Developing an Intelligent Inventory Control Model, Applying Fuzzy Logic and Association Rule Mining

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 9, September 2012)

149

Developing an Intelligent Inventory Control Model, Applying

Fuzzy Logic and Association Rule Mining

Hamid Reza Rezaei

Computer management Pune University, Pune, India

Abstract - The key issue of inventory management is the problem of safety stock control. The existence of imprecise data makes this control complex. Fuzzy logic (FL) is widely used to develop expert system, due to its ability in representing imprecise data. Therefore, in this study a fuzzy logic system and theory have been used that incorporate the linguistic variable more practically and also help in eliminating the imprecision and vagueness of the system. In addition to it, weighted association rule has been applied to extract related target items as inputs to Fuzzy Inference System (FIS) according to their significance in the dataset rather than their frequency alone. Three inputs to FIS are: 1-proposed index, i.e., WFSN(Weighted- Fast Slow-Non moving) which take both the item movement in inventory and value into account, computed based on support in association rule.2-WC(Weighted cost), extracted from association rule 3-Leadtime and output is Safety stock ,based on interview with experts. In this paper we propose integration of weighted association rule and FIS to develop an intelligent model of inventory control system. Then a calculation example is presented in MATLAB7.8.0 (R.2009.a) to test the feasibility of the model.

Keywords - fuzzy inference system, fuzzy logic, safety stock, weighted association rule, wfsn (weighted fast –slow- non moving) item.

I. INTRODUCTION

Fuzzy logic(FL), originally introduced by Lotfizadeh [1], is widely used to design and develop an Expert System over the past few years, due to its ability in representing the vagueness and imprecise data. Therefore we decided to apply it in inventory control to develop an intelligent inventory control system. Inventory control system is crucial in supply chain management. In traditional model, most of current management, effects of variation in lead time as well as demand are computed based on probability and occurrence of stock out. Reliable amount of safety stock can decrease, out of stock cost, capital cost as well as storage cost. In this study safety stock is considered a fuzzy output and three inputs namely lead time, weighted cost and a proposed index for speed movement of an item in inventory i.e., WFSN(weighted fast-slow-non moving) extracted from association rule which is discussed in section III.

It is important to mention that, in certain situation and real life, existence of imprecise data for lead time, safety stock and demand rate was assumed, because of a variety of parameters such as season, special festivals, availability of items in market, transportation and so on. So unlike to conventional model which parameters are considered precise and mathematically, in this situation uncertainties are due to fuzziness and in this case the fuzzy set theory is applicable. The aim of this research work was to design a Fuzzy Expert System to control and improve inventory performance to obtain safety stock in retail sector. So rules were designed which were based on defined membership functions. Rules are expressed in antecedent-consequent form, such as:

Rule 1: If x is A, then y is B, Where A and B represent fuzzy propositions. Output is later defuzzified to obtain a crisp value. [2].

In this paper, FL incorporates a Rule-based approach to solve inventory control and prediction system rather than attempting to model a system mathematically. So it focuses on operator’s experience as well as association rule data mining and uses imprecise but very descriptive language to deal with input data more like a human operator to determine safety stock. Data could extract based on association rule mining as well as experience and pre-processed to classify in fuzzy model. It is important to mention that, association rules should not be used directly for prediction without further analysis or domain knowledge .They do not necessarily indicate causality. They are, however, a helpful starting point for further exploration, making them a popular tool for understanding data. [3]. so we combined weighted association rule with fuzzy inference system to develop a model for controlling safety sock.

II. ASSOCIATION RULE BASIC

Let the mining association rules be as follows: I= {i1,

i2, ... , in} is a set of items, T={t1, t2, ... , tm} is a set of

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An association rule is an implication of the form: X→ Y, where X⊂ I, Y⊂I and X ∩Y= ∅. X (or Y) is a set of items, called item set. The rule X



Y holds in the database D with support degree s, which means that percentage of transaction records containing X



Y in D is s.

s=support(X



Y) =p(X



Y)

Apriory is a first well-design algorithm proposed by R.Agrawal and R.Srikant in 1994 for mining frequent item sets for Boolean association rules that is incorporated in many data mining software. Pseudo code is written based on Apriory algorithm.TableI. [3][4][5]

For each given transaction database D, f (D) = Mm*n, where M is defined as follows:

M ij=

1

0

J i

j i

I T

I T

 







Where m denotes the number of records and n denotes the number of items. After scanning the transaction database Boolean matrix would be created. For example the transaction database shown in table II is mapped into matrix M. [4]

Table. 1

---

Pseudo-code-Association Rule

Join Step: Ck is generated by joining Lk-1with itself

Prune Step: Any (k-1)-item set that is not frequent cannot be a subset of a frequent k-item set

Ck: Candidate item set of size k

Lk: frequent item set of size k

L1= {frequent items};

for(k= 1; Lk!=∅; k++) do begin Ck+1= candidates generated from Lk;

for each transaction t in database do

increment the count of all candidates in Ck+1that are contained in t

Lk+1= candidates in Ck+1 with min_support

end

return ∪k Lk ;

---Table 2

TID Item

T1 I2,I3

T2 I1,I2,I5 T3 I1,I4 T4 I2,I4,I5 T5 I2,I3,I4

In this matrix rows show transaction (t), columns indicate items of transaction Support-count (IJ) =

1

m

ij i

t





If the support degree of an item set is greater than a minimum threshold that means item set satisfies the minimum threshold .Then the item set is called frequent item set. All the frequent k-item set is denoted as Lk.

Different weights to different item as well as item set are given according to the relative profit of them which it improves traditional association rules algorithm considering items in the database in an equal and consistent manner.[4].In addition to different weights to different item and item set [4] ,we propose WFSN (weighted Fast-Slow-Non moving) as an evaluation index to evaluate the importance of inventory items in terms of weighted consumption figure of item extracted from association rule mining.

III. DEFINITION OF RELATED CONCEPT

In Boolean matrix of transaction given item set I={i1,i2,…,in} and transaction T={t1,t2,…tm} , we propose and compute WFSN(weighted fast-slow-non moving) as a index to evaluate item movement along with value-usage. 1. Item speed movement, FSN stands for fast-slow-non moving:

FSN (ij) =

 

1

support

count

support

count

j

n

j J

i





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2. Item weight: W (Ij) =

1

( )

j n

j j

profit i





3. Weighted speed movement (PROPOSED INDEX) WFSN for each item is computed as below:

WFSN (ij) =W (ij)*FSN (ij)

4. Transaction weight: Transaction weight is a type of item set weight which is value attached to each of transaction.

W (tk) =

( )

j

i t

k

w i

t





,

t

_k is the amount of items in transaction tk

5. Weighted support: Given an item set X and X



I,

weighted support of X is denoted as wsp(X):

Wsp(X) = &

( )

k k

k

t D X t

k

t D

w t

 





6. Weighted value-usage: WC(x) = wsp(X)

cos ( )

j

i X

t i





, cost (ij) is the cost or value-usage of item ij.

7. Lead time fluctuates between Max and Min lead time for each item.

8. In this paper safety stock (SS) is output as per simulated data and 3 fuzzy inputs namely WFSN, WC (weighted cost) and lead time.

Table. 3

No: Input to Fuzzy Inference System(FIS)

Output of FIS

1- WFSN(Weighted Fast-Slow-non Moving)

Safety Stock 2- Weighted Cost(WC)

3- Lead Time

IV. FUZZY INFERENCE SYSTEM

Fuzzy inference systems (FISs) are also known as fuzzy rule-based systems, fuzzy model, fuzzy expert system, and fuzzy associative memory.

This is a major unit of a fuzzy logic system [6]. This system formulates the mapping from a given input to an output using fuzzy logic. The most important types of fuzzy inference method are Mamdani’s fuzzy inference method, which is the most commonly seen inference method. This method was introduced by Mamdani and Assilian (1975) [7]. Another well-known inference method is the so-called Sugeno or Takagi–Sugeno–Kang method of fuzzy inference process. This method was introduced by Sugeno (1985) [8].This method is also called as TS method. The main difference between the two methods lies in the consequent of fuzzy rules. Mamdani fuzzy systems use fuzzy sets as rule consequent whereas TS fuzzy systems employ linear functions of input variables as rule consequent [6]. There are five primary GUI tools for building , editing, and observing fuzzy inference system or FIS editor, the Membership Function Editor, the Rule Editor, the Rule Viewer and Surface Viewer .Fugure.1 [9]. In this research, it has been assumed that rules are being laid down by experts and the fact that expert opinions are being used in the framework of different procedures of weighting to determine the weight of rules. Thus, these researches are not taken into account in the learning process.

Figure1.Fuzzy Inference System

[image:3.612.337.551.638.680.2]

The primary function of the system as per figure 2 is to establish a mapping from a given input to an output using fuzzy logic.

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 Mamdany Method

Mamdani FIS is the most known or used in developing fuzzy models. The output of the system is generally defuzzified resulting fuzzy sets are combined using

aggregation operator from the consequent of each rule of the input.

A single if-then rule is written as; IF “X” is A, THEN “Y” is B

Where, A and B are linguistic values defined by fuzzy sets on the ranges; X and Y, respectively. The if-part of the rule “x is A” is called the antecedent or premise, while the then-part of the rule “Y is B” is called the consequent or conclusion. [9].

V. DEVELOP AFISIN THE SPECIAL CASE (INVENTORY CONTROL)

Input and Output variables in the fuzzy inference system are effectively defined in Table.3

The process of fuzzy inference was applied for:  Defining Membership Function

 Designing Fuzzy Logic Inference If-Then rules  Defuzzificaton

The Mamdani was selected as the fuzzy inference system (fis). Two membership functions were selected to be combined; these are the generalized triangular (trimf) and the Gaussian curve (gaussmf). The model designed to accommodate the learning process, triangular and Gaussian curve for each fuzzy variable was adjusted to show system performance approaching optimum as in Figures.3

To identify safety stock twenty seven rules could be formulated. Rule reduction also would be applied. Some of these rules are:

-If WFSN =Low, WC=Low Lead-time=Low Then Safety stock is Low

-If WFSN =Low, WC=Med Lead-time=Med Then Safety stock is Med

Demonstrated in Figure.4

Figure.3: FIS editor in MATLAB

The defuzzification method selected in this study is Centroid of area (COA).

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VI. TESTING ACCURACY OF FIS

Fuzzy inference system provides some in-built tools which could be used to verify the result. The Rule viewer was used to verify the result Figure.4.”evalfis” by MATLAB was used to perform fuzzy inference calculation. Output=evalfis (input, fismat)

It is noticeable, in model designing to accommodate the learning process, triangular and gaussian terms parameter for each fuzzy variable should have set to actual data in any different case. This model provides a general framework to predict safety stock based on fuzzy logic and membership function , in each study membership function should be optimized by different algorithm such as Genetic algorithm or assigned by Neural network, otherwise the model will have large error.

VII. CONCLUSION

This paper combines fuzzy logic and weighted association rule to develop a model for inventory control. Taking advantage of the strong ability of weighted inter correlation of association rule, we can obtain the core knowledge from a lot of original data, which greatly enhances the model efficiency. And fuzzy logic can fully approximate any linguistic relationship, due to existence of imprecise data.

This model provides a general framework to predict safety stock and membership function of each fuzzy variables to be optimized corresponding to data set.

REFRENCES

[1 ] Zadeh, L. A. (1965), “Fuzzy sets. Information and Control”, Vol. 8, pp.338–353

[2 ] Timothy J.Ross.(1995),”Fuzzy logic with engineering applications”, New Mexico, McGraw Hill

[3 ] Han.J, Kamber .M..”Data Mining Concepts and Techniques”,2nd edition, Elsevier,2006,PP 239-274

[4 ] L. Zhenyu, W. J. Yan, Zhenying,”Application Of Association Rules Mining In Inventory Classification” ,2009,IEEE,Second International Workshop on Computer Science and Engineering,pp.599-602

[5 ] M.H.Dunham,” Data Mining Introductory And Advanced Topic ”,Pearson, Education ,2003,PP164

[6 ] Sivanandam.S.N,Sumathi.S,Deepa.S.N,” Introduction To Fuzzy Logic Using MATLAB”,Springer,2007

[7 ] Mamdani EH, Assilian S (1975) An experiment in linguistic synthesis with a fuzzy logic controller. Int J Man_Machine Studies, 7(1), PP 1-13.

[8 ] Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15(1),PP 116–132