An application of fuzzy cognitive mapping in optimization of inventory function among auto component manufacturing units in sme sector

International Journal of Management (IJM), OF MANAGEMENT (IJM) –
INTERNATIONAL JOURNAL ISSN 0976 – 6502(Print), ISSN 0976
6510(Online), Volume 3, Issue 2, May-August (2012)

ISSN 0976 – 6367(Print)
ISSN 0976 – 6375(Online)
Volume 3, Issue 2, May- August (2012), pp. 13-24 IJM
© IAEME: www.iaeme.com/ijm.html
Journal Impact Factor (2011): 1.5030 (Calculated by GISI) ©IAEME
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AN APPLICATION OF FUZZY COGNITIVE MAPPING IN OPTIMIZATION
OF INVENTORY FUNCTION AMONG AUTO COMPONENT
MANUFACTURING UNITS IN SME SECTOR

*N.Balaji &** Y.Lokeswara Choudary
Research Scholar, SRM University, Kattankulathur, Chennai-603203.
Asst.Professor & Research Supervisor, SRM B-School, SRM University, Vadapalani,
Chennai-600026.
Contact: balajineelisetty@gmail.com
1.0 ABSTRACT

Optimization of inventory quantity is a vital issue among the manufacturer and
supply chain. Optimization is a complex task due to classification of inventories on the
basis of cost and due to dynamic movement behavior of various inventories in the supply
chain. The primary objective of the present paper is to develop the optimization model
for the 2D criteria base classified stocks in the SMEs working in the auto component
manufacturing industry. The matrix is framed by combining three ranges of cost and
three types of movement behavior. A 3 X 3 matrix is frame and the cells were
responding as Ax, Ay,Az, Bx,By,Bz and Cx,Cy, Cz. The critical cost is identified and
the basis of the same models was fixed. Node`s importance or cognitive or conceptual
gives an indication of the importance that the node by measuring the degree. The
importance of the node is evaluated as Imp (i) = in (i) +Out (i).

The present study identified that, the inventory cost in auto component
manufacturing industries is influenced by the variables like, Purchase Cost of the
components (Base cost= Vendor invoice cost +order costs), Easy to carry and fix,
Strength and weightage of the materials as components, Brand image of the components
purchased from outside from the SMEs, Availability of suppliers for components, Safety
and reliability, Design and appearance the component. The optimization can be done on
the basis of design and development of the inventory function strategy applicable to the
independent firms based on the nature of products, size of operations and financing
capacity.

13

International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –

Key words: Inventory cost-dynamic behaviour-fuzzy cognitive mapping-vital variables-
optimization.

1.1 INTRODUCTION

Optimization of inventory quantity is a vital issue among the manufacturer and
supply chain. Optimization is a complex task due to classification of inventories on the
basis of cost and due to dynamic movement behavior of various inventories in the supply
chain. The present paper in focused on finding a unique optimization model considering
and classifying the inventories in a 2 D matrix. The primary objective of the present
paper is to develop the optimization model for the 2D criteria base classified stocks in the
SMEs working in the auto component manufacturing industry. The 2D Criteria is
developed by combining the two basic elements relating to inventory cost among the
industries. They are Value of the inventory and other one is consumption behaviour/issue
behaviour/movement behaviour of different inventories. The term inventory includes
basic raw materials, work in progress and the finished goods. In majority of the SMEs in
auto component manufacturing sector, the number of components is high in number in
terms of basic inventories, work-in-Progress inventory and finished components.

Another significant observation made among the SMEs is the proportion of
selected inventories to total inventory cost is high in Ax, Ay and Az stocks. A survey
report says the composition of inventory cost of these stocks (Ax+Ay+Az) to total
inventory cost is 70 percentage across the sector. This made us to think to focus on these
stocks and to optimize them in order to control the total inventory costs. Based on this
assumption we have developed a 2D Matrix and fixed the definite area to focus for
optimization.
Matrix showing the Classification of Inventory based on 2D model

Quantity of consumption of inventory
X y z
Value of
inventor

A Ax Ay Az
B Bx By Bz
y

C Cx Cy Cz

The unique feature of this model is identifying and classifies the intensity and impact of
stocks on the basis of cost and quantity. It also involves segregation of high sensitive and
low sensitive inventories in term of total cost of an inventory and the hidden cost due to
over stock. Therefore a unique model may not be suitable for the entire range of
inventories, Hence, two fold approach is followed and at that basis simple and practical
models are developed and empirically validated on the SME`s in the sample area.

1.2 REVIEW OF LITERATURE

Cognitive Mapping (CM) model were introduced by Axelrod in the late 1970` and
were widely used for analyzing the sociological problems and decision making in

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sociological problems. The introduction of fuzzy logic give new representing capabilities
to CM`s and led to development of Fuzzy cognitive maps (FCM) by kosoko in the late
1980`s. FCM create models as collections of concepts and the various casual relations
that exists between these concepts. The concepts are represented by nodes and the causal
relationships by directed arcs between the two nodes. Each arc is accompanied by a
weight which defines the degree of relation between the two nodes. The sign of the
weight the positive or negative or casual relation between the two concept nodes.

1.3 METHODOLOGY

Inventory models will have dynamism and probability behavior in general.
Combination of cost and movement behavior is Hyper dynamic in nature. This was
observed by physical verification of cost and movement behavior of Hyper dynamic in
nature. This was observed by physical verification reasons of the 416 SMEs in the Auto
hub area. The physical verification of inventory data base is taken to the study. Finally
a two dimension (2D) matrix is constructed by considering cost and inventory moment of
the stocks. The matrix is framed by combining three ranges of cost and three types of
movement behaviour. A 3 X 3 matrix is frame and the cells were responding as Ax,
Ay,Az, Bx,By,Bz and Cx,Cy, Cz. The critical cost is identified and the basis of the same
models was fixed. FCM create models as collections of concepts and the various causal
relations that exist between these concepts. The concepts are represented by nodes and
the causal relationships by directed arcs between the nodes. Each arc is accompanied by
a weight which defines the degree of relation between the two nodes. The sign of the
weight the positive or negative or zero causal relation between the two concept nodes.

1.4 Development of FCM Models in the study about problems faced by SMEs in the
sample area.
The reliability of an FCM model depends on whether its construction method follows
rules that ensure its reliability. Since the model is created by the personal opinions and
points of view of the experts on the specific topic, the reliability of the model is heavily
depended on the level of expertise of the domain experts. These are two main methods
for the construction of FCM`s:
1. The documentary coding method which involves the systematic encoding of
Documents that represents the assertions of specific topic.
2. The questionnaire method which involves interview and filling in a questionnaires
by domain experts.

In our case we used the second method, discussion, interviewing, analyzing and also
supplying with questionnaires to a domain expert. The domain expert providing the
actors and factors, the possible alternative scenarios as well as the analysis of the
findings.

1.5 NEED FOR THE STUDY
There are several reasons manufacturers are increasing focus on optimizing
inventory by applying the latest tools and techniques for inventory control. Traditionally

15


competitive pressure has always driven Manufacturers to seek enhanced capabilities to
reduce inventory levels and to enhance service levels and supply availability; and to
establish the right product inventory mix and level in each geography and channel. Many
manufacturers also focus on inventory as part of shifting their operations to achieve
demand-pull replenishment across their supply network – hoping to achieve the
performance demonstrated by leading manufacturers.

A key driver of the renewed focus on inventory lies in the recognition that
traditional techniques are failing to reign in inventories in the wake of increased supply
chain complexity. This complexity is characterized by increased uncertainty. Demand
is more volatile and therefore less predictable. This is true not only for aggregate
demand but for forecasting splits and volumes across channels and markets.
Traditionally, three strategies have been employed by manufacturers to address
uncertainty:

a) Increase inventory levels to hedge against uncertainty.
b) Develop supply chain flexibility to be more responsive to uncertainty.
c) Improve forecast accuracy so that less uncertainty propagates to the
manufacturing floor. Inventory optimization techniques and technologies map to
the flexibility and accuracy strategies.

Globalization is on e big drive, the evolution of emerging markets such as China
and India present new challenges in effective product distribution with low inventory
levels. Globalization of supply networks means that key functions such as R&D,
product design and manufacturing are now geographically spread out, which hampers
inventory reduction efforts, that are often best executed by a cross function team working
together very closely. Increased rates of new product introduction and product
innovation are also driving complexity into supply networks. Finally , SMEs needs to
have customized strategy for the different kinds of inventory they deal with. It can help
in controlling the total cost and optimizing success of the organizations.

1.6 INVENTORY OPTIMIZATION DEFINED
Inventory Optimization (IO) is the application of a range of latest techniques and
technologies for improving inventory visibility, control, and management across an
extended supply network. These techniques and technologies are driving improvements
beyond what traditional inventory management techniques - even advanced techniques -
have been able to deliver IO Techniques.
IO techniques apply rigorous and discrete analysis to analyzing inventory
performance. They the use the analysis to identify product specific changes to inventory
stocking and replenishment policies; to identify the supply network configuration or, to
correlate inventory investments to item revenue or profit generation. On the planning
side, a key inventory optimization technique is profit-driven analysis, where the profit
each individual product contributes is ranked. Expanding the use of collaborative and
demand pull replenishment scheme such as a vendor – or supplier –managed inventory

16


to drive highly precise replacement and fulfillment activity. These techniques are also
benefiting from improved supply chain planning and control. Lean seeks to optimize
inventory by driving out non-value added inventory management tasks in the factory or
warehouse and by improving planning and control a granular level across each
manufacturing or distribution step.

1.7 Variables Identified

On the basis of review of literature and stock records verification and observation
among the SME`s, the following 15 attributes are taken as major components influencing
the inventory cost in the supply chains.

S1: Purchase Cost of the components (Base cost= Vendor invoice cost +order costs)
S2: Easy to store/preserve of basic components bought and manufactured (Because
some materials will be bought in the form of RM, WIP and FG)
S3: Easy to carry and fix: Material handling costs are also vital in inventory issue cost.
Handling equipments, repairs and usability of the same are also important
determinants in inventory costs.
S4: Strength and weightage of the materials as components
S5: Brand image of the components purchased from outside from the SMEs
S6: Availability of suppliers for components required in the process of manufacturing
the other component with suitability and flexibility.
S7: Safety and reliability of the component of the equipments bought from different
suppliers.
S8: Design and appearance the component (Design plays a major role in terms of
suitability for all the models and all brands developed).
S9: Multiplicity of uses of the same component
S10: Alternatives availability for all the types of inventory.
S11: Mode of packing and transport of the raw materials, WIP and Finished goods.
S12: Reparability and reuse of the component in case of damages in transport.
S13: Carrying costs (Interest charges payable on the funds blocked / charged by the
supplier for the credit period)
S14: Transport costs (From the vendor place to store and consumption point)
S15: Legal costs (In case of inter state / import of materials or components/ taxes levied)

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1.8 Application for using FCM model
The adjacency matrix for the problem is:
FCM MATRIX FOR THE INVENTORIES

Factors S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15
S1 0 1 0 0 -1 1 -1 -1 0 1 -1 1 1 1 -1
S2 1 0 -1 1 0 0 0 1 0 0 1 0 1 0 0
S3 1 0 0 1 -1 -1 0 1 -1 0 0 0 0 0 0
S4 -1 1 1 0 -1 0 1 0 1 -1 0 1 0 1 0
S5 1 0 -1 1 0 1 1 1 1 -1 1 1 0 0 1
S6 -1 0 0 0 1 0 1 1 0 1 0 1 1 1 0
S7 1 0 1 1 1 0 0 1 -1 1 0 1 0 0 0
S8 1 1 1 -1 1 0 1 0 0 1 0 -1 0 0 0
S9 0 0 0 0 -1 -1 0 1 0 -1 -1 0 -1 0 0
S10 0 0 1 0 0 0 0 0 1 0 0 -1 1 0 0
S11 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1
S12 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0
S13 1 1 1 0 -1 1 0 0 0 1 0 -1 0 0 0
S14 -1 1 1 1 0 -1 0 1 0 0 0 0 1 0 0
S15 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0

Diagram: 1.0: Showing the relationship between the variables influencing
Total inventory costs in supply chains are presented below:

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1.9 STATIC ANALYSIS

The static analysis of the model is based on studying the characteristics of the
weighted directed graph that represent the model, using graph theory techniques. The
first way to examine statically the models graph is by calculating its density. The
density `d’ is given by d= m/n(n-1) where `m’ is the number of arcs in the model and `n’
is the number of concepts of the model. Product n(n-1) is equal to the maximum number
of arcs that a graph of n nodes can have . Density give and indication of the complexity
of the model. High density indicates increased complexity in the model and respectively
to the problem that the model represents. For this problem d = 104/(15)(14) =0.5 which
indicate the complexity of the problem.

Graph theory also provides the nodes importance that assists the static analysis of FCM
models. Node`s importance or cognitive or conceptual gives an indication of the
importance that the node by measuring the degree. The importance of the node is
evaluated as Imp (i) = in (i) +Out (i).

Where in (i) = number of incoming arcs of the node i
Out (i) = number of outgoing arcs o node i.
According to this definition, the importance of the nodes of the FCM mode is given by

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15
IN 11 6 6 9 11 8 8 8 6 4 8 3 7 7 3
OUT 10 6 9 7 9 7 7 8 5 9 6 9 6 4 2
Total 21 12 15 16 20 15 15 16 11 13 14 12 13 11 5

It is found the most central or important concepts were S1,S3,S4,S5,S6,S7,S8

19


2.0: DYNAMIC BEHAVIOUR

If S1 IS ON A1 = [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
A1*E = A2 = [0 1 0 0 -1 1 -1 -1 0 1 -1 1 1 1 -1] --- A2 =
[1,1,0,0,0,1,0,0,0,1,0,1,1,1,0]
A2*E = A3 = [0 3 2 3 -1 1 0 2 1 4 1 0 5 2 -1] --- A3 =[1,1,1,1,0,1,0,1,1,1,1,0,1,1,0]
A3*E= A4 = [1 6 5 2 -2 0 3 4 1 2 -1 1 4 4 0] --- A4 = [1,1,1,1,0,0,1,1,1,1,0,1,1,1,0]
A4*E=A5 = [3 5 5 4 -3 -1 1 4 0 3 0 0 3 2-1] --- A5 = [1,1,1,1,0,0,1,1,0,1,0,0,1,1,0]
A5*E =A6 = [ 3 5 5 3 -2 0 1 3 0 3 0 0 4 2 -1]---- A6 = [1,1,1,1,0,0,1,1,0,1,0,0,1,1,0]

There fore S1 is on then, S2, S3, S4, S7, S8, S10, S13, S14 are on and S5, S15 becomes
negative.
This means to say that the S1- Purchase cost of the components is associated with the
S2: Easy to store/preserve of basic components bought and manufactured (Because some
materials will be bought in the form of RM, WIP and FG)
suppliers.
Represented as:

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POSITIVE ASSOCIATION
WITH
S2-Easy to store
S3-Easy to carry
S4-Material strength
S7-Safety and reliability
S1- BASIC S8-Design and appearance
PURCHASE COST S10-Alternatives availability
OF INVENTORY S13-Carrying cost
S14-Transport cost

NEGATIVE ASSOCIATION
WITH
S5 –Brand image
S15-Legal cost

If S2 is on
B1 = [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
B1*E=B2=[1 0 -1 1 0 0 0 1 0 0 1 0 1 0 0] -----B2 = [1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]
B2*E= B3=[2 5 3 0 -1 3 2 0 1 2 0 1 2 3 0] ----B3 = [1,1,1,0,0,1,1,0,1,1,0,1,1,1,0]
B3*E=B4=[2 3 3 5 -2 -1 0 5 -1 4 0 1 4 2-1]---B4 = [1,1,1,1,0,0,0,1,0,1,0,1,1,1,0]
B4*E=B5=[2 5 4 3 -3 0 1 2 1 3 1 -1 4 2 -1]--- B5 = [1,1,1,1,0,0,1,1,1,1,1,0,1,1,0]
B5*E=B6 = [3 6 6 3 -2 0 2 4 0 2 -1 1 3 3 0]---B6 = [1,1,1,1,0,0,1,1,0,1,0,1,1,1,0]
B6*E=B7 =[3 5 5 4 -2 0 1 3 0 4 1 0 4 2-1]---B7 = [1,1,1,1,0,0,1,1,0,1,0,0,1,1,0]

There fore S2 is on then, S1, S3, S4, S7, S8, S10, S13, S14 are on and S5, S15 becomes
negative. This means to say that the S2- Ease to store and preserve the components is
associated with the
S1- Purchase cost of the components
suppliers.

21



The second rotation concluded with static behaviour of the attributes with the same
association between the attributes. Hence, we will be discussing the casual relation
between the important nodes S1, S3, S4, S5, S6, and S8.
Similarly if S15 is on S1S2, S3, S4, S5, S6, S7, S8, S13 and S14 are all on.
Next we will discuss the causal relation between the important nodes S1, S3, S4, S5, S6,
S7, and S8.
The adjacency matrix is given by:

 
 S1 S3 S4 S5 S6 S 7 S8 
 
S1 0 0 0 -1 1 1 -1 
 
S3 1 0 1 0 0 0 1 
 S4 - 1 1 0 -1 0 1 0 
 
 S5 1 0 1 0 1 1 1 
 S6 0 0 0 1 0 1 1 
 
S7 1 1 1 1 0 0 1 
 S8 1 1 0 1 0 1 0 
 

Suppose If S1 is on then A = [1,0,0,0,0,0,0]

A1 =[0,0,0,-1,1,-1,-1] …….. A1 = [1,0,0,0,1,0,0]
A2 = [-1, 0,0,0,1,0,0] …….. A2 =[1,0,0,0,1,0,0]
If S1 is on S5 Is on

Suppose If S3 is on then B = [0,1,0,0,0,0,0]
B1 = [1 0 1 -1 -1 0 1] …….. B1 = [1,1,1,0,0,1,1]
B2=B1*E
B2 = [2 3 1 -1 0 1 1] ……... B2=[1,1,1,0,0,1,1]
If S3 is on S2,S3,S6,S7 is on

If S4 is on then C = [0,0,1,0,0,0,0]
C1=C*E
C1 = [-1 1 0 -1 0 1 0] …… C1=[0,1,1,0,0,1,0]
C2= C1*E
C2=[ 1 2 2 0 0 1 1] …….C2 = [1,1,1,0,0,1,1]
C3=C2*E
C3= [2 3 1 -1 0 1 1] …… C3 = [1,1,1,0,0,1,1]
If S4 is on then S1,S3,S7,S8 is on

22


If S5 is on then D = [0,0,0,1,0,0,0]
D1 = D*E
D1 =[1 -1 1 0 1 1 1] …… D1 = [1,0,1,1,1,1,1]
D2 = D1*E
D2 =[1 2 1 1 2 3 2] …… D2 = [1,1,1,1,1,1,1]
D3=D2*E
D3 =[2 2 2 0 1 3 3] ….. D3 = [1,1,1,1,1,1,1]
If S5 is on then S1,S3,S4,S6,S7,S8 is on

If S6 is on F=[0,0,0,0,1,0,0]
F1=F*E
F1 =[-1 0 0 1 0 1 1] …..F1=[0,0,0,1,1,1,1]
F2=F1*E
F2 =[2 1 1 3 1 3 3 ] …… F2 = [1,1,1,1,1,1,1]
F3=F2*E
F3 =[2 2 2 0 1 3 3] …… F3 = [1,1,1,0,1,1,1]
F4=[1 3 1 0 0 2 2] ……F4 = [1,1,1,0,1,1,1]
If S6 is on then S1,S3,S4,S7,S8 is on

If S7 is on G = [0,0,0,0,0,1,0]
G1=G*E
G1 =[1 1 1 1 0 0 1] …… G1 = [1,1,1,1,0,1,1]
G2=G1*E
G2=[3 2 2 -1 1 2 2] ……. G2 = [1,1,1,0,1,1,1]
G3 = G2*E
G3 =[1 3 1 0 0 2 2] …… G3 = [1,1,1,0,0,1,1]
G4 = G3*E
G4 =[2 3 1 -1 0 1 1] ……G4 = [1,1,1,0,0,1,1]
If S7 is on S1,S2,S3,S6,S7 is on

If S8 is on H = [0,0,0,0,0,0,1]
H1 = [1,1,-1,1,0,1,0]……H1=[1,1,0,1,0,1,1]
H2= [4,1,2,0,1,1,2] …..H2= [1,1,1,0,1,1,1]
H3 = [1,3,1,0,0,2,2] …..H3 = [1,1,1,0,0,1,1]
H4= [2,3,1,-1,0,1,1] …..H4=[1,1,1,0,0,1,1]
If S8 is on S1, S2, S3, S7

There fore it is identified that, the variables influencing inventory cost in dynamic
behavior and static behavior is one and the same.

3.0 SUMMARY

Inventory problem is universal in nature. But the solutions for the same are
multiple. The selection and application to address the issue is purely depends on the
independent firms in the industry. In the auto component industry is basically featured

23


with SME nature in the sample area. The present study identified that, the inventory cost
in auto component manufacturing industries is influenced by the following variables.
S1: Purchase Cost of the components (Base cost= Vendor invoice cost +order costs)
S5: Brand image of the components purchased from outside from the SMEs
S6: Availability of suppliers for components required in the process of manufacturing the
other component with suitability and flexibility.
suppliers.

The optimization can be done on the basis of design and development of the
inventory function strategy applicable to the independent firms based on the nature of
products, size of operations and financing capacity. No unique policy can be suggested to
all due to heterogeneity in the product nature and capacity of the firms. However the
critical factors influencing inventory cost is common. A common problem addresses by
different firms in the industry is possible through customization of standard techniques.
For these firms has to come forward with commitment and intention to change the
existing climate. This can resolve the inventory optimization in a better way in the years
to come.

REFERENCES

1. Kosooko `B’ Fuzzy Cognitive Maps. International journal of Man-Machine
studies pp65-75, 1986,
2. Kandaswamy, Vasantha and W.B.Florentin, S.Fuzzy Cognitive Maps and
Neutrosophic Cognitive Maps, Xiquan, U.S.A.2003
3. Athanuasis, K.Tsadirus, Iluis Using FCM as a Decision Support system for
political decisions; The cas of Trukey`s Integration into European Union.
Springer, Verlag 2005.
4. Giordano, R.,Vurro, M.,Fuzzy Cognitive Map to support Conflict Analysis in
Drought Management, PP.403-425 STUDDFUZZ
5. Petelas, Y.G. and Pasopolulos, K.F., Improving FCM Lerning through Memetic
Partical Swarm optimization soft Comput(2009) 13C77-94 .
6. Sidling, Margret, A study of Attitude of Teachers Towards Athlet, es in Middle
School USA 1994.
7. Solven Treadles A research on Relationship between High school students and
Teachers Norway 1987. Snyder, A study on stress.

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An application of fuzzy cognitive mapping in optimization of inventory function among auto component manufacturing units in sme sector

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An application of fuzzy cognitive mapping in optimization of inventory function among auto component manufacturing units in sme sector