designing an efficient optimization system to maximize the ......• these operational processes...

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

I F O R SInternational Federation of Operational Research Societies

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


• 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


• 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


Introduction

• It is expected that annual waste generation rate will reach 2.2 billion tons by

2025, accordingly.

https://www.statista.com


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).


Economical aspects:

Introduction


• 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.


Social aspects:

Introduction


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.


Introduction

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

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


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


Assumptions


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


• 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


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


• 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


• 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


• 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


• 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


• 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


• Total cost of the waste management network should not exceed the available budget.

• Domain of the variables is defined.

Augmented ε-constraint method


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


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


Aghaei et al. (2011)

Implementation of the proposed methodology


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


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


• 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


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


• 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


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


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


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


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


Thank you very much for your attention!

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Scientific Visits and Conferences Medan – North Sumatra, Indonesia, March 21-29, 2020

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