Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
Modelling and Simulation of Multi Echelon Dynamic
Sustainable Supply Chain
Dr. Shahul Hamid Khan
Dynamic supply chain model is a technique of constructing & running a model
of an abstract system in order to study its behaviour without disrupting the
environment of the real system. Simulation are generally employed when the
complexity of the system being modelled is beyond what static supply chain
model or other techniques can represents. A supply chain becomes
sustainable when the effect of carbon is included in supply chain network. The
main Objective of this paper is to model and simulate a multi echelon dynamic
sustainable multi echelon supply chain network model. The design figures out
determining the appropriate number of facilities such as plants and warehouse,
the location and size of each facility and allocating space for the products in
each facility. A new Genetic algorithm is proposed and the model is evaluated
with the new proposed GA.
Key words: Dynamic Supply chain, Genetic algorithms, Simulations
1.0 Introduction
A supply chain is said to be comprised of two main business processes: Material
management and Physical distribution. Material management which is also said as
inbound logistics is concerned with the acquisition and storage of raw materials,
parts and suppliers. To elaborate material management supports the complete cycle
of material flow from the purchase & internal control of production materials to the
planning & control of work in process, to the ware housing, shipping & distribution of
finished products. On the other hand physical distribution which is also referred as
outbound logistics activities related to providing customer service. These activities
include order receipt & processing, inventory deployment, storage & handling,
outbound transportation, consolidation, pricing, promotional support, return product
handling and life cycle support. Issues related to supply chain is mainly divided in to
three areas. Strategic level deals with the decision that has long lasting effect on the
firm. This includes decisions regarding product design, supplier selection, strategic
partnering, and outsourcing & off shoring, information technology and decision
support system. Tactical level is updated anywhere between once every quarter and
once every year. Example: purchasing & production decision, inventory policies,
transportation strategies. Operational level is day to day decisions such as
scheduling, routing, truck loading, production, transport, demand fulfilment. Initially
an appropriate network design is needed to control efficiently all the elements in all
stages, to be flexible against the changing situation, to provide coordination along
the supply chain, and to be successful in supply chain network design is very
important and attempts to increase the most efficient supply chain for the company’s
operating environment. The supply chain network which is commonly defined as the
integrated system in encompassing raw material, vendors, manufacturing &
assembly plants and distribution centre to ensure solution for effectively meeting
Dr. Shahul Hamid Khan, Indian Institute of Information Technology Design and Manufacturing
(IIITDM-Kancheepuram), Chennai, Tamilnadu. India. E. Mail: bshahul@iiitdm.ac.in
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Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
customer requirements such as low cost, high product variety, quality and shorter
lead times. Network is characterized by procurement production and distribution
function. It starts with the material/information supplier and end with the customer.
There are three types of flow that of materials, information and finance flow of
information is two ways where as flow of product is outbound and flow of income is
inbound.
2. Literature Review
The area of supply chain management is being increasingly investigated by both
academia and industry. All supply chain are different and lot of companies struggle
to understand the dynamics of their supply chain. So every company has their own
supply chain model and also problem associated with is different for different
industry.
Sameer and Anvar (2011) investigated the impact of demand variability and
lead time on performance of a system dynamics analysis on food supply chain with
non perishable product under monopolistic environment. He used cause and effect
analysis for framing the system dynamics model. Jelena & Jack (2012) has focused
on designing robust food supply chain. Robust supply chain will be able to resist
disruption like natural disaster or fires, traffic accident and has used influence
diagram.
Chaabane-Ramadin (2012) has used mixed integer linear programming based
frame work for sustainable supply chain design that considers life cycle assessment
principle to find GHG and also used environmental cost with in supply chain design.
Wang, Xiaofan (2011) has described network design problem with environmental
concerns. Supplier selection, which facility to open, and finally how to distribute
product considering carbon. Carbon emission is considered in the each network
Pareto frontier is used to show the decision influence on network. Froto Neto (2008)
develops a frame work for the design & evaluation of sustainable logistics network
when activities affecting the environment & cost efficiency in logistics networks are
considered.
An editorial written in European journal in 2004 by A.Gunasekaran (2004) has
stressed that in present relevant literature only few attempts had been made in
developing models for integrated supply chain and vast majority of already published
literature can be said as traditional operation research models dedicated for solving
inventory problems. There is need to work on modelling the dynamics of supply
chains with respect to selection of performance measures.
3. Objective
Objective of this paper is to model and simulate a multi echelon dynamic
sustainable supply chain which is assumed to have a moderate complexity of four
echelons.
i.
To design an algorithm for multi product multi echelon sustainable supply
chain network where an initial investment on environment protection
equipment or techniques should be determined in the design phase. The
investment can influence the environmental indicators in the operation phase.
ii.
To measure its performance under different operating condition and finally
understanding and identifying its dynamic behaviour. Experiment to be carried
out on the model involving a number of different scenarios.
General Assumptions
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Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
ix.
x.
xi.
xii.
The number of customer and demand are known
The number of potential plants, distribution centre, and their maximum
capacity are known.
Customers are supplied products from a single distribution centre.
Model is built around a make to order medium (MTO) sized organization that
serve as the central manufacturing operating within a broader supply chain
network.
Four echelons are assumed supplier, manufacturer, distributors and retailers
and its dynamics are studied from the operational perspective.
None of the companies that form the network has a draftmanship with any of
the companies of the network.
The companies forming the echelon of the supply chain model are assumed
to have no interaction with any company outside the supply chain.
The central company cooperates with warehouses and distribution centre
which drive the company’s demand.
The demand at the retailer’s level is determined by the normal distribution and
order policy. Demand refers to 10 different end products and there is no
assembly operation and it is over the year open to the customer.
Production capacity of the manufacturer is 50 components per week.
Production time follows a normal distribution.
The suppliers order and receive raw material from an external source.
Model includes information and material flows. Cash flow is not considered
due to complexity.
4. Structure for sustainable supply chain network
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Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
4.1 Mathematical model
The problem can be formulated as follows
Objective function1:
MinZ1   o j z j   v j dil yij   g k pk   vlk xlk   t skr bskr   cijl qijl   a jkl f jkl   g km zkm
j
i
j
l
k
l
k
s
k
r
i
j
l
j
k
l
k
Objective function 2:
MinZ 2   xalkm nlkm   f jkl ebklj   qijl eclji   bskr earsk
k
l
m
k
l
j
l
j
i
r
s
k
Constraints :
y
 1i
ij
j
n d
l
i
yij  W j z j j
il
l
z
W
j
j
qijl  d il yij i , j & 1

f jkl 
q
ijl
k
b
 spsr s & r
skr
k
u
j & 1
i
rl
xlk 
l
b
skr
r & k
s
m
l
xlk  Dk pk k
l

f jkl  xlk k & 1
j
p
k
 P
k
z km  pk M
Objective function definition:
o z
j
J
  g k pk 
j
k
 v d
j
i
j
yij 
: Net cost of product 1 from DC
l
 v
l
il
lk
: Fixed cost for plants and distribution centre (DC) it operates
xlk 
: Production net cost for product l at plant k
k
 t
b
skr skr
-: Transportation & purchasing net cost for a raw material r from
supplier s to plant k
cijl qijl 

i
j
l
: Transportation net cost for product 1from DC j to customer i
a jkl f jkl

j
k
l
-: Transportation net cost for product 1 from plant k to DC j
s
k
r
4
m
Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
 g
z :
km km
Environment investment for plant k at environment protection
xlkm nlkm  :

l
k m
Total CO2 emission in all the plants, for each product, plant k, and
each unit of flow in the plant, an amount of nkm of CO2 is generated.
k
m
 f
k
l
jkl
eb jkl  :
j
product1
 qijl eclji  :
l
j
i
Total arc dependent CO2 emission between DC j and customer i for
product 1
 bskr ea rsk  :
r
s
k
Total arc dependent CO2 emission between plant k and DC j for
Total arc dependent CO2 emission between supplier s and plant k
for raw material r
4.2 Logic of influence diagram for dynamic supply chain
The model identifies each echelon and the links between them that need to be
incorporated into the model. Supplier, manufacturer, distributors and retailers are
denoted as s, m, d and r. Variables are very rarely independent as they usually have
strong inter relationships and the influence is mostly one way. This causes a loop in
which variables influences one another. Next process in the modelling process is
construction of influence diagram. Variables are very rarely independent as they
have strong interrelationships and the influence is in the most of the cases one way.
Due to this a loop is constructed in which variables influence one another.
Fig-1 Dynamic hypothesis for the proposed supply chain network
There are two distinct loops in above figure 1, controlling the inventory and the
second one controlling the backlog of orders. The first loop shows that the inventory
has a counteractive effect on the order rate. Therefore, when inventory is low the
order rate will be high. The order rate in turn has positive influence on the delivery
rate. Finally the delivery rate has a positive influence on the inventory level. The
whole loop is negative.
The second loop represents the desired shipment rate and backlog which are
influenced by the order rate. This is because the desired shipment rate is the order
rate plus any backlogged orders and the backlog is the difference between the order
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Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
and shipment rates. The backlogged inventory influences the desired shipment rate
in the same direction (+). Therefore as the number of backlogged orders increases
the desired shipment rate will also be increased. As the desired shipment rate
increases the influence on the shipment rate is again positive. Finally the shipment
rate has a counteractive effect on the backlogs. As the whole loop is negative loop
will always try to reduce the backlog to zero. Outside the loop the shipment rate has
a negative influence on the inventory represented in the first loop.
5.0 Methodology for Network allocation
Genetic Algorithm
Genetic algorithms (GA) to class of adaptive search procedures based on the
principles derived from natural evolution and genetics. GA is known to offer
significant advantages over conventional methods by using simultaneously several
search principles and heuristics. The most important ones include a population wide
search, a continuous balance between convergence and diversity. GA can be
implemented in a several different ways to solve any problem. In our implementation
we use steady state GA where one offspring is created in every generation and
competes with the parents. This section presents the GA for the single source, multi
product, multi stage SCN design problem.
5.1 Representation
Representation is one of the important issues that affect the performance of
GA. Usually different problems have different data structures or genetic
representations. Tree based representation is known to be one way for representing
network problems. There are three ways of encoding tree: (1) Edge based encoding
(2) Priority based encoding and (3) Edge and vertex based encoding. In our
algorithm we extend the priority based encoding of transportation trees to a multi
product case. When the priority based encoding is applied to a single product
transportation problem.
1. A chromosome consists of priorities of sources and depots to obtain a
transportation tree and its length equals to total number of sources K and
depots J i.e. K+J
2. The chromosome based on the priority based encoding consists of L parts
and the length of each part id K+J
3. The gene value of the chromosome are between 1 & L (K+J)
4. Each part of the chromosome is used to obtain a transportation tree for the
corresponding product i.e. lth part of the chromosomes used for the health
product.
5. Transportation tree for the set of products are generated by sequential
appending between sources depots.
5.2 Generating initial population
Greedy Heuristics to obtain good solution. This method is used to find the
solution in less time without searching a whole population we allot the value
according to the following assumption.
a. Assigning by minimum total transportation cost
b. Assigning the customers to DCs considering min total cost
c. List the DCs in increasing order of their fixed cost
d. DCs to be opened until they meet the total demand
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Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
5.3 A sample transportation tree and its encoding
Priority based encoding procedure is used to establish the tree between the
sources and depots. We take a case of four sources and five depots and establish
the chain between them for better understanding. The cost matrix between them
sources and depots are used for this purpose. Chromosomes are developed in this
step in order to find the optimum solutions between various possibilities of tree
connection. The basic procedure of encoding is explained in the steps below.
5.4 Structure of proposed GA
i : Set of sources
j : Set of depot
: Capacity of source
: Demand on depot
: Total cost of one of product from source I to depot j
: Amount of goods transported from source I to depot j
[ ] : Chromosome
L
: Length of Chromosome
V
: Value of the Chromosome
I.
V = i+j
II. [i_new, j_new] = position of min ( )
III.
= min [
]
IV.
V.
[
]
VI.
VII.
= 0 then V[i_new]= v ; v= v-1;
VIII.
[]
IX.
+1; return to step ii
The transportation tree corresponding with a given chromosomes is generated
by iterations .In every iteration a source /depots is selected and is connected to a
source/depots of minimum cost. At each iteration only one map is added to tree
based on the cost matrix. Figure represent a transportation tree with four sources
and five depots, its costs value and priority based encoding.
Fig4:- Optimized supply chain network
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Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
5.5 Chromosome
Supplier
1
2
4
5
8
6
3
4
5
1
1
4
Plant
3
2
7
3
9
Plant
1
2
3
4
5
1
2
Distributer
2
3
4
1
7
3
5
Distributer
2
3
1
1
6
Customer
2
8
3
2
4
5
7
1
4
5
8
6
2
3
5.6 Cost matrix data
Csp 1
2
3
4
5
1
2
3
4
9
7
13
8
10
11
9
16
4
18
5
12
15
10
7
17
6
8
10
14
Cpd
1
2
3
4
5
Cdc
1
2
3
1
11
10
15
13
17
1
7
10
9
2
5
6
12
2
14
15
9
10
18
3
10
11
8
5.7 Crossover operation
Iteration Value
0
9
1
8
2
7
3
6
3
16
18
19
12
20
4
13
17
15
5
16
14
17
Ai
500, 450,
300, 250
250, 450, 300,
250
0, 450, 350.
250
0, 100, 300 ,
250
Bj
400, 350, 400,
250, 100
400, 350, 400, 0 ,
100
150, 350, 400, 0,
100
150, 0, 400, 0 ,
100
i,j
1,
4
1,
1
2,2
V[L]
0000|00090
2,
1
8600|07090
8000|00090
8000|07090
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Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
4
5
0, 0, 300, 250
5
4
0, 0, 0, 250
6
3
0, 0, 0, 200
7
2
0, 0, 0, 100
50, 0, 400, 0 ,
100
50 , 0, 100, 0 ,
100
0, 0 , 100, 0,
100
0, 0 , 0 , 0 , 100
8
1
0 , 0, 0, 0
0, 0, 0 , 0, 0
0
8
1
7
2
3
4
5
6
7
6
5
4
3
2
1
0
8
500, 350, 650
1
7
50, 350, 650
2
6
0, 350, 650
3
5
0, 350, 450
4
5
6
7
4
3
2
1
0, 350, 200
0, 350, 0
0, 50, 0
0, 0, 0
400, 350, 400, 250,
100
400, 350, 50, 250,
100
400, 0 , 50, 250, 100
250, 0 , 50, 250, 100
250, 0, 50, 0, 100
0, 0 , 50, 0 , 100
0, 0 , 0 , 0, 100
0, 0 , 0 , 0, 0
3,
3
4,
1
4,
3
4,
5
8650|07090
8650|47090
8650|47390
8650|47392
8651|47392
500, 350,650
3,2
07000|080
500, 0 , 650
2,1
07000|680
150, 0, 650
0, 0, 650
0, 0, 400
0, 0, 150
0,0,100
0, 0, 0
1,1
4,3
1, 3
3,3
5,3
-
07050|680
47050|680
47350|680
47350|682
47350|682
47351|682
300, 450, 200,
250, 300
300, 0 , 200, 250,
300
250, 0, 200, 250,
300
250, 0 , 0, 250,
300
0, 0 , 0, 250, 300
0, 0 , 0, 50, 300
0, 0 , 0, 50, 0
0, 0, 0, 0, 0
1,2 000|08000
1,1 700|08000
3,3 700|08600
3,1 700|58600
3,4
2,5
2,4
-
704|58600
704|58603
704|58623
714|58623
6.0 GA based heuristics
Input module
The input given in the two stage supply chain fixed charge distribution problem will
be
1. p, q, r, Si ( i= 1 to p) and Dk ( k = 1 to r)
2. Cij and Fij (i= 1 to p and j= 1 to q)
3. Cjk and Fjk (j=1 to q and k= 1 to r)
Initialization method
A feasible distribution plan that satisfies the customer requirement from the DC
forms a chromosome. A chromosome is a matrix of order j*k in which each element
will be Gene. A gene will indicate the number of units Xjk distributed to customer k
through DC j. Three chromosomes will be generated by applying least cost
allocation method with the following cost data CFjk, Cjk Fjk. The other seven will be
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Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
generated randomly. This total 10 population will form the initial population. The
allocation is done in such a way that customer demand Dk (k= 1 to r) is satisfied.
6.0 Results
A feasible distribution plan that satisfies the customer requirement from the DC
forms a chromosome. A chromosome is a matrix of order j*k in which each element
will be Gene. A gene will indicate the number of units Xjk distributed to customer k
through DC j. Three chromosomes will be generated by applying least cost
allocation method with the following cost data CFjk, Cjk Fjk. The other seven will be
generated randomly. This total 10 population will form the initial population. The
allocation is done in such a way that customer demand Dk (k= 1 to r) is satisfied.
c
Initial
populatio
n
j
X jk
Evaluatio
n Module
k
1
2
3
1
0
150
0
1
2
0
1
0
0
TC-2
Aj
X ij
TC1
fit(c)=z
new _ fit (c)
selection
module
cp (c )
Random number R
New Chromosome
selected/not sele.
crossover
After crossover
New
populatio
n
After Mutation
X jk
4
0
270
0
1
0
150
0
0
1
0
0
0.1624
0.100315
0.100315
0.92
10
p(C )
X jk
1
2
3
0
0
80
100
0
0
17250
600
0
2
3
250
0
350
0
19100
36350
0
150
0
0
150
0
3
0
100
0
4
0
270
0
0
3
0
0
1
0
0
150
80
1
0
80
0.1624
0.100315
0.20063
0.41
5
not selected
0
0
80
100
0
0
0
0
80
2
2
0
80
0
17250
600
2
250
350
19100
36350
100
0
0
0
270
0
0
150
0
270
0
0
0
0
150
3
0
100
0
4
0
0
270
420
3
150
270
1
0
150
0
370
1
20
350
0.1399
0.086416
0.287046
0.98
10
not selected
0
0
80
100
0
0
0
80
0
3
2
80
0
0
24400
100
2
100
0
14930
39330
100
0
0
0
270
0
0
150
0
270
0
0
0
150
0
3
100
0
0
4
270
0
0
0
3
0
0
0.1786
0.110321
0.397367
0.22
3
selected
80
0
0
100
0
0
0
80
0
4
2
0
80
0
24450
230
2
230
0
10000
34450
0
0
100
270
0
0
0
0
150
0
270
0
0
0
150
selected
0
100
80
0
0
0
80
0
0
100
0
0
10
0
0
270
0
0
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Proceedings of 20th International Business Research Conference
4 - 5 April 2013, Dubai, UAE, ISBN: 978-1-922069-22-1
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11