most important
factors that is almost the basis of all related studies is the economic factor concerning the land cost (Gbanie et al., 2013). The
amount of communication between people and selected locations
determines the critical criterion of the road network for location
(Şen et al., 2011). The distance to landfill site criterion follows a
reduction in transportation and consequently a reduction in the
pollution and costs (Nas et al., 2010). The effects of contamination from waste disposal centers on health facilities such as hospitals can be controlled by desirable distances (Mitropoulos
et al., 2006). The criterion “waste sorting culture” is one of the
Waste Management & Research 37(3)
Figure 1. Hierarchical structure of the study.
Figure 2. Final results for criteria weights.
innovations of this study which is the primary and essential basis
relevant to the social aspect of the present research. Figure 1
shows the overall hierarchical structure of the criteria and the
resulting criteria weights obtained by AHP with an inconsistency
rate of 0.04.
Figure 2 shows that the highest degree of importance, with a
significant difference, is related to the criterion “waste sorting
culture.” According to experts from sociology and psychology, a
comprehensive and measured questionnaire consisting of two
dimensions of assessment for perceptual and stimulus motives
was designed so that it could be used as accurately as possible to
estimate this criterion in society. Perceptual motives were
designed based on people’s thinking and logic of their environment and social conditions, but the stimulus motives identify the
external factors motivating individuals on subjects of society, and
determine whether their direction is promoting or hindering.
After weighing the questionnaire questions by AHP and determining the sample size, using the Cochran’s sample size formula,
the layers related to the GIS software were defined according to
four urban areas.
Criteria descriptive classification
table and map
To create the desired layer according to the opinion of the relevant experts and concerning the type and need of the intended use
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Farahbakhsh and Forghani
Table 1. Criteria descriptive classification.
Criteria
Weight
Sub-criteria
Very suitable
Suitable
Almost suitable
Unsuitable
Very unsuitable
0.33
0.26
0.2
0.14
0.07
Physical
Environmental
Economic
Social
Road
network (m)
Land space Distance
Distance Land cost
Waste
(m-2)
to health
to landfill (IRRa m-2) *106 sorting
centers (km) (km)
culture
Population
density
(person block)
–
0–50
50–100
100–200
> 200
> 350
250–350
150–250
< 150
–
> 1,450
251–1,450
75–250
0–74
–
–
–
>2
1–2
0–1
0-14
14–18
18–22
22–26
> 26
< 20
20–30
30–40
> 40
–
Region2
Region1
Region3
Region4
–
Note: aIranian Rial (IRR) is the currency of Iran.
Figure 3. Map of distance to hospitals.
for each criterion, a classification table for each criterion was
established. The population density layer according to the available data from demographic blocks is looking for points that have
a relatively high density to increase the productivity of the facility. The land cost layer is based on the Kerman property value
calendar published by the Provincial Tax Administration which
seeks to reduce the price for the selected land. In the application
of the road network criterion, easy access for people to these
centers and the coverage of all communication paths is noted. In
the distance to landfill site and distance to health centers layers,
the reduction and increase of the corresponding distance to
reduce transportation costs and the biological contamination are
considered, respectively. Experts addressed the land space layer
according to the site area that can be constructed (Table 1).
The maps that were generated in accordance with the classification table in the GIS software are shown in Figures 3–9.
Except for the layer of “waste sorting culture” which had not
been created before due to its newness, the rest of the layers
related to the GIS software were provided by the Kerman Crisis
Management Organization.
The final optimal map resulted from casting the maps in
accordance with layers based on the weights obtained by the
AHP method is shown in Figure 10. Also 17 optimal points
resulted from the final map for establishing sorting centers and
four recycling plants in the city are shown in Figure 11.
Problem modeling
The intended problem is a symmetric capacitated vehicle routing
problem, that is a closed loop and multiproduct problem.
Combining social approaches, such as service time and environmental approaches, namely, reducing emissions of polluting
gases, as well as economic approaches, namely reducing costs,
are important issues in the proposed model. In this model, it is
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Waste Management & Research 37(3)
Figure 4. Map of distance to landfill.
Figure 5. Map of land space.
assumed that the vehicles belonging to each plant are similar and
have the same fixed cost, but the type and fixed cost of assigning
machines to each plant is different from each other. Also, the
number and capacity of machines, plants, and sorting centers are
limited and determined. The calculation of the distance between
each of these network components is Euclidean. The amount of
CO2 emissions is determined by traversing each distance unit by
each of the different vehicles which depends on the loading
amount on the vehicle in question. Further, the customers’
demand (production) is constant and defined, and we encounter a
single period model with all its parameters definite and constant.
The sets used in this model include a set of all network nodes (N)
consisting of two sets of origin nodes (four recycling factories)
(Np) and destination nodes (17 sorting centers) (Ns) and indices
Farahbakhsh and Forghani
293
Figure 6. Map of distance to roads.
Figure 7. Map of population density.
that include the counting indices of each network node both
source and destination (i & j), the counter index for the machines
of each plant (k), and the counter index of the factories (l). The
parameters and variables in the model are as follows:
Fc(l ) : The fixed cost of assigning each machine related to the
factory l.
Cv ( l ) : The capacity of each machine related to the factory l.
m ( l ) : The number of machines available for the factory l.
Ef ( l ) : The amount of CO2 emission by each machine related to
factory l when it is fully loaded (Hill et al., 2013).
Ee ( l ) : The amount of CO2 emission by each machine related to
factory l when it is empty (Hill et al., 2013).
V ( l ) : Average speed of each machine related to factory l.
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Waste Management & Research 37(3)
Figure 8. Map of land cost.
Figure 9. Map of waste sorting culture.
T : Maximum service time.
E : Maximum CO2 emission.
d ij : Euclidean distance from node i to node j.
pil : The node i production amount from the type of waste associated with the plant l.
Z : The objective function.
X l : 1, if the path from node i to node j is assigned by machine
ijk
k of plant l
0; otherwise
Ql : The load of the car k related to the factory l in the path
ijk
from node i to node j.
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Farahbakhsh and Forghani
Figure 10. Final optimal map.
Figure 11. Map of optimal points.
The final model in the form of an objective function and 13 constraints, and related explanations are given below.
Objective function
MIN Z =
∑ ∑ ∑( ) ∑ d .X + ∑ ∑ ∑( ) ∑ Fc(l ).X
ij
i∈N j∈N i ≠ j k ≤ m l
l ∈N p
l
ijk
i∈N p j∈N k ≤ m l l∈N p
l
ijk
The objective function seeks to minimize the two main parts that
are total transport cost between nodes and the fixed costs of vehicle allocation. Reduction in transportation, in addition to reducing related costs, decreases environmental pollution and improves
the service quality which are the three main topics in the VRPs.
This issue shows the significance of this section in the objective
function clearly. In the second part, the objective function seeks
to reduce the allocation of costs by reducing the number of
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Waste Management & Research 37(3)
machine allocations. Due to the high fixed costs associated with
this section, cost optimization will have a high impact on the final
solution with respect to the existing constraints.
Constraints
∑( ) ∑ X
k ≤m l
≤ m(l )
∀ l∈N p
∑ ∑
∑ ∑
j∈ N i ≠ j k ≤ m ( l )
∑
l
X ijk
=
j∈ N i ≠ j
l
X ijk
≤1
∀ i∈Ns , l∈N p
(2)
X ljik ≤ 1
∀ i∈Ns , l∈N p
(3)
∀ i ∈ N , k ≤ m ( l ) , l ∈ N p (4)
X ljik
j∈ N i ≠ j
∑ ∑( ) Q − ∑ ∑( ) Q
l
ijk
j∈ N k ≤ m l
l
jik
= p (i, l )
∀ i∈Ns , l∈N p
j∈ N k ≤ m l
l
l
Qijk
≤ CV (l ). X ijk
∀ i ∈ N , j ∈ N, i ≠ j ,
k ≤ m (l ) , l ∈ N p
∑ ∑ ∑( ) Q
i
ijk
= 0 ∀l ∈ N p
(5)
(6)
(7)
i∈N p j∈N k ≤ m l
∑X
j∈
l
ijk
≤1
∀ i ∈ N , k ≤ m (l ) , l ∈ N p
(8)
Ns
∑ ∑( ) ∑ X
i∈N k ≤ m l
l
iik
=0
(9)
l ∈N p
∑ ∑ ∑( ) ∑ X
l
ijk
=0
i∈N p i ≠ l j∈N k ≤ m l l∈N p
∑ ∑ ∑( ) ∑
i∈N j∈N i ≠ j k ≤ m l
∑∑
l∈N p
( Ef (l ) − Ee(l )). 
 l

dij .  Qijk
≤E
l 
 CV (l ) + Ee(l ). X ijk 


l
dij . X ijk
i∈N j∈N i ≠ j
V (l )
≤T
∀ l ∈ N p , k ≤ m (l )
X l ∈ {0,1} Ql ≥ 0
ijk
ijk
Ef(l)
Ee(l)
V(l)(km h)
Fc(l)
Cv(l)(kg)
m(l)
l
1.00792
0.82015
0.60127
1.00792
0.67194
0.63789
0.51219
0.67194
10
30
40
20
80
60
50
70
20000
10000
5000
15000
7
4
4
6
1
2
3
4
(1)
j∈ N
j∈ N i ≠ j k ≤ m ( l )
∑
l
ljk
Table 2. Model parameters values.
(10)
(11)
(12)
plant. Constraint (2) forces that the number of paths entered into
each node related to each plant is not higher than one. Constraint
(3) forces that the number of paths left from each node for each
factory is not higher than one. Constraint (4) ensures that the
number of paths entered into each node corresponding to each
machine for each plant is equal to the number of paths that exit
from that node. Constraint (5) shows that the difference in the
amount of load for the machine related to each plant in the case
of entry and exit for each node is equal to the production rate of
that node from the material belonging to the same plant (the corresponding machine must collect all production of each node); it
also prevents forming a loop. Constraint (6) forces that the loading rate of each machine in each path is not higher than that
machine capacity. Constraint (7) ensures that the loading rate of
machines at the beginning of the route, namely moving from the
plants, must be zero (that is, all the load accumulated is offloaded
in the plant). Constraint (8) ensures that each machine can be
assigned a maximum of one load. Constraint (9) prevents forming a path between a node and itself. Constraint (10) ensures that
when a machine starts its movement from each node, that node
must be a plant, and the machine must belong to the same node or
plant. Constraint (11) forces that the CO2 emission in all paths is
not higher than the defined value “E.” Constraint (12) forces that
the service time to each node will not be greater than the defined
value “T.” Constraint (13) represents the type of problem variables. According to the problem conditions, the model’s parameters are determined in accordance with Table 2.
The maximum service time for each customer is four hours
(T = 4), and the maximum amount of CO2 emissions is 500 kg for
the entire set of routes and machines (E = 500). In addition,
according to the number of centers and the daily production of
each region, the production capacity of each center (Pil) is determined. The proposed model was solved with the data related to
the case study presented before, in GAMS software version 24.7,
by the AlphaECP solver in a personal computer with core i5 2.67
GHz central processing unit and 4 GB random access memory.
The computation time was about two hours and the results are
given below.
Results and discussion
(13)
Constraint (1) ensures that the number of machines assigned to
each plant is not higher than the number of machines in that
The number of machines assigned, the optimal route, and the
loading amount for each machine are specified in Figures
12–15.
Considering the importance of parameters, the maximum service time and the maximum CO2 emission rate, with fixing the
297
Farahbakhsh and Forghani
Figure 12. Optimal number, route, and capacity for node 1 vehicles.
Figure 13. Optimal number, route, and capacity for node 2 vehicles.
value T = 4 and changing the range of E, from 450 to 650, the
objective function values are obtained, which indicate that if the
CO2 emission decreases from 450 kilograms in all routes with
this type of machine, there is no longer a feasible solution for this
model. Besides, since more increase in the amount results in
more solution space by the constraint, we get to a better optimal
solution compared to the previous case. This issue continues to
the point (E = 600), and since then, with the increase in the maximum amount of emissions, the objective function value is not
changed, which indicates that this is an ineffective constraint
(Figure 16).
Then, by keeping the value E = 500 fixed and changing the T
range from 3.5 to 5.5, the objective function value is obtained,
which indicates that if the maximum service time is reduced from
3.5 hours per car, then there is no feasible solution for the model.
Since more increase in the amount results in more solution space
by the constraint, a better optimal solution is obtained compared
to the previous state. This issue continues to the point (T = 5), and
then the objective function value does not change with the
increase in the maximum service time, which indicates that this is
an ineffective constraint (Figure 17).
The proposed model can be multi-objective and with socialrelated constraints, in which it is necessary to solve it with heuristic and meta-heuristic algorithms. Since the methods used in
this research are well-known and valid ones, the resulting answers
are reasonable and close to a realistic scenario.
298
Waste Management & Research 37(3)
Figure 14. Optimal number, route, and capacity for node 3 vehicles.
Figure 15. Optimal number, route, and capacity for node 4 vehicles.
Conclusion
The purpose of this study was to find the optimal locations for the
construction of waste collecting and sorting centers in Kerman to
prevent the loss of existing economic resources in the program
context and to avoid the environmental pollution from the burial
and dumping waste. For this purpose, seven useful criteria were
considered based on which, the optimal locations with geographical latitude and longitude were defined which had an equilibrium based on the priority of criteria. In this study, for the first
time in continuous location context by GIS, a criterion was presented that was developed based on social attitudes. The careful
299
Farahbakhsh and Forghani
Figure 16. Chart of objective function changes according to
change in E (T = 4).
function, changing the maximum emission rate and service time,
the desired numbers should be selected among the specified
intervals to get to a useful and practical solution. Future scientific
and practical studies with the proper use of social criteria can
have a more realistic perception of the community and certainly
will bring forth more useful and accurate results to use.
Government agencies such as municipalities, municipal waste
management, environmental organizations, and privately-owned
recycling companies, can make valuable use of the findings in
this study by establishing sorting centers in optimal points
resulted from this research and managing the transportation
related to these points according to optimal routs given by the
model. Also, using the various constraints used in the routing
model, we can create more realistic conditions for such research.
Declaration of conflicting interests
The authors declared no potential conflicts of interest with respect to
the research, authorship, and/or publication of this article.
Funding
Figure 17. Chart of objective function changes according to
change in T (E = 500).
consideration of such criteria and their multiplicity can have new
and beneficial effects on determining optimal locations. The criterion “waste sorting culture,” which has a foundation in human
sciences and sociology and has never been used and expressed in
the former studies, was noted to be of the highest importance
among other criteria by experts in this context. The notable effect
of the layer “waste sorting culture” can be perceived in the number of points assigned to each of the four urban areas. The reason
for this is apparent because people are the main effective factor in
the production of garbage, and if people of a community stand at
a reasonable cultural and intellectual level in respect to waste
sorting and recycling, it is indeed possible to invest more in this
regard; further, its effective economic, social, and environmental
impacts become clearer. After determining the optimal points for
these locations, it is necessary to serve these locations effectively
and efficiently from different aspects including minimizing costs
and distance traveled, reasonable service time, reducing environmental pollution, and full coverage of centers. For this purpose,
by using a vehicle routing model, optimal routes for service were
identified. According to a sensitivity analysis, if an organization
actually wants to determine the maximum level of pollution for
these data, then the choice of these limits should be very careful
because if it is less than 450 kg, it will have to bear surplus costs;
on the other hand, if it exceeds the 600 kg limit, it has no control
over the amount of pollution. Also, if it wants to specify a maximum service time for these data less than 3.5 hours, it will have
to bear changing the vehicles’ types or changing the nodes’ coverage; on the other hand, if it exceeds the value of five hours,
there is no satisfactory service. Therefore, by creating a reasonable three-way equilibrium between the changes in the objective
The authors received no financial support for the research, authorship, and/or publication of this article.
ORCID iD
Amin Farahbakhsh
https://orcid.org/0000-0002-9576-0496
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