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Designing an Efficient Optimization System to Maximize the Total Value of Reverse Logistics
in Waste Management
Department of Industrial Engineering, Yazd University, Yazd, Iran
Gerhard-Wilhelm Weber
Faculty of Engineering Management, Chair of Marketing and Economic Engineering, Poznan University of Technology, Poland; Institute of Applied Mathematics, METU, Ankara, Turkey
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Alireza Goli
Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran
Erfan Babaee Tirkolaee
Scientific Visits and Conferences Medan – North Sumatra, Indonesia, March 21-29, 2020 (Virtual)
• Introduction
• Literature review
• Problem description/Mathematical model
• Augmented ε-constraint method
• Illustrative example
• Model validation
• Sensitivity analysis
• References
Outline
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• Uncontrolled urban expansion and the massive increase in urban
populations have led to a vast amount of consumption and different types of
waste generation over the past years.
Introduction
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• In 2012, various cities in the world generated 1.3 billion tons of solid waste,
equivalent to 1.2 kg per person per day.
https://www.statista.com
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Introduction
• It is expected that annual waste generation rate will reach 2.2 billion tons by
2025, accordingly.
https://www.statista.com
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Introduction
• This amount of waste generation definitely leads to an increase in the necessary
funds for collection, transportation, processing and disposal operations, which
contains a huge amount of fixed/variable costs (Tirkolaee et al., 2020).
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Economical aspects:
Introduction
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• These operational processes must be done within shortest possible time
to prevent from spread of potential contamination and infections.
Environmental and health aspects:
Introduction
• The main social aspects include citizens’ satisfaction and creating
job opportunities at recovery/recycling facilities.
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Social aspects:
Introduction
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Questions:
1. How can we investigate
the economical,
environmental and social
aspects of the problem?
•Identifying the main
parameters, variables and
assumptions.
•Formulate the problem
using OR concepts and
techniques.
2. How can we optimize
the amount of required
budget and the amount of
contamination?
•Developing a bi-objective
mathematical model
considering all the defined
assumptions.
•Implementing an efficient
solution technique to deal
with the bi-objectiveness of
the problem; i.e., Augmented
ε-constraint method.
3. How can we
evaluate the effects of
demand changes?
•Performing sensitivity
analyses.
•Interpreting the behavior of
the objectives against the
demand changes.
Introduction
A bi-objective model is proposed to
design an efficient waste management
system for maximizing the Total Value
of Reverse Logistics and maximizing
the total job opportunity.
Environmental pollutions are studied as
penalty costs in the budget constraint.
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Introduction
Literature Review
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Reference
Problem Condition Objective/Criterion
Case
study
Solution technique
Loca
tio
n
Allo
cati
on
Inve
nto
ry
Det
erm
inis
tic
Un
cert
ain
Eco
no
mic
Soci
al
Envi
ron
me
nta
l
Lahdelma et al. (2002) Stochastic multi-criteria acceptability analysis
with ordinal criteria
Erkut et al. (2008) Lexicographic minimax approach
Khadivi and Ghomi
(2012) ANP and DEA
Ghiani et al. (2014) Heuristic approaches and MILP
Wang and Yang (2014) LINGO software
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Literature Review
Reference
Problem Condition Objective/Criterion
Case
study
Solution technique
Loca
tio
n
Allo
cati
on
Inve
nto
ry
Det
erm
inis
tic
Un
cert
ain
Eco
no
mic
Soci
al
Envi
ron
me
nta
l
Chauhan and Singh
(2016) Fuzzy MCDM technique
Yadav et al. (2018) Interval optimization algorithm
Muneeb et al. (2018) Fuzzy GP and AMPL software
Rathore and Sarmah
(2019) MILP, ArcGIS and CPLEX solver
Gambella et al.
(2019) MILP and CPLEX solver
Current study Robust MILP and CPLEX solver
Consider the schematic
view of the given area
in Isfahan.
The aim is to design
the waste
management system
based on the defined
conditions in the
problem.
Problem Description
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Assumptions
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The main assumptions of the problem are as follows:
• Metropolitan area is divided into different regions.
• A planning horizon is regarded.
• Each region contains predefined demand nodes such that the demand value varies in
each period.
• Different household waste of paper, glass, plastic and metal are considered.
• Collection facilities can be permanent or temporary.
• Processing/disposal facilities are permanent and are capable of being established in the
suburb of the urban network graph.
• Ratio of recycled and recovered waste are predefined for processing/disposal facilities.
Assumptions
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• Ratio of transported waste from collection facilities to each processing/disposal facility
is predefined.
• Traditional and modern technology is considered for these facilities with different
capacities and establishment costs.
• Each collection or processing/disposal facility has different operational costs,
establishment costs, capacity and transportation costs.
• Number of permanent and temporary facilities to be established in each region is
limited.
• Regarding the pollution emission of each collection facility, a penalty cost is considered
which is proportional to its distance from the demand node.
• Penalty costs are imposed on the system for non-collected waste.
Objectives
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The main objectives of the problem are represented as follows:
Maximizing total amount of income from the reverse logistics
in waste management
Maximizing total job opportunity
Economically and Socially Sustainable Waste Management
System
Mathematical Model
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• 1st objective function is to maximize the total value of the reverse logistics including the income provided from the recycled and recovered items by processing/disposal facilities.
• 2nd objective function indicating the total job opportunity provided by establishing different collection and processing/disposal facilities.
Mathematical Model
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• Demand nodes must be allocated to one of the collection facilities to receive service in each period.
• Collection facilities should be allocated to at least one processing/disposal facility in each period.
• The number of permanent and temporary facilities to be established in each region should not exceed their maximum allowable number, respectively.
Mathematical Model
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• A demand node is covered by the collection facility when it has already been established in the region.
• A collection facility is allocated to a processing/disposal facility if it has already been established in the region.
• No waste will be collected until the demand node is allocated to its corresponding collection facility.
Mathematical Model
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• No waste is processed/disposed until the collection facility is allocated to its corresponding processing/disposal facility.
• Capacity constraints of facilities per each type of waste in each region.
• Total transported waste from the collection facility to processing/disposal facility does not exceed its capacity.
Mathematical Model
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• Maximum amounts of collected waste in each region is equal to the amount of generated waste at any node of that region.
• Amounts of not-collected waste in each region.
• Amounts of transported waste to each processing/disposal facility from any collection facility.
Mathematical Model
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• Total cost of the waste management network should not exceed the available budget.
• Domain of the variables is defined.
Augmented ε-constraint method
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Augmented ε-constraint technique was proposed by Mavrotas (2009) to generate
efficient Pareto solutions in multi-objective mathematical programming:
• Lexicographic approach is used to determine the range of objective functions’
values (as its benefit compared to the traditional ε-constraint technique).
• Then, the augmented ε-constraint always generates efficient Pareto fronts and
prevents from inefficient ones.
Augmented ε-constraint Method
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Formulation of the augmented ε-constraint:
Mavrotas and Florios (2013)
p Sub-objective function
Direction of i-th objective (i.e., -1 for minimization type, and +1 for maximization type)
Changing parameter to obtain efficient solutions
Slack variable
ε Very small value between 0.001 and 0.000001
Augmented ε-constraint method
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Aghaei et al. (2011)
Implementation of the proposed methodology
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The values of the parameters are
provided by the municipality’s experts.
To validate the proposed robust bi-
objective MILP model, CPLEX solver of
GAMS 24.1 is employed.
Model Validation
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The execution steps of the augmented ε-constraint method to provide
efficient Pareto solutions:
In the next step, the subsidiary objective function (2nd objective function)
is divided into 8 equal intervals (grid points):
2nd objective value 1st objective value Single-objective minimization
187 53697.29 1st objective
253 46394.46 2nd objective
Lexicographic payoff table
Grid points
7 6 5 4 3 2 1 0
253 243.5714 234.1429 224.7143 215.2857 205.8571 196.4286 187
Model Validation
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• We can generate all the efficient Pareto solutions using different grid points:
Obj 2 Obj 1 Pareto solution
188 53154.54 1
198 51772.52196 2
206 50112.69491 3
217 48642.60442 4
225 47905.28469 5
235 46896.92635 6
249 46382.93604 7
253 46394.46 8
• Now, decision-maker can choose his/her most preferred solution among the 8 efficient Pareto solutions.
It is represented by a green arrow.
40000
42000
44000
46000
48000
50000
52000
54000
180 190 200 210 220 230 240 250 260
1st o
bje
ctiv
e
2nd objective
Pareto front
Sensitivity analysis
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Objective functions Change interval of 𝑫𝒆𝒎𝒊𝒋𝒓𝒕
-20% -10% 0% 10% 20%
1st objective 45288.6752 47602.1391 48643 49771.1128 59842.4966
2nd objective 203 215 217 221 243
• We analyze different conditions in the problem to simulate and study the instability of the real world. To this end, a sensitivity analysis of the demand parameter is done.
• It is based on the best Pareto solution, and its corresponding ε-value.
Sensitivity analysis
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• This figure can be investigated in order to be employed as effective managerial tool.
• Obviously, the behaviors of the objectives are corresponding to each other under
changes of the parameters.
180
190
200
210
220
230
240
250
-20% -10% 0% 10% 20%
0
10000
20000
30000
40000
50000
60000
70000
2N
D O
BJE
CTI
VE
CHANGE INTERVAL
1ST
OB
JEC
TIV
E
Sensitivity analysis First objective Second objective
Conclusion
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Establishing an optimal waste collection system leads to an economically,
environmentally and socially sustainable waste management.
Economic, environmental and social aspects were studied through the 1st
objective, pollution penalty costs in the budget constraint and 2nd objective,
respectively.
There is a trade-off between the total value of the reverse logistics and the job
opportunities in the case study problem.
Conclusion
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Augmented ε-constraint technique could efficiently generate Pareto solutions
and represent the trade-off between the economical and environmental
aspects of the problem.
Demand parameter plays an important role to calculate the value of the system
and job opportunities.
The 1st and 2nd objectives increase by an increase of the demand parameter;
however, the 2nd objective is more sensitive.
Future Research Directions
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For future studies, the following directions are suggested based on some limitations of our research:
o Heuristic and metaheuristic methods may be implemented to solve the problem in larger sizes efficiently, such as those proposed by Tirkolaee et al. (2018), Palanci et al. (2017).
o Uncertainty techniques such as fuzzy logic (Babee Tirkolaee et al., 2020), robust optimization (Tirkolaee et al., 2020) and stochastic optimal control (Temoçin and Weber, 2014) may be compared to the current robust optimization approach.
o Other objective functions including collection reliability maximization or citizens’ satisfaction maximization can be studied, too.
o Ahmed, W., and Sarkar, B. (2018). Impact of carbon emissions in a sustainable supply chain management for a second generation biofuel. Journal of Cleaner Production, 186, 807-820.
o Babaee Tirkolaee, E., Goli, A., Pahlevan, M., and Malekalipour Kordestanizadeh, R. (2019). A robust bi-objective multi-trip periodic capacitated arc routing problem for urban waste collection using a multi-objective invasive weed optimization. Waste Management and Research. DOI: https://doi.org/10.1177/0734242X19865340.
o Babaee Tirkolaee, E., Mahdavi, I., Seyyed Esfahani, M.M., and Weber, G.-W. (2020). A hybrid augmented ant colony optimization for the multi-trip capacitated arc routing problem under fuzzy demands for urban solid waste management. Waste Management and Research. DOI: https://doi.org/10.1177/0734242X19865782.
o Chauhan, A., and Singh, A. (2016). A hybrid multi-criteria decision making method approach for selecting a sustainable location of healthcare waste disposal facility. Journal of Cleaner Production, 139, 1001-1010.
o Cheikhrouhou, N., Sarkar, B., Ganguly, B., Malik, A. I., Batista, R., and Lee, Y.H. (2018). Optimization of sample size and order size in an inventory model with quality inspection and return of defective items. Annals of Operations Research, 271(2), 445-467.
o Dong, A.V., Azzaro-Pantel, C., and Boix, M. (2019). A multi-period optimisation approach for deployment and optimal design of an aerospace CFRP waste management supply chain. Waste Management, 95, 201-216.
o Eiselt, H.A., and Marianov, V. (2015). Location modeling for municipal solid waste facilities. Computers and Operations Research, 62, 305-315.
o Erkut, E., Karagiannidis, A., Perkoulidis, G., and Tjandra, S.A. (2008). A multicriteria facility location model for municipal solid waste management in North Greece. European Journal of Operational Research, 187(3), 1402-1421.
References
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o Gambella, C., Maggioni, F., and Vigo, D. (2019). A stochastic programming model for a tactical solid waste management problem. European Journal of Operational Research, 273(2), 684-694.
o Ghiani, G., Manni, A., Manni, E., and Toraldo, M. (2014). The impact of an efficient collection sites location on the zoning phase in municipal solid waste management. Waste Management, 34(11), 1949-1956.
o Gupta, N., Yadav, K.K., and Kumar, V. (2015). A review on current status of municipal solid waste management in India. Journal of Environmental Sciences, 37, 206-217.
o Habib, M.S., Sarkar, B., Tayyab, M., Saleem, M.W., Hussain, A., Ullah, M., ... and Iqbal, M.W. (2019). Large-scale disaster waste management under uncertain environment. Journal of cleaner production, 212, 200-222.
o Khadivi, M.R., and Ghomi, S.F. (2012). Solid waste facilities location using of analytical network process and data envelopment analysis approaches. Waste Management, 32(6), 1258-1265.
o Kim, M.S., and Sarkar, B. (2017). Multi-stage cleaner production process with quality improvement and lead time dependent ordering cost. Journal of Cleaner Production, 144, 572-590.
o Palancia, O., Olgun, M.O., Ergun, S., Gok, S.Z.A., and Weber, G.W. (2017). Cooperative Grey Game: Grey Solutions and an Optimization Algorithm. International Journal of Supply and Operations Management, 4(3), 202-214.
o Temoçin, B.Z., and Weber, G.W. (2014). Optimal control of stochastic hybrid system with jumps: a numerical approximation. Journal of Computational and Applied Mathematics, 259, 443-451.
o Tirkolaee, E. B., Mahdavi, I., and Esfahani, M.M.S. (2018). A robust periodic capacitated arc routing problem for urban waste collection considering drivers and crew’s working time. Waste Management, 76, 138-146.
o Tirkolaee, E. B., Mahdavi, I., Esfahani, M. M. S., & Weber, G. W. (2020). A robust green location-allocation-inventory problem to design an urban waste management system under uncertainty. Waste Management, 102, 340-350.
References
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Thank you very much for your attention!
gerhard.weber@put.poznan.pl
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e.babaee@ustmb.ac.ir
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a.goli@stu.yazd.ac.ir
Scientific Visits and Conferences Medan – North Sumatra, Indonesia, March 21-29, 2020
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