Operational Research in Engineering Sciences: Theory and Applications
Vol. 5, Issue 3, 2022, pp. 194-209
ISSN: 2620-1607
eISSN: 2620-1747
DOI: https://doi.org/10.31181/oresta221122151h
* Corresponding author.
zahrahassanzadeh.s@gmail.com (Z. Hassanzadeh), irajarashrediffmail.com (I. Mahdavi),
ali_tajdin@yahoo.com (A. Tajdin), h.fazl@du.ac.ir (H. Fazlollahtabar)
DESIGNING A SUSTAINABLE LOGISTICS MODEL WITH A
HETEROGENEOUS COLLABORATION APPROACH
Zahra Hassanzadeh1, Iraj Mahdavi1, Ali Tajdin1, Hamed Fazlollahtabar 2*
1 Department of Industrial Engineering, Mazandaran University of Science and
Technology, Babol, Iran
2 Department of Industrial Engineering, School of Engineering, Damghan University,
Damghan, Iran
Received: 17 August 2022
Accepted: 14 November 2022
First online: 22 November 2022
Research paper
Abstract: This paper aims at designing a sustainable logistics model with a
heterogeneous collaboration approach. In this regard, we worked on a logistics system
by transmitting raw materials to a factory and then sending various products to
consumption centers. Accordingly, three logistics layers of supply, production, and
consumption were designed and the parameters of collaboration within and between
the logistics layers were evaluated. After that, as novelty of our paper, the interactions
of sustainability indicators with the logistics network and their effects on the
collaboration were analyzed through productivity. In this paper, we use two objectives
includes minimizing the supply chain costs and maximizing the productivity of the
collaboration parameter affecting the sustainability indicators at different levels.
Finally, the developed mathematical model is solved and validated in GAMS
optimization software to analyze the performance of the proposed approach using
epsilon constraint method.
Key words: sustainable logistic model, heterogeneous collaboration, epsilon constraint
method, multi-level model
1. Introduction
Today, rapid developments and changes have led organizations to research
logistics and supply chain to overcome their uncertain environment. Supply chain
management is a two-way interaction with new technologies such as outsourcing,
lean logistics, virtual logistics, etc. This volume of theory shows that different
organizations consider the major significance of supply chain and logistics
(Shafizadeh, 2004). In 2021, the global logistics industry that hit from COVID-19
Designing a Sustainable Logistics Model with a Heterogeneous Collaboration Approach
195
pandemic, recovered with market size of 8.43 trillion euros approximately. By 2027,
the logistics industry scale is forecasted to exceed 13.7 billion euros that is very huge
value (data gathered from statista1). Logistics is a big part of the supply chain, which
includes matters related to supply, transportation, storage, distribution, etc. Logistics
and supply chain variables can be used to assess the logistics status of an
organization (David et al., 2004). Figure 1 show the North American net revenue of
leading logistics companies in the United States in 2021.
Figure 1- the North American net revenue of leading logistics companies in the United
States in 2021
Today, with improvements in production processes, many industry executives
have realized that improving internal processes and flexibility in just the company's
capabilities is not enough to stay in the market. Rather, suppliers of parts and
materials must produce the required supplies with the best quality and lowest cost;
in addition, distributors of products must be closely related to the development
policies of the producer market (Kazimieras Zavadskas et al., 2020). With such an
attitude, logistics, supply chain, and supply chain management approaches have
emerged. Logistics is a planning orientation and a framework that seeks to create a
unique program for the production and flow of information through businesses. The
concept of Supply chain management is presented after this approach and seeks to
create the link and coordination between the processes of other organizations in this
1 https://www.statista.com/
Hassanzadeh et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 194-209
196
linking line (Zakeri et al., 2015). Logistics processes directly or indirectly affect
almost all areas of activity in the industry sector.
In this regard, coordination is a strategic response to the challenge posed by
supply chain partners. Coordination is the act of controlling the institutions'
affiliations by working together to achieve mutually defined goals. The benefits of
coordination include better use of resources, reduced operating costs, increased
profits, improved customer satisfaction, and increased productivity in developing
productions (KASSAMI et al., 2022). The concept of collaboration is both linked to
supply chain coordination and seen as a complementary aspect of a comprehensive
concept of coordination. Collaboration can be between members of a supply chain or
between multiple supply chains. It occurs when several organizations and companies
work together and engage in normal business relationships. It is the response to the
fact that organizations and companies cannot separately solve common problems to
achieve the expected performance indicators (Nu et al., 2004).
The concept of sustainability led to the formation of a new approach to designing
logistics networks. Evidently, there are sustainability dimensions that lead to the
formation of differences when comparing general logistics networks. It is the use of
various resources to meet the needs of the present generation industries without
jeopardizing the ability of the next generation. Sustainable supply chain management
comprises all dimensions of sustainability, including economic, environmental, and
social dimensions. These processes include the entire life cycle of an organization or
factory supply chain from the purchase of raw materials to the stage of product
design and development, storage and distribution, and finally, the delivery of the final
product. The important features of sustainable supply chain management are the
sustainability based on environment and social responsibility (Hassanpour and
Pamucar, 2019). Therefore, by taking the sustainability of the supply chain and
financial profitability into account, disadvantageous environmental effects and social
effects can be decreased.
The most important aspects of sustainability are the economic dimension, which
deals directly with cost and benefit parameters. In logistics networks, economic
decision-making concerning costs leads to a profitable optimal design. Another
important dimension of sustainability is the environmental dimension, which is
generally focused on clean air and land, as well as the reduction of any pollution or
encroachment on nature. The main difference between general logistics networks and
sustainable logistics networks is the focus on the pollution caused by the transport
fleet. Accordingly, in a sustainable logistics network, transmission routes and the
location of logistics facilities in nature are designed with an environmental approach.
Another dimension is the social factor which includes partner satisfaction,
coordination, and collaboration leading to greater sustainability.
On the other hand, in today's business world, influenced by the globalization of
markets, there is a basic need to understand customers’ changes to maintain the
sustainability of systems. As a result, companies are constantly looking for new
strategies to improve their logistics performance and ensure their competitiveness in
today's market (Allaoui, et al., 2020), especially in the distribution network of their
goods, which represents a key component in all supply chains (Williamser et al.,
2019). In this regard, logistics collaboration is deemed as one of the most effective
mechanisms for companies that want to increase their logistic efficiency and achieve
their goals of economic, environmental, and social sustainability (Vanovermeire, &
Designing a Sustainable Logistics Model with a Heterogeneous Collaboration Approach
197
Sörensen, 2017; Jouida et al., 2014). Collaboration is critical to the success of
sustainable logistics operations. Modern logistics systems are under increasing
pressure to achieve environmental goals, reduce rush hours, and make parking
spaces and vehicles accessible. For example, regulations on the timing, access, and
size of cars, areas, timing, and size of vehicles restrict cargo delivery. Similarly, tax
relief policies may encourage people to use vehicles consuming clean energy or apply
methods of distributing energy-efficient goods. Under these circumstances, it seems
that collaboration is a logical and performable strategy for many logistics systems to
create sustainability and achieve operational performance as well as successfully
achieve environmental goals (Soysal et al., 2018). Accordingly, the concepts of
collaboration and sustainability are very important in supply chain and logistics
networks.
Therefore, this study aims at designing a sustainable multilevel logistics model
with a heterogeneous participation approach based on the uncertainty approach. In
order words, in this study we use two objectives includes minimizing the supply
chain costs and maximizing the productivity of the collaboration parameter affecting
the sustainability indicators at different levels. In this study, coordinated sustainable
logistics is taken into account in terms of economic factors (time and cost), social
factors (general consumer satisfaction and 3PL system satisfaction), and
environmental factors (co2, vehicle depreciation, and less damage to natural
resources). Also, in this study, Collaboration is considered between members of the
supply chain and between layers of the supply chain. The parameters of collaboration
in this research include Communication, Bargaining Power, and Opportunism.
The research design consists of different sections including section 2, in which
previous studies will be reviewed and the research gap will be illustrated. Then, in
section 3, the research problem is stated. In section 4, the developed model will be
reviewed and in the next section, i.e., section 5, the operation of the model will be
examined and analyzed using a real example in Gamz software, and sensitivity
analysis will be performed. Finally, in section 6, the research results will be discussed.
2. Literature Review
Liotta et al. (2014) developed a new solution method based on optimization and
simulation for multilevel production and transportation problems with precise
dynamic distribution schemes under the influence of demand uncertainty. The
objective function of the optimization model, the costs of supply, production,
transportation, and emission of CO2 as well as collaboration in a multilevel network
are all taken into account. In this research, the computational experiments are based
on real samples. The results showed that the developed approach can be effectively
used for CO2 emission swap analysis, the effects of demand uncertainty, and Joint
distribution strategies on the economic and environmental function of supply chains.
Reverse logistics (RL) can be applied as a proper tool and technique to achieve
loyalty and satisfaction of customer and also decrease operating costs with
maximizing the used products recovery. Nowadays, industries face different
problems that is as a barrier to suitable implementation of RL, including lack of
financial constraints, capabilities, facilities, and market constraints.
Basiri et al. (2017) examined the subject of green channel coordination in a two-
stage supply chain (SC). Demand for the products is a function of the retail price, the
Hassanzadeh et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 194-209
198
green quality of the products, and the efforts of the retailer. Both the retail price and
the amount of effort for selling the green product are determined by the retailer,
while the green quality of the product is a variable of the manufacturer. Three
decision scenarios are modeled and compared: (1) a non-integrated scenario in
which each member decides independently based on their benefits, (2) an integrated
scenario in which there is one decision-maker in the system, and (3) a participatory
scenario in which the goal is to increase the channel's overall profit provided that
Pareto is improved for each member. Numerical studies showed that the proposed
collaboration model can increase SC profit almost close to the integrated model; it
also guarantees higher profits for both channel members than that of the non-
integrated decision-making scenario. Vargas et al. (2020) proposed a Freight Share
Laboratory Platform (FSLP) and introduced its embedded business model intending
to facilitate and encourage horizontal collaboration in transportation logistics. The
idea of FSLP is to create collaborative clusters of transport operators and related joint
operational plans, through specialized decision support algorithms and multi-fleet
optimization. In addition, a profit-sharing business model embedded in FSLP
algorithms guarantees that participants, mainly logistics service providers and
transport operators, can maintain their profit margins and fairly share the profits of
the partnership. A case study focusing on a major UK transport operator is presented
to evaluate key FSLP algorithms in a real-world context. The results show the
potential for significant financial and environmental benefits to industry and society.
Aloui et al. (2019) proposed a joint decision-making method for planning of the
sustainable supply chain. This structure improves the development of multilateral
partnerships across a network in order to improve the sustainability of the offered
products. The platform supports the new ICT system and creates an insightful
platform for infrastructure. The proposed decision support system simultaneously
offers collaboration and sustainability capabilities that are not available in many
supply chain planning systems. Konstantakopoulos et al. (2021) describe a
sustainable approach in which logistics companies collaborate in routing and
scheduling operations by sharing fleets and resources. To estimate the improvement
in the system, in terms of pollution and cost reduction, the state in which companies
operate independently is compared to the state of partnership. The data used in their
study are derived from the daily distribution cases encountered by third-party
logistics companies in Greece. These are examined daily by a meta-heuristic
algorithm, either separately to study how they work today, or jointly to determine
common benefits.
Given that sustainability in different aspects has become increasingly important in
today's supply chain, Emamian et al. (2021) presented an integrated model for
production routing in the sustainable closed-loop supply chain. A three-objective
mathematical model is also proposed for minimizing supply chain costs, maximizing
social responsibility, and ultimately minimizing environmental emissions. The data of
proposed method analyzed for different scales groups with considering the BCO
technique. Also, the results of this mentioned method eventually compared with the
experimental results of NSGA-II technique for different features for example quality,
variability, and distance as well as execution time to solution. Mancini et al. (2021)
investigated a centrally organized multi-period partnership automobile routing
problem in which telecommunications companies could exchange customers who
regularly need services. In addition, telecommunications companies may only be
willing to cooperate if a minimum market share can be guaranteed. To consider all
Designing a Sustainable Logistics Model with a Heterogeneous Collaboration Approach
199
these issues, the matter of common automobile routing was proposed while
considering the sustainability of time and service. An iterative local search algorithm
was used to solve the developed model. They showed that both methods reach near-
optimal solutions in very short computational times. Ding et al. (2018) develop a
model for examining the opportunity to outsource a pollutant reduction service to
overcome environmental constraints. The service supply chain consists of a coal-fired
power plant (end user) and a pollution reduction service provider that the former
outsources the services to the latter. They studied the profit improvement policy of
this service supply chain according to which, profit allocation is made through
outsourcing price negotiations between the two partners. The results showed that the
price of outsourcing green services is related to the government's incentive policy
that defines the shares of two partners. Finally, they hey examined the integration of
complex factors affecting supply chain cooperation, such as green services, profit-
sharing and etc.
The concept of emergency energy supply chain collaboration has become a
business necessity with various energy trading organizations so that its problems
could be solved in consensus. Jiang (2020), developed an intelligent model for
emergency power supply chain cooperation, which bridges the gap between
optimizing emergency supply chain collaboration with consensus decision-making
and reinforcement learning. The simulation results show that the proposed model
has a significantly less running time of 40%, reducing the minimum cost of energy
recovery by 7% and CO2 emissions by an average of 10.8%. The two-tier supply chain
model consists of two separate components with different purposes. Yaldim et al.
(2022), provided a model of a two-tier supply chain consisting of a supplier, a
retailer, and a product in a drug supply chain (P-SC). The main goal of their proposed
model is to maximize the profit of whole of the supply chain.
Akbari-Kasgari et al. (2022) designed a new supply chain based on resilience and
sustainable concepts in copper industry. Aloui et al. (2022) proposed the integrated
planning problem to design two-echelon green logistics model based on collaborative
and non-collaborative conditions. They assess the benefits of collaboration between
different layers in integrated transportation optimization. Anes et al. (2022)
developed a new model for evaluating risk value in logistics companies with
considering collaborative networks. Proposed model increases the sustainability of
collaborative model in the logistics network by reducing reputational risk. In another
research, Mishra et al. (2022) investigated a new structure to environmental
collaboration between logistic network layers to consider sustainability in
production. The sale takes place in a drug retailer and the demand is random and the
order periods are determined by the number of visits by the drug supplier. By
considering these visits, the drug retailer follows a periodic review inventory model.
For the retailer, the decision variable is the safety factor, which is determined by the
level of the announced order. The problem stated in this paper was optimized with
two different scenarios and two different models: the traditional SC model and the
two-tier supply chain model. Table 1 presents the studies conducted by research
indicators.
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200
Table 1. Literature Review
Author(s) Year
Logi-
stics
Mathematical
model Collabo-
ration
sustainability
Single-
purpose
Multi-
purpose
environ-
mental
eco-
nomic
social
1 Lyut et al. 2014
2 Basiri et al. 2017
3 Vargas et al. 2020
4 Alvi et al. 2019
5
Constantako
-poulos et al.
2021
6 Imams et al. 2021
7 Mansini et al. 2021
8 Ding et al. 2018
9 Jiang et al. 2020
10 Yildet al. 2022
11
Akbari-
Kasgari et al.
2022
12 Aloui et al. 2022
13 Anes et al. 2022
14 Mishra et al. 2022
15 Present study
According to the studies given in Table (1), it is recognized that collaboration and
sustainability in all dimensions have been less addressed simultaneously. Also, due to
the importance of collaboration in logistics systems and its impact on sustainability
in economic, social, and environmental dimensions, the previous research has not
addressed the role of intra-layer and inter-layer collaboration at all levels. Also, the
gap of studied research show that the collaboration parameter affecting the
sustainability indicators are not considered at different levels of supply chain.
Therefore, in the present study, it is dealt with designing a sustainable logistics
network with a heterogeneous participation approach in which the issue of intra-
layer and inter-layer collaboration at different levels of the supply chain and its
impact on supply chain sustainability have been considered under conditions of
uncertainty.
3. Statement of the Problem
Logistics is a planning orientation and framework that seeks to create a unique
program for the production and flow of information through a business. Supply chain
management is created after this framework and aims at achieving links and
coordination between the processes of other organizations in this link line. Logistics
processes directly or indirectly affect almost all areas of human activity. One of the
important subjects of logistics processes is coordination within the overall structure
of the supply chain. Coordination is the act of controlling the dependencies of an
institution by working together to achieve mutually defined goals. Supply chain
coordination can be supported through functions such as forecasting, production
management, maintenance management, distribution, and transportation
management, product design, and upstream and downstream interfaces. It may also
be related to simple activities. Collaboration can be between members of the supply
chain or between layers of the supply chain. Such collaboration occurs when several
organizations and companies work together and engage in normal business
Designing a Sustainable Logistics Model with a Heterogeneous Collaboration Approach
201
relationships. It is the answer when organizations and companies alone cannot find
solutions for common problems to achieve the expected performance indicators.
On the other hand, the concept of sustainability led to the formation of a new
paradigm in the design of logistics networks. Clearly, there are sustainability
dimensions that lead to the formation of differences compared to general logistics
networks. The most important dimension of sustainability is the economic
dimension, which deals directly with cost and benefit parameters. In logistics
networks, economic decision-making concerning costs leads to a profitable optimal
design. Another important dimension is the environmental one, which is generally
focused on clean air and land and the reduction of any pollution or encroachment on
nature. One of the differences between general logistics networks and sustainable
logistics networks is the special focus on the pollution of the transport fleet.
Additionally, the design of transport routes and location of logistics facilities in
nature is created with an environmental approach in a sustainable logistics network.
Another dimension is the sustainability of the social factor, including the satisfaction
of partners, coordination, and collaboration that leads to greater sustainability. The
proposed model in the present study deals with the design of a sustainable logistics
network with a heterogeneous collaboration approach. In other words, due to the
necessity to reduce environmental hazards such as greenhouse gas emissions, use of
natural resources, energy consumption, costs such as transportation, and delay in
operations, and also to increase access to facilities, the concept of designing a
sustainable multilevel logistics network with a heterogeneous collaboration
approach is investigated. Accordingly, the logistics system is designed based on
sending raw materials to the factory and then sending different products to
consumption centers. The main purpose of this study is to investigate the effect of the
collaboration parameter on sustainability indicators for nodes within a layer and
between different layers of the supply chain. The proposed model has two objectives,
the first target function includes minimizing the supply chain costs and the second
one is to maximize the productivity of the collaboration parameter affecting the
sustainability indicators at different levels. In this study, coordinated sustainable
logistics is taken into account in terms of economic factors (time and cost), social
factors (general consumer satisfaction and 3PL system satisfaction), and
environmental factors (co2, vehicle depreciation, and less damage to natural
resources). Also, the parameters of collaboration in this research include
Communication, Bargaining Power, and Opportunism.
Communication indicator ensures that tasks are augmented and transferred from
one point to the other without delay. In addition, the Bargaining Power index refers
to the pressure that suppliers can put on different firms by decreasing the availability
of their products, increasing their prices, or lowering their quality. The Opportunism
index also is defined as behavior that is self-interest seeking with guile. It is
manifested in behaviors such as stealing, cheating, dishonesty, and withholding
information. Essentially, these concepts lead institutions to cooperate (Doodi et al.,
2016).
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4. The Developed Mathematical Model
In this section, the developed model will be described.
4.1. Indices:
Index for nods 1, ...,i I 1, ...,j J , 1, ...,i I
Index for layer 1, ...,k K , 1, ...,k K
Index for collaboration parameter 1, ...,w W
Index for sustainability indices 1, ...,s S
4.2. Variables:
1
:
0
ws
X ikjk
If collaboration parameter w is established about sustainability index
s with node i in layer k and node j in layer k’
1
:
0
ws
Y ii k
If node i with node i’ in layer k has a collaboration parameter w
about sustainability index s
4.3. Parameters:
ws
B
Budget available to establish the collaboration parameter W affecting
the sustainability index S
ws
ii k
p
The efficiency of collaboration parameter w affecting the sustainability
index s between nodes i and i’ in layer k
ws
ikjk
p
The efficiency of collaboration parameter w affecting the sustainability
index s from node i in layer k to node j in layer k’
w s
ik
A
The degree of collaboration w affecting the sustainability index s for
node i
in layer k
ws
ii k
CA
Collaboration capacity of collaboration parameter w affecting the
sustainability
index s between nodes i and i’ in layer k
ws
ikjk
CA
Collaboration capacity of collaboration parameter w affecting the
sustainability
index s from node i in layer k to node j in layer k’
ws
ii k
C
Cost of creating the collaboration parameter w affecting the
sustainability
index s between nodes i and i’ in layer k
ws
ikjk
C
Cost of creating the collaboration parameter w affecting the
sustainability
index s from node i in layer k to node j in layer k’
4.4. Mathematical Model:
1
1 1 1 1 1 1
min . .
I K J K I I K
i k j k i i k
ws wsws ws
z C CX Yikjk ii kikjk ii k
(1)
2
1 1 1 1 1 1
max . .
I K J K I I K
i k j k i i k
ws wsws ws
z P PX Yikjk ii kikjk ii k
(2)
Designing a Sustainable Logistics Model with a Heterogeneous Collaboration Approach
203
S.t.
1 , ' 1
ws
k K k kX ikjks wi j i
(3)
1
ws
ky ii ks wi i i
(4)
,. .
1
ws ws
ws wsws
B w sX YC Cikjk ii ki j i ii kk K kk k i iikjk
(5)
,. '
1 ' 1
ws ws
ws CA w sX ikjkAiki j ikjkk K k k i k K j k k
(6)
,.
'
ws wsws
w sY CAii kAiki iii k ik ki
(7)
1 , ,.
'' 1
ws
ws
i k K wX Y
ikjksjk k i ii k
(8)
0
'
ws
X
ikjk
kkjiwsk ',,,,,1 (9)
, 0,1
ws ws
X Yikjk ii k
(10)
4.5. Model Description:
This research consists of a two-objective mathematical model. The first target
function represents the minimization of the total costs created by the collaboration
parameter effective on the sustainability index between and within the different
mentioned layers. The second target function represents the maximization of
productivity resulting from the collaboration parameter affecting the sustainability
index. Equation (3) shows that between each of the two different layers and
according to the collaboration and sustainability, at least one connection between
different nodes of the mentioned layers should be selected. Equation (4) shows that
between two nodes in a particular layer, at least one connection between different
nodes should be selected concerning collaboration and sustainability. Equation (5) is
the total costs incurred by the collaboration parameter affecting the sustainability
index from one node to another in each layer with the costs incurred by the
collaboration parameter affecting the sustainability index between different layers
that should be less than the total budget available for establishing a collaboration
parameter. Equations (6) and (7) indicate that the amount of collaboration between
and within different layers should not exceed the collaboration capacity of the
collaboration parameter. Equation (8) shows that for each layer and its
corresponding node, there is exactly one collaboration parameter for each
sustainability index. Equation (9) ensures that communication between the two
layers is done sequentially. Equation (10) shows the type of decision variables.
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5. Solution methodology
In this paper, a bi-objective sustainable logistic model presented based on a
heterogonous collaboration approach. The first objective function represents the
minimization of the total costs created by the collaboration parameter effective on
the sustainability index between and within the different layers. The second objective
function represents the maximization of productivity resulting from the collaboration
parameter affecting the sustainability index. To reformulating bi-objective
mathematical model to a single one, we used epsilon-constraint method. Finally, the
developed model of the present study was encoded using GAMZ 24.1.2 software and
the program was written by a computer with 2.3 GHz processor specifications, core i7
with 4GB RAM memory.
6. Numerical Study
In this section we present a numerical example to illustrate and analyze the
performance of proposed bi-objective model based on problem goals. As mentioned, the
proposed model was solved by GAMZ 24.1.2 software. After solving the proposed
model, with regarding to 3237 repetitions, the model reached its optimal value and
the time to achieve the optimal answer took 3.00 seconds. Some of the used data and
parameters are applied in the model using real data that are shown in Table (2).
Other data are generated to handle the optimization model. Also, the validity of the
model was performed by analyzing the sensitivity of some effective parameters in the
model and the efficiency of the model was evaluated. In the developed model,
sustainability with index s = 1,2,3 includes three economic, social, and environmental
indices. Also, the parameter of collaboration with index w = 1,2,3 includes
Communication, Bargaining Power, and Opportunism. Table (2) shows the available
budget for establishing the collaboration parameter W affecting the sustainability
index S (
ws
B ).
Table 2. Budget available for the establishment of collaboration (
ws
B )
ws
B
s
1 2 3
w
1 787 579 647
2 523 577 574
3 663 566 753
After solving the developed model using the values defined for the problem
parameters, the model achieves the optimal answer and the values of the variables
ws
X ikjk
(if the collaboration parameter w is established in relation to the
sustainability index S with node i in layer k with node j in layer k’) and
ws
Y ii k
(if node i
with node i’ in layer k has parameter collaboration w in relation to the sustainability
index S) which are equal to 1 and shown in Tables (3) and (4).
Designing a Sustainable Logistics Model with a Heterogeneous Collaboration Approach
205
Table 3. Operation of the developed model and the optimal value of the objective
function
The results of Table (3) show that the optimal value of the weighted integrated
objective function of the developed model after running in GAMS software with 1265
repetitions, the value of 269,000 has been obtained. The results also show that the
running time of the model to achieve the optimal answer was 3 seconds. The results
related to the optimal values of the developed model variables including and
ws
X ikjk
are shown in Table (4). This table shows the establishment of collaboration
parameters with respect to sustainability indices in the interlayer mode and between
different layers. For example, the value obtained
13
211Y
shows that between nodes 2
and 1 in the first layer, the collaboration parameter 1 (Communication parameter)
affects the sustainability index 3 (environmental index) that reduces system costs
and increases the efficiency resulted from the collaboration parameter affecting the
sustainability index. Also, the value obtained
21
3223X
shows that between node 3 from
the second layer and node 2 from the third layer, the collaboration parameter 2
(Bargaining Power parameter) affects the sustainability index 1 (economic index)
that reduces the cost of the entire system and increases the efficiency of the
cooperation.
Table 4. Optimal values of the variables in the developed model
VARIABLE
Y(1,1,3,1,1) 1
Y(1,2,1,3,3) 2
Y(1,2,2,3,2) 3
Y(1,2,3,1,2) 4
Y(1,3,1,2,1) 5
Y(1,3,1,3,2) 6
Y(1,3,2,1,1) 7
Y(2,1,3,2,1) 8
Y(2,2,1,3,1) 9
Y(2,2,2,1,2) 10
Y(2,2,3,1,2) 11
Y(2,3,1,3,2) 12
Y(2,3,2,3,1) 13
Y(3,3,1,2,1) 14
Y(3,3,1,2,2) 15
Y(3,3,2,1,1) 16
Y(3,3,2,1,2) 17
Y(3,3,3,1,2) 18
Y(3,3,3,2,1) 19
X(1,1,3,1,1,2) 20
X(1,2,2,2,2,3) 21
Total solver
iterations
Extended solver steps
Gams
Obj Time
3237 268 291.000 3.00
Hassanzadeh et al./Oper. Res. Eng. Sci. Theor. Appl. 5(3)2022 194-209
206
X(1,2,3,2,1,3) 22
X(1,3,1,1,1,2) 23
X(1,3,1,2,2,3) 24
X(1,3,2,1,3,2) 25
X(2,1,3,1,3,2) 26
X(2,2,1,1,1,2) 27
X(2,2,2,2,2,3) 28
X(2,2,3,2,1,3) 29
X(2,3,1,2,3,3) 30
X(2,3,2,1,2,2) 31
X(3,3,1,1,3,2) 32
X(3,3,1,2,1,3) 33
X(3,3,2,1,1,2) 34
X(3,3,2,2,1,3) 35
X(3,3,3,1,3,2) 36
X(3,3,3,2,3,3) 37
Also, the results of the proposed model based on the optimal values of the
variables and are shown in Fig. 2 and 3. In these figures, collaboration
parameters and sustainability indicators are shown with symbols w and s,
respectively. Also, layers 1 to 3 including nodes within layers 1 to 3 are considered
for each layer. With respect to the Fig. 2 and 3, the relations of collaboration
parameters and sustainability indices in different layers and nodes are shown with
arrows and they are assigned to each other based on the optimal values obtained for
the mentioned variables.
Figure 2. Optimal values of the variable in the developed model
Designing a Sustainable Logistics Model with a Heterogeneous Collaboration Approach
207
Figure 3. Optimal values of the variable in the developed model
7. Conclusion
In this paper, a model is developed to evaluate the sustainability interaction with
inter-layer and intra-layer collaboration of a two-tier logistics network. First, indices
of economic, social, and environmental sustainability along with the parameters of
collaboration, Communication, Bargaining Power, and Opportunism on different
layers of logistics were examined. According to the capacity of collaboration and the
cost required to establish collaboration, the problem was modeled and solved with
the objectives of minimizing costs and maximizing productivity resulting from
collaboration and improving sustainability indices. One of the advantages of this
sustainable logistics model with a heterogeneous collaboration approach is that the
decision maker or policy maker with the capabilities of this model can identify the
effective parameters of collaboration on sustainability in each layer of the logistics
network and also can improve the efficiency of collaboration in the logistics system
by focusing on the parameters with the greatest impact on the degree of
sustainability. Evaluation of the proposed method based on fuzzy robust uncertainty
can be considered as a future research suggestion. Also using multi-product and multi
time with a tri-level programming structure can be considered as another area of
future study.
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© 2022 by the authors. Submitted for possible open access publication under the
terms and conditions of the Creative Commons Attribution (CC BY)
license (http://creativecommons.org/licenses/by/4.0/).
https://doi.org/10.1016/j.ejor.2020.12.064
https://doi.org/10.1016/j.jclepro.2022.130619
http://dx.doi.org/10.1080/13675567.2018.1513467
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http://dx.doi.org/10.1016/j.ijpe.2014.11.012
https://DOI:%2010.31181/oresta2003034z
https://DOI:%2010.31181/oresta2003034z
DESIGNING A SUSTAINABLE LOGISTICS MODEL WITH A HETEROGENEOUS COLLABORATION APPROACH
Zahra Hassanzadeh1, Iraj Mahdavi1, Ali Tajdin1, Hamed Fazlollahtabar 2*
1. Introduction
2. Literature Review
3. Statement of the Problem
4. The Developed Mathematical Model
4.1. Indices:
4.2. Variables:
4.3. Parameters:
4.4. Mathematical Model:
4.5. Model Description:
5. Solution methodology
6. Numerical Study
7. Conclusion
References