Data mining Aided Proficient approach for optimal inventory control in supply chain management

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Data mining Aided Proficient approach for optimal inventory control in supply chain management Powered By Docstoc
					                                                           (IJCSIS) International Journal of Computer Science and Information Security,
                                                           Vol. 8, No. 2, May 2010




    Data mining Aided Proficient approach for optimal
     inventory control in supply chain management

                     Chitriki Thotappa                                                       Dr. Karnam Ravindranath
Assistant Professor, Department of Mechanical Engineering,                                          Principal
      Proudadevaraya Institute of Technology, Hospet.                              Annamacharya Institute of Technology, Tirupati
 Visvesvaraya Technological University, Karnataka, India                                     kravi1949@yahoo.com
                    thotappa@gmail.com


Abstract— Optimal inventory control is one of the significant              supply and demand, globalization, reduction in product and
tasks in supply chain management. The optimal inventory                    technology life cycles, and the use of outsourcing in
control methodologies intend to reduce the supply chain (SC) cost          manufacturing, distribution and logistics resulting in more
by controlling the inventory in an effective manner, such that, the        complex supply networks, can lead to higher exposure to risks
SC members will not be affected by surplus as well as shortage of          in the SC [8].
inventory. In this paper, we propose an efficient approach that
effectively utilizes the data mining concepts as well as genetic               The ultimate goal of every SC is to maximize the overall
algorithm for optimal inventory control. The proposed approach             value generated by the chain, which depends on the ability of
consists of two major functions, mining association rules for              the organization to fulfill customer orders faster and more
inventory and selecting SC cost-impact rules. Firstly, the                 efficiently [9]. While the separation of SC activities among
association rules are mined from EMA-based inventory data,                 different companies enables specialization and economies of
which is determined from the original historical data. Apriori, a          scale, many important issues and problems need to be resolved
classic data mining algorithm is utilized for mining association           for a successful SC operation which is the main purpose of
rules from EMA-based inventory data. Secondly, with the aid of             supply chain management (SCM) [14]. SCM is a traditional
genetic algorithm, SC cost-impact rules are selected for every SC          management tool [1] which has attracted increasing attention
member. The obtained SC cost-impact rules will possibly signify            in the academic community and in companies looking for
the future state of inventory in any SC member. Moreover, the              practical ways to improve their competitive position in the
level of holding or reducing the inventory can be determined
                                                                           global market [4]. SCM is an integrated approach to plan and
from the SC cost-impact rules. Thus, the SC cost-impact rules
that are derived using the proposed approach greatly facilitate
                                                                           control materials and information flows [3]. Successful SCM
optimal inventory control and hence make the supply chain                  incorporates extensive coordination among multiple functions
management more effective.                                                 and independent companies working together to deliver a
                                                                           product or service to end consumers [2]. Inventory control has
   Keywords-SC cost; SC cost-impact rule; EMA-based inventory;             been considered as a vital problem in the SCM for several
Apriori; Genetic Algorithm (GA).                                           decades [10].

                         I. INTRODUCTION                                       Inventory is defined as the collection of items stored by an
                                                                           enterprise for future use and a set of procedures called
    Nowadays, supply chains are at the center stage of                     inventory systems assist in examination and control of the
business performance of manufacturing and service enterprises              inventory. The inventory system supports the estimation of
[5]. A SC consists of all parties involved directly or indirectly          amount of each item to be stored, when the low items should
and in satisfying a customer request. It includes suppliers,               be restocked and the number of items that must be ordered or
manufacturers, distributors, warehouses, retailers and even                manufactured as soon as restocking becomes essential. The SC
customers themselves [6]. Because of the intrinsic complexity              cost was hugely influenced by the overload or shortage of
of decision making in supply chains, there is a growing need               inventories [11]. Since inventory is one of the major factors
for modeling methodologies, which help to identify and                     that affect the performance of SC system, the effective
innovate strategies for designing high performance SC                      reduction of inventory can substantially reduce the cost level
networks [5]. Research on supply chains makes an attractive                of the total SC [13]. Thus, inventory optimization has
field of study, offering several approach roads to                         emerged as one of the most recent topics as far as SCM is
organizational integration processes. Some of the problems are             considered [11]. Inventory optimization application organizes
considered as most important, which canalize research project              the latest techniques and technologies, thereby assisting the
in the area of supply chains that are related to demand                    enhancement of inventory control and its management across
variability and demand distortion throughout the SC [7].                   an extended supply network. Some of the design objectives of
Modern supply chains are highly complex and dynamic; the                   inventory optimization are to optimize inventory strategies,
number of facilities, the number of echelons, and the structure            and thus used in enhancing customer service, reducing lead
of material and information flow contribute to the complexity              times and costs and meeting market demand [11].
of the SC [9]. In addition, increases in the uncertainties in



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                                                                                                      ISSN 1947-5500
                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                        Vol. 8, No. 2, May 2010



    Under the influence of the SCM, conventional inventory              confidence from a given database. Association rule mining is a
control theories and methods are no longer adapted to the new           two step process [27]:
environment [12].         The optimal inventory control
methodologies intended to reduce the SC cost in the SC                     •    Finding those itemsets whose occurrences exceed a
network. They minimize the SC cost by controlling the                           predefined threshold in the database, these itemsets are
inventory in an optimal manner and so that the SC members                       called frequent or large itemsets.
will not be affected by surplus as well as shortage of                     •    Generating association rules from those large itemsets
inventory. In order to control the inventory in an optimal                      with the constraints of minimal confidence.
manner, we propose an efficient approach with the effective
utilization of data mining concepts as well as GA. The rest of              The basic problem in mining association rules is mining
the paper is organized as follows. Section II gives a brief             frequent itemsets [30]. Frequent item set mining problem has
introduction about the data mining and generating association           received a great deal of attention [28] from its introduction in
rules using Apriori and Section III reviews some of the recent          1993 by Agarwal et al [35]. Frequent item sets play an
related works. Section IV details the proposed approach for             significant role in several data mining tasks that tries to
optimal inventory control with required mathematical                    determine interesting patterns from databases, such as
formulations. Section V discusses about the implementation              association rules, correlations, sequences, episodes, classifiers,
results and Section VI concludes the paper.                             clusters and much more [29]. There have been several various
                                                                        algorithms developed for mining of frequent patterns, which
                        II. DATA MINING                                 can be classified into two categories. The first category,
    Data mining is one of the newly emerging fields, which is           candidate-generation-and test approach, such as Apriori and
concerning the three worlds of Databases, Artificial                    second category of methods includes FP-growth and Tree
Intelligence and Statistics. The information age has enabled            Projection [30].
several organizations in order to gather huge volumes of data.              Apriori is one of the most popular data mining approaches
But, the utility of this data is negligible if “meaningful              for determining frequent itemsets from transactional datasets.
information” or “knowledge” cannot be extracted from it [15].           The Apriori algorithm is the key basis of several other well-
Data mining has been emerging as an effective solution to               known algorithms and implementations [31]. The Apriori
analyze and extract hidden potential information from huge              algorithm uses two values for rule construction: 1.) a support
volume of data. The term data mining is used for techniques             value and 2.) a confidence value. Depending on the setting of
and algorithms that allow analyzing data in order to determine          each index threshold, the search space can be reduced, or the
rules and patterns describing the characteristic properties of          candidate number of association rules can be increased.
that particular data. [21].                                             However, experience is necessary for setting an effective
    Usually, data mining tasks can be categorized into either           threshold [32]. The basic idea of Apriori algorithm is to
prediction or description [18]. Clustering, Association Rule            generate a specific size of the candidate projects set, and then
Mining (ARM) [19] and Sequential pattern mining are few                 scan the database time’s line counts, to determine whether the
descriptive mining techniques. The predictive mining                    candidate frequent item sets [33].
techniques involve tasks like Classification [20], Regression                                  III. RELATED WORKS
and Deviation detection [34]. Data mining is utilized in both
the private and public sectors. Data mining is usually used by               Some of the recent research works available in the
business intelligence organizations, financial analysts and also        literature are described in this section. A. L. Symeonidis et al.,
used for healthcare management or medical diagnosis to                  [36] have introduced a successful paradigm for coupling
extract information from the enormous data sets generated by            Intelligent Agent technology with Data Mining. Considering
modern experimental and observational methods [16] [17].                the state-of-the-art Multi-Agent Systems (MAS) development
                                                                        and SCM evaluation practices, they have proposed a
    Generally, Data mining is used to extract interesting               methodology to identify the appropriate metrics for DM-
knowledge that can be represented in several various                    enhanced MAS for SCM and used those metrics to evaluate its
techniques such as clusters, decision trees, decision rules and         performance. They have also provided an extensive analysis of
much more. In these, association rules have been proved to be           the methods in which DM could be employed to improve the
effective in identifying interesting relations in massive data          intelligence of an agent, agent Mertacor. A number of metrics
quantities [25]. Association Rule Mining (ARM), initially               were applied to evaluate their results before incorporating the
introduced by Agrawal et al. [35], is a well-known data mining          selected model with their agent. Their mechanism proved that
research field [24]. ARM correlates a set of items with other           their agent was capable of increasing its revenue by adjusting
sets of items in a database [23]. It aspires to mine interesting        its bidding strategy.
correlations, frequent patterns, associations or casual
structures among sets of items in the transaction databases or              Steven Prestwich et al. [37] have described a simple re-
other data repositories [22]. ARM has a extensive range of              sampling technique called Greedy Average Sampling for
applications in the fields of Market basket analysis, Medical           steady-state GAs such as GENITOR. It requires an extra
diagnosis/ research, Website navigation analysis, Homeland              runtime parameter to be tuned, but does not need a large
security and so on [26]. ARM is to identify the association             population or assumptions on noise distributions. While
rule which satisfies the pre- defined minimum support and               experimented on a well-known Inventory Control problem, it
                                                                        performed a large number of samples on the best




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                                                                                                    ISSN 1947-5500
                                                         (IJCSIS) International Journal of Computer Science and Information Security,
                                                         Vol. 8, No. 2, May 2010



chromosomes yet only a small number on average, and was                        IV. THE PROPOSED APPROACH FOR OPTIMAL INVENTORY
more effective than the other four tested techniques.                                                       CONTROL
   Mouhib Al-Noukari et al [38] have explained a data                        In the proposed approach for optimal inventory control,
mining application in car manufacturing domain and                       two major functions are included, namely, association rules
experimented it. Their application results demonstrated the              mining for inventory and recognizing optimal inventory rules
capability of data mining techniques in providing important              to be maintained. Prior to perform the two aforesaid functions,
analysis such as launch analysis and slow turning analysis.              a database of historical data has to be maintained. The
Such analysis helped in providing car market with base for               database holds the historical record of inventory over N p
more accurate prediction of future market demand.
                                                                         periods in N s SC members, say, [ I ij ] N P × N S ; 0 ≤ i ≤ N P − 1
    Tao Ku et al. [39] have presented a complex event mining
                                                                         and 0 ≤ j ≤ N S − 1 . Initially, the Exponential Moving
network (CEMN) and defined the fundamentals of radio-
frequency     identification    (RFID)-enabled     SC     event          Average (EMA) is determined for the historical data as
management. Also, they have discussed how a complex event                follows
processing (CEP) could be used to resolve the underlying
architecture challenges and complexities of integrating real-             I ema lj = I prev lj + α ( I (l + n) j − I prevlj ) ; 0 ≤ l ≤ N P − (n + 1) (1)
time decision support into the supply chain. Finally, a
distributed complex event detection algorithm based on
                                                                         where,
master-workers pattern was proposed to detect complex events
and trigger correlation actions. Their results showed that their
approach was more robust and scaleable in large-scale RFID                                    I ema (l −1) j ; if l > 0
application.                                                                                 
                                                                                             
                                                                                  I prevlj =  1 n −1                                                (2)
    Se Hun Lim [40] has developed a control model of SCM
sustainable collaboration using Decision Tree Algorithms
                                                                                             
                                                                                             n i=0
                                                                                                       ∑I ij     ; otherwise
                                                                                             
(DTA). He has used logistic regression analysis (LRA) and
multivariate determinate analysis (MDA) as a benchmark and
compared the performance of forecasting SCM sustainable                      The EMA values of the original historical data for N P − n
collaboration through three types of models LRA, MDA,                    periods,  [ I emalj ] ( N P − n) × N S from     (1),    where,
DTA. Forecasting SCM sustainable collaboration using DTA
was considered as the most outstanding feature. The obtained             α = 2 /(n + 1) (termed as constant smoothing factor), is
result has provided useful information of SCM sustainable                subjected for a decision making process as follows
collaboration determining factors in the manufacturing and
distributing companies.                                                                        shortage ; I
                                                                                                            ema lj < I th
    Shu-Hsien Liao et al. [41] have investigated functionalities                    '          
that best fit the consumer’s needs and wants for life insurance                   I ema lj   = balance ; I ema lj = I th                            (3)
products by extracting specific knowledge patterns and rules                                   
                                                                                               excess ; I ema lj > I th
from consumers and their demand chain. They have used the                                      
apriori algorithm and clustering analysis as methodologies for
data mining. Knowledge extraction from data mining results                   As       given        above,      EMA-based          inventory        data
was illustrated as market segments and demand chain analysis                 '
on life insurance market in Taiwan in order to propose                   [ I emalj ] ( N P − n)× N S   is obtained in which the original
suggestions and solutions to the insurance firms for new                 historical data is converted into three different states of
product development and marketing.                                       inventory which include shortage, balance and excess.
    Xu Xu et al. [42] have proposed an approach that                     Subsequently, the association rules for inventory are mined
combines expert domain knowledge with Apriori algorithm to               from the previously obtained EMA-based inventory data.
discover the pattern of supplier under the methodology of                A. Mining Association rules for inventory using Apriori
Domain-Driven Data Mining (D3M). Apriori algorithm of
                                                                             One of the two major functions of the approach, mining
data mining with the help of Intuitionistic Fuzzy Set Theory
                                                                         association rules for inventory is described in the sub-section.
(IFST) was employed during the process of mining. The
                                                                         Mining the association rules for inventory is to find the
obtained overall patterns help in deciding the final selection of
                                                                         relationship between the inventories of the SC members. In the
suppliers. Finally, AHP was used to efficiently tackle both
                                                                         proposed approach, we utilize Apriori, a classic algorithm for
quantitative and qualitative decision factors involved in
                                                                         learning        the        association        rules.        Let,
ranking of suppliers with the help of achieved pattern. An
                                                                           '          '       '           '       be the itemset taken from
example searching for pattern of supplier was used to                      I ema , I ema , I ema , L , I ema     
demonstrate the effective implementation procedure of their                     l1      l2      l3          lN S 

method. Their method could provide the guidelines for the
decision makers to effectively select their suppliers in the
                                                                         the EMA-based inventory data I ema      {  '    }
                                                                                                                      lj ( N − n )× N
                                                                                                                            P         S
                                                                                                                                        . The itemset

current competitive business scenario.




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                                                                                                            ISSN 1947-5500
                                                                     (IJCSIS) International Journal of Computer Science and Information Security,
                                                                     Vol. 8, No. 2, May 2010



                  '   {
and the dataset I emalj       }( N   P − n)× N S
                                                   are subjected to Apriori            rules are obtained where each set has R 'j number of rules and
for mining association rules. Initially, the Apriori finds the                         they need not to be in equal number. From the N s set of rules,
frequent itemsets with a minimum support threshold s min , and                         a rule per each SC member (i.e. a rule per set) is selected using
determines the rule which states the probabilistic relationship                        GA. The rules are chosen in such a way that they have major
between the items in the frequent itemsets with a minimum                              impact over the SC cost.
confidence of c min .
                                                                                       B. Selecting SC cost-impact rules using GA
    The Apriori determines the association rules from the                                  The obtained rules from apriori are the frequently occurred
frequent itemset by calculating the possibility of an item to be                       events in the past and so they illustrate that they have a good
present in the frequent itemset, given another item or items is                        impact over the SC cost, but not strongly. To identify the rules
                                                                                       that have strong impact over the SC cost (SC cost-impact
present. For instance, considering a frequent itemset, I '                    ,
                                                                      emal1            rules), it is essential to consider the shortage cost and holding
                                                                                       cost. It is already known that the SC cost increases, when
I '         and I '       in which a rule may be derived as when                       either of the shortage and holding costs increases. Hence, by
 emal 2          emal 3
                                                                                       considering the shortage or holding cost in the GA, SC cost-
the inventory in I '              and I '          are excess in a period              impact rules can be obtained. The process of selecting SC
                          emal1           emal 2
                                                                                       cost-impact rules using GA is explained as follows
                                                      '
l ; l ∈ (0, N P − (n + 1)) , then the inventory in I ema is likely
                                                                l3                        Step              1:                      Generate                              initial
to be shortage. The general syntax of the rule for the aforesaid                       chromosomes, X a = [ x (a ) x ( a ) x ( a ) L x ( a ) ] ;     0 ≤ a ≤ N pop − 1 ,
                                                                                                             0      1        2         N −1
example                         is                         given                                                                            S

       '                  '                        '
as ( I ema l1 = excess, I ema l 2 = excess ) → ( I ema l 3 = Shortage)                 where N pop is the population size. The j th gene of the
; c ≥ c min . Hence, by using the apriori, the association rules                       chromosome x (ja ) ; 0 ≤ j ≤ N S − 1 is an arbitrary integer in the
are mined with a minimal confidence c min based on the
                                                                                       interval (0, | R 'j | −1) , where, R 'j is the cardinality of the rule
frequent itemset with a minimal support s min .

      The      mined      rules        are    given       as { A}q → {B}q ;            set belongs to the j th SC member.
0 ≤ q ≤ N r − 1 , where, { A}q and {B}q are the antecedent and                             Step 2: Determine fitness of the chromosomes present in
                                                                                       the population pool using the fitness function
                          th
consequent of the q            rule respectively and N r be the
number of association rules generated. The antecedent and                                                                           1
consequent consists of one or more items that belongs to the                                f (a) =                                                                          (6)
                                                                                                      N S −1
                                                                                                                                                            
        
itemset  I '
                  
           ema lj 
                                   
                    (i.e. { A} q ⊆  I '
                                            
                                      emalj 
                                                        
                                              , {B} q ⊆  I '
                                                                 
                                                           emalj 
                                                                   )                                   ∑      C I × µ ema ( R 'j ( x ( a ) )) × c ' ( a ) 
                                                                                                              j          j           j           R j (x j ) 
                                                                                                  j =0                                                
and also it satisfies { A}q ∩ {B}q = φ . After obtaining the
                                                                                       where,
association rules, they are allocated for j th SC member based
on the consequent of the rules. The final rules after allocation                                        S ; if µ               ' (a)
are obtained as follows                                                                                  cj          ema j ( R j ( x j )) < 0
                                                                                                        
                                                                                                                                      (a)
                                                                                               CI j   =  H c j ; if µ ema j ( R 'j ( x j )) > 0                             (7)
                            R 'j = R j − φ                                (4)                           
                                                                                                        0 ; if µ              ' (a)
                                                                                                                    ema j ( R j ( x j )) = 0
where,                                                                                                  


                                                                                                                                            ∑
                                                                                                                           1
              { A} → {B} ; if I '     ∈ {B}q                                          µ ema j ( R 'j ( x (ja ) )) =                                        I ema k          (8)
               q        q       emalj                                                                                 F       (a )                                   j
         Rj =                                                            (5)                                          R 'j ( x j ) k ∈(0, N P − ( n +1))
              φ
                         ; else
                                                                                           In (6), f (a ) is the fitness value of a th chromosome, C I j
      Using (5), the rules R 'j which have the element I '     in
                                                        ema lj                         (determined using (7)) is the inventory cost incurred by the
                                                                                                                                 (a )
the consequent are assigned to the j th SC member. Each SC                              j th SC member, µ ema j ( R 'j ( x j )) ( determined using (8)) is
member has its own rules that illustrate its inventory’s state                         the mean EMA value of the I ema l that are taken only from
with respect to other SC member or members. So, N s set of                                                                              j




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                                                                                                                           ISSN 1947-5500
                                                            (IJCSIS) International Journal of Computer Science and Information Security,
                                                            Vol. 8, No. 2, May 2010



                                              (a )
the pattern which satisfies the rule R 'j ( x j ) and c ' ( a )                                     N S −1
                                                                                                             C × µ        ' best 
                                                       R j (x j )                   SC   best
                                                                                                =    ∑        Ij
                                                                                                             
                                                                                                                    ema ( R j ( x j )) 
                                                                                                                                       
                                                                                                                                                         (9)
                                      (a )
is the confidence of the rule R 'j ( x j ) . In (7), S c j is the                                    j =0

shortage cost incurred for a unit of shortage in j th SC                                             N S −1
                                                                                                      ∑ c R j ( xbest )
                                                                                           1
member, H c j is the holding cost incurred for a unit to hold in                 c best =                                                               (10)
                                                                                          NS                     j
                                                                                                      j =0
the j th SC member. In (8), F ' ( a ) is the frequency of
                             R j (x j )                                        Similarly, the mean SC cost and the mean confidence are
                                                           (a )
occurrence of data pattern that satisfies the rule R 'j ( x j ) and         determined for all the remaining rules in the rule set R 'j .               { }
                                                                            Then, the efficacy is compared by determining the difference
I emak is the EMA value of inventory in j th SC member that                 between the SC cost and confidence of the final SC cost-
       j
                                                                            impact rule and the mean SC cost and the mean confidence of
                                                                          the remaining rules, respectively.
are available in the data pattern, where, I emak ∈  I emal  .
                                                j         j
                                                                                                     V. RESULTS AND DISCUSSION
   Step 3: Select the best N pop / 2 chromosomes, which
                                                                                 The proposed approach for optimal inventory control has
have minimum fitness, from the population pool.                             been implemented in the working platform of JAVA (version
   Step 4: Crossover the selected chromosomes with a                        JDK 1.6) and the results are discussed in this section. The
                                                                            inventory data (weekly data) has been simulated for five years
crossover rate of CR so as to obtain N pop / 2 children
                                                                            (i.e. N p = 260 ) by considering five SC members
chromosomes.
                                                                            (i.e. N s = 5 ), an agent A1 and four retailers, R1 , R2 , R3
   Step 5: Mutate the children with a mutation rate of MR                   and R4 . In the simulated inventory data, the negative and
which leads to N pop / 2 new chromosomes.
                                                                            positive values represent the shortage amount of inventory and
                                                                            excess amount of inventory respectively. All the SC members
   Step 6: Place the N pop / 2 new chromosomes and
                                                                            have been considered to have the shortage cost and holding
N pop / 2 parent chromosomes in the population pool.                        cost as S c = Rs.2.50 and H c = Rs.1.00 respectively. The
                                                                               '
                                                                             I ema determined from the simulated data with n = 7 is given
   Step 7: Go to step 2, until the process reaches a maximum
number of iterations N g . Once the process reaches N g ,                   in the Table I.
terminate it and select the N pop / 2 best chromosomes, which                 TABLE I. A SAMPLE OF EMA-BASED INVENTORY DETERMINED FROM THE
have minimum fitness value.                                                                                   SIMULATED DATA


   The best chromosomes obtained from the GA indicate                         Sl.
                                                                                     A1               R1             R2          R3            R4
N pop / 2 set of rules in which each set has N s rules (one rule              No
                                                                              1      Excess           Shortage       Excess      Excess        Excess
per SC member). From the rule obtained for a particular SC
member, it can be decided that                                                2      Excess           Shortage       Excess      Shortage      Shortage
                                                                              3      Excess           Shortage       Excess      Shortage      Shortage
   •        The inventory will likely to be as in the rule given for
           the inventory of the associated SC members.                        4      Excess           Shortage       Excess      Shortage      Excess

   •        Either by reducing or by increasing the holding level               The first major function of the proposed approach, mining
           of inventory (can be decided from the rule) in the SC            association rules for inventory using Apriori has been
           member, an optimal level of inventory can be                     implemented with the aid of data mining software WEKA
           maintained in the upcoming days.                                 (version 3.7). The Table II and the Table III consist of some
    Hence, by the optimal inventory control, the SC member                  frequent itemsets with s min = 10% that are discovered from
will not be suffered either by increased shortage cost or by                      '
                                                                            the I ema and some of the association rules generated from the
increased holding cost. This ultimately helps to keep the SC
cost in a controlled manner.                                                discovered frequent itemset respectively. The rules that are
                                                                            categorized based on the consequent are shown in the Table
C. Evaluation of Rules                                                      IV.
    The efficacy of the rules is demonstrated by comparing the
obtained rules with all the remaining rules. To accomplish
this, the SC cost and the confidence of the rule associated to
the best chromosome are determined as




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                                                                                                                 ISSN 1947-5500
                                                                  (IJCSIS) International Journal of Computer Science and Information Security,
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                  TABLE II. SOME FREQUENT ITEMSETS DISCOVERED FROM
                                                                               '
                                                                             I ema AT LENGTHS L1 , L2 , L3   AND   L4 , AND THEIR SUPPORT.

                     Length of
                                                                    Frequent itemset                                     Support %
                     the itemset
                                        R1=Shortage 0.536                                                                53.6
                     L1                 R1=Excess 0.476                                                                  47.6
                                        R2=Excess 0.6                                                                    60
                                        R1=Shortage, R2=Excess 0.316                                                     31.6
                     L2                 R1=Shortage, R2=Shortage 0.22                                                    22
                                        R1=Shortage, R3=Excess 0.224                                                     22.4
                                        R1=Shortage, R2=Excess, R3=Excess 0.128                                          12.8
                     L3                 R1=Shortage, R2=Excess, R3=Shortage 0.188                                        18.8
                                        R1=Shortage, R2=Excess, R4=Excess 0.132                                          13.2
                                        R1=Shortage, R2=Excess, R3=Shortage, R4=Shortage 0.1                             10
                     L4
                                        R1=Shortage, R2=Excess, R3=Shortage, A1 =Shortage 0.104                          10.4

                               TABLE III. SOME GENERATED ASSOCIATION RULES WITH c min = 30% AND THEIR CONFIDENCE

                    Sl.
                                                             Association Rules                                         Confidence %
                    No
                    1         R2=Excess, R4=Shortage, A=Excess ==> R1=Shortage                                         79
                    2         R1=Excess, A=Excess ==> R3=Shortage                                                      76
                    3         R1=Excess, R4=Excess, A=Shortage ==> R2=Excess                                           75
                    4         R1=Shortage, R4=Shortage, A=Excess ==> R2=Excess                                         72

                             TABLE IV. SOME OF THE RULES THAT ARE CATEGORIZED BASED ON THE CONSEQUENT OF THE RULES

            Sl. No        Rule for A1               Rule for R1              Rule for R2           Rule for R3               Rule for R4
                          (R1=Excess,               (R2=Excess,              (R1=Excess,                                     (R1=Excess
                                                                                                   (R1=Excess,
                          R3=Excess)         →      R4=Shortage,             R4=Excess,                                      ,R2=Excess,
            1                                                                                      A1=Excess) →
                          A1=Shortage               A1=Excess) →             A1=Shortage)                                    R3=Shortage)
                                                                                                   R3=Shortage
                                                    R1=Shortage              → R2=Excess                                     → R4=Excess
                                                                             (R1=Shortage,         (R4=Excess,               (R1=Excess,
                          (R2=Shortage,             (R3=Excess,
                                                                             R4=Shortage,          A1=Excess) →              R2=Excess) →
            2             R3=Excess)    →           A1=Excess) →
                                                                             A1=Excess) →          R3=Shortage               R4=Excess
                          A1=Shortage               R1=Shortage
                                                                             R2=Excess
                          (R1=Shortage,             (R3=Excess,              (R1=Excess,           (R2=Shortage,             (R1=Shortage
            3             R2=Shortage) →            R4=Shortage)             R4=Excess)      →     A1=Excess) →              ,R3=Excess) →
                          A1=Shortage               → R1=Shortage            R2=Excess             R3=Shortage               R4=Shortage
                                                                             (R1=Excess,           (R1=Shortage,
                          (R2=Shortage              (R2=Excess,                                                              (R2=Shortage,
                                                                             R3=Shortage,          R2=Excess,
            4             ,R4=Shortage )→           R4=Shortage)                                                             R3=Excess) →
                                                                             R4=Excess) →          A1=Shortage)
                          A1=Shortage               → R1=Shortage                                                            R4=Shortage
                                                                             R2=Excess             → R3=Shortage

In selecting the SC cost-impact rules, the GA has been                             TABLE V. THE RULES ASSOCIATED TO THE CHROMOSOME, WHICH IS GIVEN IN
                                                                                                               THE FIG. 1.
initialized    with    a    chromosome     length     =  5
(i.e. number of genes = 5 ), N pop = 10 and N g = 50 . The                           Gene. no                    Associated rules
generated initial chromosome and the rules that are associated                       0               R4 = -12.46 --> R1 = -11.7, R3 = -8.64
to the chromosome are given in the Fig. 1 and the Table V,                           1               R3 = -11.32 --> R2 = -9.09
respectively.                                                                        2               R4 = -12.46 --> R1 = -11.7, R3 = -8.64
                                                                                     3               R2 = -8.84 --> R4= 6.26
                                                                                     4               R1 = -11.91 --> A1 = -45.6

 Figure 1. An initial chromosome of length ‘5’ with random values in their            The generated chromosomes have been subjected to
                                 genes
                                                                                   crossover with CR = 0.6 and the obtained children have been



                                                                              48                                   http://sites.google.com/site/ijcsis/
                                                                                                                   ISSN 1947-5500
                                                                    (IJCSIS) International Journal of Computer Science and Information Security,
                                                                    Vol. 8, No. 2, May 2010



subjected to mutation with MR = 0.4 . In the mutation, the                         The final SC cost-impact rules that are associated to the
gene values in the mutation point are changed arbitrarily so                       obtained best chromosomes are given in the Table VI.
that new chromosome is obtained from the child chromosome.
                  TABLE VI. SOME OF THE FINAL SC COST-IMPACT RULES ASSOCIATED TO THE BEST CHROMOSOMES OBTAINED FROM GA.

              Solution                                            Best SC cost-impact Rules
                no.        A1                          R1                R2              R3                                  R4
                           R4 = -11.84 →               R4 = -10.33 →                     R4 = 9.67                     →
                                                                         R4 = -11.62 →                                       R3 = -8.55 →
                  1        R2 = -10.89, A1 =           R1 = -12.02, A1                   R1 = 14.12,                   R3
                                                                         R2 = -10.02                                         R4 = -12.11
                           -45.89                      = -46.68                          = -12.52
                           R4 = -11.84 →               (R2 = 10.15, A1                   R4 = 9.67                     →
                                                                         R4 = -11.62 →                                       R3 = -8.55 →
                  2        R2 = -10.89, A1 =           = 25.94) → R1                     R1 = 14.12,                   R3
                                                                         R2 = -10.02                                         R4 = -12.11
                           -45.89                      = -11.56                          = -12.52

    All the obtained rules in a solution provide their combined                    impact rules. It could also be decided, whether the inventory
contribution in the SC cost. The SC cost given by the solution                     has to be reduced or increased in the particular SC member.
was very high in the past records and so, by considering those                     Also, an EMA level of inventory to be reduced or increased
rules in the solution, the SC cost can be reduced in the future.                   can also been determined from the obtained SC cost-impact
The cost reduction can be accomplished by inverse holding of                       rules. Thus, the SC cost will be reduced proficiently by the
inventory that has been obtained as a rule for a particular SC                     proposed optimal inventory control approach that paves the
member. From Table VI, by keeping 46, 12, 10, 13 and 12                            way for effective SCM.
(approximately) units of products additionally in the SC
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                                                                                                        Mechanical Engineering from Gulbarga and Karnataka
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                                                                                                        Universities, Karnataka, INDIA in 1991 and 1994
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                                                                                                        respectively, he is currently pursuing the Ph.D. degree in
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      2005.                                                                                             Ravindranath. He is presently working as a Assistant
[27] Kamrul Abedin Tarafder , Shah Mostafa Khaled , Mohammad Ashraful                 Professor in the Department of Mechanical Engineering, Proudadevaraya
      Islam , Khandakar Rafiqual Islam, Hasnain Feroze, Mohammed                      Institute of Technology, Hospet. Visvesvaraya Technological University,
      Khalaquzzaman and Abu Ahmed Ferdaus, "Reverse Apriori Algorithm                 Karnataka India and also visiting faculty for Diploma, and P.G Courses. And
      for Frequent Pattern Mining", in proc. of Asian Journal on Information          is a member for Professional bodies like MISTE and MIE.
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      of the 2004 ACM symposium on Applied computing, Nicosia, Cyprus,                                  M.E (Industrial Engg.) Degrees from Sri Vekateshwara
      pp: 530-534, 2004.                                                                                University, Tirupati Andra Pradesh India in 1971 and 1976
[29] Bart Goethals, "Survey on Frequent Pattern Mining", Technical report,                              respectively and later completed his Ph.D from Institute of
      Helsinki Institute for Information Technology, 2003.                                              Technology, Delhi in 1985. He worked as a Professor and
                                                                                                        Head, Department of Mechanical Engineering and also
[30] M.H.Margahny and A.A.Shakour, "Scalable Algorithm for Mining
                                                                                                        Principal of Sri Venkateshwara College of Engineering, Sri
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                                                                                      Venkateshwara University, Tirupati Andra Pradesh INDIA. During this period
[31] E. Ansari, G.H. Dastghaibifard, M. Keshtkaran and H.Kaabi, "Distributed          he has visited Pennsylvania University, USA, and Hamburg University,
      Frequent Itemset Mining using Trie Data Structure", in proc. of Intl.           Germany and presented papers in International conference. He has awarded
      Journal on Computer Science, vol. 35, no. 3, 21 August 2008.                    best teacher by the Govt. of Andhra Pradesh in 2007, and having a teaching
[32] Ayahiko Niimi and Eiichiro Tazak, "Rule Discovery Technique Using                experience of 32 years, he worked as a Dean faculty of Engineering, Chairman
      Genetic Programming Combined with Apriori Algorithm", Lecture                   Board of Studies (UG and PG) and also Dean of Examinations. He has more
      Notes In Computer Science, Springer-Verlag, vol. 273- 277, London,              than 70 research paper publications in International and National journals in
      UK, 2000.                                                                       his credit. He has produced 7 Ph.D scholars and another 8 are in pipeline.
                                                                                      Presently working as a Principal of Annamacharya Institute of Technology,
                                                                                      Tirupati. And is a member for Professional bodies like MISTE and MISME.




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