Decision Support System for Inventory Management

ISBN 978-602-95532-9-1

Decision Support System for Inventory Management in Pharmacy Using Fuzzy Analytic Hierarchy Process and Sequential Pattern Analysis Approach Rendra Gustriansyah

Faculty of Computer Science University of Indonesia Depok, Indonesia [email protected]

Dana Indra Sensuse


Abstract—A pharmacy typically store pharmaceutical products in warehouses before being sold to the customer. Stacking of products in the warehouse can reduce the efficiency of the warehouse and increase the costs associated with inventory, which raised the problem of how to predict the stock of each product to the right in order to avoid excess/shortages. Therefore, this study aims to develop a decision support system for inventory management in pharmacy, especially to predict next inventory using FAHP and SPA approach, so the prospect of inventory management will be more optimal. The study also proposes a model to predict inventory. These results indicate that the inventory prediction accuracy using this model approach more accurate 18% than the inventory prediction accuracy by a pharmacy inventory manager, so this approach can be referred to as a decision support system. Keywords—inventory management; sequential pattern analysis

pharmacy;

FAHP;

Arief Ramadhan


Generally, studies using the FAHP method discuss the issue of selections [14–16], location [17], services [18], [19], classification [20], evaluation [21], [22] and valuation [13]. While studies using the SPA method, generally try to find patterns of buying customers behavior [6], [9], [23]. In addition, most studies of inventory management is associated with the Supply Chain Management (SCM) in an industry. Meanwhile, the studies that implement inventory management in the pharmacy is still very little [1], [24]. Therefore, it is developing a decision support system (DSS) for pharmacy inventory management in a way to predict the next period of purchase of pharmaceutical products with FAHP and SPA approaches, in order to reduce excess stock and avoid shortages, so the costs associated with inventory management in pharmacy can be minimized.

I. INTRODUCTION

II. LITERATURE

In the pharmaceutical world, inventory is the largest investment in a pharmacy, whose value continues to increase due to the growth of varieties and the cost of pharmaceutical products [1]. In order for the inventory to be maintained, then the pharmacy should be able to predict the next inventory quantity.

A. Decision Support System The concept of Decision Support System (DSS) was first disclosed in the early 1970s by Michael S. Scott Morton with the term Management Decision Systems [25].

Previous studies indicate that the neural network [2], [3], a mathematical model [4], [5] or data mining [6–9] can be adopted to predict future inventory. In the field of data mining, Sequential Pattern Analysis (SPA) is an effective approach for identifying recurring patterns of products included in time series [6]. But other factors affecting inventory management in pharmacy should be included in the SPA, so that inventory management can be efficient [10]. The importance of these factors can be identified through experts opinion [11]. Experts opinion will be analyzed by the Fuzzy Analytic Hierarchy Process (FAHP) method, which can overcome the uncertainty and inaccuracy in the decision-making process [12]. FAHP method is adopted to minimize subjectivity of experts assessment matrix [13].

International Conference on New Media (CONMEDIA) 2015

DSS is a system of specific information intended to assist the management to take decisions relating to issues that are semi-structured, and does not replace the function of the decision maker to make decisions [25]. B. Inventory Management Inventory management is a branch of business management focused on planning and inventory control [26]. Inventory management is a function that is responsible for all decisions regarding the stock in an organization. In inventory management made policies, activities and procedures to ensure the proper amount of stock of each product for a certain time [27]. From a financial and operational perspective, efficient inventory management plays an important role in the

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ISBN 978-602-95532-9-1

pharmaceutical world [28]. From a financial perspective, efficient inventory management increase in gross profit and net profit by reducing the cost of pharmaceutical products obtained and related operational costs [28]. In addition, cash flow will increase purchases and generate cost savings of storage of the product is lower, so the cash flow can be used to pay operating costs and invest in other services [28]. From an operational perspective, an effective inventory management can satisfy customers and meet the demands of patients [28].

Where: CR = Consistency Ratio CI = Consistency Index RI = Random Index for each matrix of order n Consistency Index (CI) of the matrix pairs can be calculated by (2).

C. Fuzzy Analytic Hierarchy Process (FAHP) FAHP is the insertion of fuzzy theory into AHP method developed by Thomas L. Saaty (2008) in the 1970s [14]. FAHP is a further analysis of AHP to overcome uncertainty and ambiguity in human decision to the next level [29]. Because of the uncertainty or ambiguity of human decisionmaking can lead to errors in the results of analysis of the model [14]. Basically the steps in FAHP method similar to the AHP method. AHP uses a scale of 1-9 for pairwise comparison criteria, while FAHP method using Triangular Fuzzy Number (TFN) for pairwise comparison criteria, and alternative made through linguistic variables [14]. TFN and linguistic variables corresponding to the Saaty scale shown in Table I [15]. TABLE I. Fuzzy Num.

Definition

Membership Function

1

~ 1

Equally important (sama penting)

(1, 1, 3)

3

~ 3

Moderately more important (sedikit lebih penting)

(1, 3, 5)

5

~ 5

Strongly more important (lebih penting)

(3, 5, 7)

7

~ 7

Very strongly more important (sangat penting)

(5, 7, 9)

9

~ 9

Extremely more important (mutlak lebih penting)

(7, 9, 11)

Intermediate Values (nilai yang berdekatan)

(1,2,3),(3,4,5), (5,6,7),(7,8,9)

CI  RI

Dimana: CI = Consistency Index λmax = the largest eigenvector value of the matrix order n n = number of elements compared/order of matrix Application of FAHP method in this study adopts the Chang analysis, because the steps of this approach is relatively easier, less time and computational cost than most other FAHP approaches, and at the same time, can overcome the shortcomings of AHP method [16]. In the proposed method of Chang, if X = {x1, x2, xi,... xn} represents a set of objects and G = {g1, g2, gj,... gm} represents the set of goals and there are a number of criteria that would m used for analysis are obtained M 1gi , M gi2 , M gij ,... M gim , i = 1, The steps in the FAHP method with further analysis of Chang in [16] as follows:

Si 



TFN can be applied after the consistency of the hierarchical model has been tested in advance by calculating the value of Consistency Ratio (CR) using (1), and its value should be less than 10%. If the value is more than 10%, the assessment procedure must be repeated and improved to increase consistency.

CR 



Step 1: Calculate fuzzy synthetic extent (Si) using criteria to i according (3).

TFN in Table I is denoted by M = {l, m, u}, where M is a set of fuzzy numbers, while l declare the smallest possible value, m declare value of the closest, and u declare the greatest possible value. The value of l, m, and u can also be determined by the decision-makers themselves [15].



max  n  n 1

2, ..., n, where the whole M gij (j=1,2,...,n) is the TFN [16].

DEFINITION AND FUNCTION OF TFN [15]

Saaty Scale

2, 4, 6, 8

CI 





m



j 1

M gij

n m     M gij  i 1 j 1 

1





gi = goal set (i= 1, 2, …, n)

M gij = fuzzy triangular number (j = 1, 2, …, m) Where

m

j  M gi is obtained by performing the addition j1

operation of the fuzzy value in the matrix using (4)

n m  and   M gij  i 1 j 1 



m



n

j 1

 i 1

n

n



i 1

i 1



j  M gi    li ; mi ; u i ;  



n m j    M gi  i 1 j 1 



1

1

obtained using (5).

 1 1 1  n , n , n m m m  u m  i 1  j 1 i i 1  j 1 i i 1  j 1 l i

     

So that (3) into (6):


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ISBN 978-602-95532-9-1 n n n   1 1 1 , n , n S i    l i ; mi ; u i ;    n m m m  i 1 i 1 i 1   i 1  j 1 u i i 1  j 1 mi i 1  j 1 l i



   



Where: l = lower limit value (lowest possible) m = the value of the most promising (possibly the middle) u = upper limit value (possibly top) Step 2: calculate the degree of possibility of S2 = (l2,m2,u2)  S1 = (l1,m1,u1) where S2 and S1 obtained from (3). The degree of possibility between two fuzzy synthetic extent stated in (7) and (8). 



V ( S 2  S1 )  hgt ( S1  S 2 )   S 2 (d ) 



 , if m2  m1  1    0 , if l1  u 2    S2 (d )   l1  u 2  , otherwise   (m  u )  (m  l ) 2 1 1  2



Step 3: Compare the degree of possibility among criteria between fuzzy numbers Mi (i = 1, 2,..., k) through (9). V(S  S1, S2,...,Sk) = V [(S  S1) dan (S  S2)…dan (S  Sk)] (9) = minV(S  Si), i = 1, 2, …, k. Step 4: Calculate vector W’ is given by (10) (10)

Assuming that d(Ai) = minV(Si  Sk) for k = 1, 2,..., n; k  i. After the vector weight in (10) are normalized, then the normalized vector weight obtained shown in (11).



W ddd

Related to the pattern associated with the extra time, Hughes and Stone in [8] introduces the analysis of recency, frequency, and monetary (RFM), which have been widely used in database marketing and to measure the values of customers according to their previous purchase history, where recency is the time interval between the time of the last transaction at this time, the frequency is the number of transactions that occurred in the history records, and the total monetary value of the rupiah payments [6], [9]. Set a number of criteria in this study refers to research on RFM [8], [35–37] and identical with research on QFR [10]. Further, RFM scores can be defined as (12), where α, β and γ show FAHP weight of each R, F and M are not the same, because of differences in industry [8].

In (7) dan (8), d represents the coordinates of the point D which is the highest point of intersection between S1 and S2. Comparison between S1 and S2 requires the values of V(S2  S1) and V(S1  S2).

W ’ = (d’(A1), d’(A2),...,d’(Ak))T

According to [34], studies using the SPA can be divided into two main categories, namely (1) improve the efficiency of mining processes; and (2) to propose additional time-related patterns, such as: frequency, recency, and others [23].



Where W is not a fuzzy numbers for each comparison matrix. D. Sequential Pattern Analysis (SPA) Data mining is the process of extracting information or patterns in large data bases [30], which is done by using the association, classification, prediction, sequential pattern, and a similar time sequences [31]. Sequential pattern analysis is inspired by the sequential pattern mining, which is generally applied to the forecasting and decision support commercial [32], which was first introduced by Agrawal and Srikant in 1995 [33].




RFM scoresα . R + β . F + γ . M



III. METHODOLOGY Research conducted at the X pharmacy is quantitative, with research steps as follows: A. Data Collection The collection of data is the most important stages in the research. The early stages of data collection, using questionnaires concerning the criteria that affect the inventory system to the three experts who are directly involved in the process of inventory management in pharmacy. Results of the questionnaires processing at the initial stage is the classification criteria that affect inventory management. The next stage is to conduct the second questionnaires to the three previous experts, to determine the pairwise comparisons among the criteria obtained from the questionnaires at an early stage before. The last stage, the third questionnaires conducted for the inventory manager to acquire the rules of assessment criteria which have been obtained from the previous second questionnaires.  The data used in this study is the result of three questionnaires to the stock administration, inventory manager, and system analyst of X pharmacy, as well as databases of product, sales and purchases transactions from January until April 2015. B. Stages of Data Analysis Stages of data analysis to predict the pharmacy inventory using FAHP and SPA approaches as shown in Fig. 1.

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ISBN 978-602-95532-9-1 Start

- Set pairwise comparison matrix - Normalization matrix

AHP

Set Criteria (Table I)

- Check CR value for each criterion (1) T

CR < 0.1? Y

- Express in TFN - Calculate the degree of possibility 2 Si (7) & (8) - Compare the degree of possibility among criteria between TFN (9)

FAHP

- Calculate fuzzy synthetic extent-Si (3) & (4)

Fig. 3. Entity Relationship Diagram of DSS for Inventory Management

IV. RESULTS AND DISCUSSION

- Calculate vector weight (10)

- Weighting SPA - Calculate SPA weights for each product

SPA

- Normalization vector weight (11)

Inventory prediction (12) End

Fig. 1. Flowchart of DSS Using FAHP and SPA Approach for Inventory Prediction

C. System Design The system design is done by modeling the use case diagram like Fig. 2.

A. Results of Data Analysis Using FAHP Method After the recapitulation of questionnaires of criteria selection is completed, then the results will be used to create a second questionnaires in the form of pairwise comparison matrix for each criterion. The whole value generated pairwise comparisons will be normalized before checking the value of Consistency Ratio (CR) using (1), where the value of Random Index (RI) is 1.49 [15]. After the entire value of CR