Ijebea15 425

International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research)

ISSN (Print): 2279-0020 ISSN (Online): 2279-0039

International Journal of Engineering, Business and Enterprise Applications (IJEBEA) www.iasir.net Optimization of the Import of Chipboard - a case study Željko Stević, Zdravko Božičković, Biljana Mićić Faculty of Transport and Traffic Engineering Doboj, University of East Sarajevo, Vojvode Mišića 52 Doboj, Bosnia and Herzegovina

Abstract: An efficient procurement, in this case import of the materials necessary for production logistics subsystem, definitely affects the overall efficiency of a company’s business. The purpose of this paper is to rank and select an optimal supplier by using the combined fuzzy AHP approach, which is used for calculation of the weight of criteria and the classic AHP utilized for its ranking. There are six most important criteria selected, based on which the evaluation of suppliers is carried out and, on the basis of input data collected in the company where the optimization of import is performed, the three suppliers, located in the territory of Poland, Italy and Slovenia, are being ranked respectively. Following the application of the fuzzy AHP approach, two criteria are being eliminated, and the ranking is carried out by classic AHP method based on the four criteria.

Keywords: Supplier; fuzzy AHP; optimization; AHP; criterion; import I.

Introduction

There are numerous of publications dealing with the adoption of certain decisions on the basis of multi-criteria analysis, which resulted in an accelerated development of this field. Among large number of methods that belong to this field, we may definitely say that AHP method represents one of the most commonly used methods for decision making. In addition to the AHP, other methods can also be employed, such as Maxmax, Maxmin, Saw, Electra (Stevic and Vasiljevic, 2013), but which are no match for the analytic hierarchy process.

The importance of this method is supported by the fact that there are conferences dedicated only to the analytic hierarchical process. However, despite this fact, there are continuous efforts to develop a better and possibly more precise problem solving. The above mentioned reason leads to expansion of the AHP method, i.e. the creation of fuzzy approach which enables a more distinct comparison, and therefore more precise definition of, in this case, the weight of criteria.

II.

Literature review

Many criteria are used for evaluation of suppliers, but the question is how to choose the right one from a given set, which will help to choose the best solution. Some authors have tried to answer this question, in particular Webber et. al. (1991) who investigated the criteria for the selection of suppliers in the manufacturing and retail environment, which was covered in the 74 documents, published from 1966 to 1991. They came to the conclusion that the quality, delivery and price were prevailing as the dominant criteria, while geographical location, financial position and production capacities fall under the second group of factors. Verma and Pullman (1998) conducted a study among 139 managers in order to examine how they make compromise when selecting a supplier. Their work indicated that the managers gave the highest priority to quality as the most important attribute of suppliers, followed by delivery and price. Karpak et.al. (2001) took reliability of delivery as the selection criteria, while Bhutta and Huq (2002) used the following four criteria for evaluation of suppliers: price, quality, technology and service.

The AHP method was used even earlier to solve the problem of supplier selection Nydick and Hill, (1992), Barbarasoglu and Yazgac, (1997) and Handfield et al., (1999).

When it comes to decision making by using fuzzy AHP methods, different approaches have been developed as an expanded fuzzy AHP method, which is based on triangular fuzzy numbers (Chang, 1996; Zhu et al, 1999), fuzzy preference programming developed by Mikhailov (2003), logarithmic fuzzy preference programming, originating from the above mentioned approach by its expansion, developed by Wang and Chin (2011).

There is a significant number of publications dealing exactly with comparison of conventional AHP and fuzzy AHP, such as Davoudi and Sheykhvand (2007); Özdağoğlu and Özdağoğlu (2007); Zhang (2010); Kabir and Hasin (2011); Noramin et al (2012); Aggarwal and Singh (2013). AHP is often used in combination with other methods, as evidenced by (Stevic et al., 2015a), where author's AHP used for assessing the weight criteria, and Topsis method for obtaining the final ranking of alternatives.

III.

Fuzzy AHP method

The theory of fuzzy sets was first introduced by Zadeh (1965), the application of which enabled decision makers to effectively cope with uncertainties. In general, the fuzzy sets use triangular, trapezoidal and Gaussian fuzzy

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numbers, which convert uncertain numbers into fuzzy numbers. According to Liao and Xu (2014: 750), fuzzy set is a class of objects characterized by membership functions, in which each object is given a degree of membership on the interval (0.1). The triangular fuzzy numbers used in this paper are marked as lij, mij and uij.

The parameters lij, mij, and uij represent the smallest possible value, the most promising value and highest possible value that describes a fuzzy event, respectively.

Chang's expanded analysis, despite the papers of Wang et al (2008) and Fazlollahtabar et al (2010) who criticize this method, is widely used for decision making in various fields. One of the more represented fields is the evaluation and selection of suppliers, where this method has found its application as evidenced by Kahraman et al (2003) and Chan and Kumar (2007), while Ho, together with co-authors (Ho et al, 2010) reviewed the bibliography for multi-criteria analysis in the above mentioned field. Some other fields where this method is applied are for instance the evaluation of energy sources (Meixner, 2009), evaluation and selection of the computers (Srichetta and Thurachon, 2012), evaluation of catering services (Kahraman et al, 2004), evaluation of impact of safety training program (SVS Raja Prasad and P.Venkata Chalapathi 2013.), etc.

According to Xu and Liao (2014:753), one of the disadvantages of the expanded AHP analysis is considered to be not taking into account the consistency degree, i.e. failure to calculate its value. However, it can be calculated by taking the crisp value.

Let us take X={x1, x2,...,xn} as a set of objects, and U={u1, u2,...,um} as set of objectives. According to expanded analysis methodology set by Chang, the expanded analysis of objective uj is conducted for each taken object. The values of the expanded analysis m for each object may be presented in the following manner: where are the fuzzy triangular numbers.

Chang’s expanded analysis includes the following steps: Step 1: Value of the fuzzy expansion for i-th object is presented with the following equation:

In order to get the expression

, it is necessary to execute additional fuzzy operations with m

values of the expanded analysis, which is presented with the following expressions:

Then, it is necessary to calculate the inverse vector:

Step 2: Degree of possibility Sb>Sa is defined:

where d is ordinate of the highest intersection in point D between μsa and μsb , as shown in the Figure 1.

Figure 1. Intersection between Sa and Sb

For comparison of S1 and S2, both values V(S1 ≥ S2) and V(S2 ≥ S1) are necessary.

Step 3: Degree of possibility for convex fuzzy number to be higher than k convex number Si (i = 1,2,...,k) can be defined with the following expression:

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The weighted vector is given in the following expression: Step 4: By normalization, the weighted vector is reduced to the following expression: where W does not represent a fuzzy number.

One of the main features of multi-criteria decision making is that criteria can not have the same importance (Stevic et al., 2015b: 88). After describing the methodology for decision-making by using expanded AHP method, i.e. fuzzy AHP to obtain the necessary results, it is necessary to compare the criteria on the basis of fuzzy triangular numbers, as shown in the Table 1 below. The comparison was made based on the scale in Sun’s (2010:7746) paper. The criteria are as follows: the cost of materials, quality, transport distance, sales assortment, delivery time and payment method. Taking crisp value CR = 0.01.

Table I Comparison of the criteria based on triangular numbers K1

K2

K3

K4

K5

K6

K1

(1,1,1)

(1/4,1/3,1/2)

(1,1,1)

(1,2,3)

(1/3,1/2,1)

(1,2,3)

K2

(2,3,4)

(1,1,1)

(2,3,4)

(3,4,5)

(1,2,3)

(3,4,5)

K3

(1,1,1)

(1/4,1/3,1/2)

(1,1,1)

(1,2,3)

(1/3,1/2,1)

(1,2,3)

K4

(1/3,1/2,1)

(1/5,1/4,1/3)

(1/3,1/2,1)

(1,1,1)

(1/4,1/3,1/2)

(1,1,1)

K5

(1,2,3)

(1/3,1/2,1)

(1,2,3)

(2,3,4)

(1,1,1)

(2,3,4)

K6

(1/3,1/2,1)

(1/5,1/4,1/3)

(1/3,1/2,1)

(1,1,1)

(1/4,1/3,1/2)

(1,1,1)

By applying the equations (3), (4) and (5) , we obtain the following values: S1=(4,583;6,833;9,5)x(1/66,666;1/49,332;1/34,733)=(0,069;0,138;0,273) S2=(12;17;22) x(1/66,666;1/49,332;1/34,733)=(0,180;0,345;0,633) S3=(4,583;6,833;9,5)x(1/66,666;1/49,332;1/34,733)=(0,069;0,138;0,273) S4=(3,117;3,583;4,833) x(1/66,666;1/49,332;1/34,733)=(0,047;0,073;0,139) S5=(7,333;11,5;16) x(1/66,666;1/49,332;1/34,733)=(0,110;0,233;0,461) S6=(3,117;3,583;4,833) x(1/66,666;1/49,332;1/34,733)=(0,047;0,073;0,139) After calculations by applying the equations (6), (7), (8), we obtain the values described in step 3 which are: d'(A1)=V(S1≥S2,S3,S4,S5,S6)=0,31; d'(A2)=V(S2≥S1,S3,S4,S5,S6)=1; d'(A3)=V(S3≥S1,S2,S4,S5,S6)=0,31 d'(A4)=V(S4≥S1,S2,S3,S5,S6)=0; d'(A5)=V(S5≥S1,S2,S3,S4,S6)=0,715 d'(A6)=V(S6≥S1,S2,S3,S4,S5)=0; By applying the equation (9) we obtain weighted values, and the equation (10) renders normalized weighted values of the criteria: W'=(0,31;1;0,31;0;0,715;0) W=(0,133;0,428;0,133;0;0,306;0) IV.

Classic AHP method

The creator of analytic hierarchy process was Thomas Saaty (Saaty, 1980) and, according to the same author (Saaty, 2008:83), AHP is a theory of measurement by pairwise comparisons and relies on the opinion of experts to derive priority scales. According to Saaty (1988: 110), with AHP it is possible to identify the relevant facts and connections that exist between them. This method consists of the decomposition of problem, where the objective is at the top, then the criteria and sub-criteria and at the end are the potential solutions, explained in more details

by Saaty (1990).

Saaty (1986) defined the axioms which the AHP is based on: the reciprocity axiom. If the element A is n times more significant than the element B, then element B is 1/n times more significant than the element A; Homogeneity axiom. The comparison makes sense only if the elements are comparable, e.g. weight of a mosquito and an elephant may not be compared; Dependency axiom. The comparison is granted among a group of elements of one level in relation to an element of a higher level, i.e. comparisons at a lower level depend on the elements of a higher level; Expectation axiom. Any change in the structure of the hierarchy requires recomputation of priorities in the new hierarchy. More details on the analytic hierarchy process are found in the book of Saaty and Vargas (2012).

Some of the key and basic steps in the AHP methodology according to Vaidya and Kumar (2006:2) are as follows: to define the problem, expand the problem taking into account all the actors, the objective and the outcome, identification of criteria that influence the outcome, to structure the problem previously explained hierarchy, to compare each element among them at the appropriate level, where the total of nx(n-1)/2 comparisons is necessary, to calculate the maximum value of own vector, the consistency index and the degree of consistency.

AHP in a certain way solves the problem of subjective influence of the decision-maker by measuring the level of consistency (CR) and notifies the decision maker thereof. If the level of consistency is in the range up to 0.10, the results are considered valid. Some authors take even greater degree of consistency as valid, which of course is not

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recommendable. This coefficient is recommended depending on the size of the matrix, so we may find in the papers of Lee et al. (2008:101) and Anagnostopoulos et al (2007:17) that the maximum allowed level of consistency for the matrices 3x3 is 0.05, 0.08 for matrices 4x4 and 0.1 for the larger matrices. If the calculated CR is not of the satisfactory value, it is necessary to repeat the comparison to have it within the target range (Saaty, 2003:89).

The elimination of the fourth and the sixth criteria by calculation of the fuzzy AHP method is followed by ranking of alternatives based on the following four criteria: material price, quality, transport distance and time of delivery. Table 2 shows a comparison of alternatives in relation to each criterion separately.

K1

A1 A2 A3

Table II Comparison of alternatives per criterion K2 K3

K4

A1

A2

A3

A1

A2

A3

A1

A2

A3

A1

A2

A3

1 1/3 1/4

3 1 1/2

4 2 1

1 2 1

1/2 1 1/2

1 2 1

1 4 5

1/4 1 2

1/5 1/2 1

1 3 4

1/3 1 2

1/4 1/2 1

After comparing the alternatives per criterion by applying the described methodology, the calculation for each alternative is performed and, based on the obtained results, the ranking is made, i.e. the selection of the optimal alternative (supplier). The following table shows the values of all the alternatives according to each criterion and its percentage, so having everything mentioned, we can be conclude that supplier from Italy is the optimum solution.

Table III Overview of all the values during the calculation by AHP method Alts Level 1 Prty Percent 39,6 Italy

cost of material (L: 0,133) product quality (L: 0,429) transport distance (L: 0,133) delivery time (L: 0,306)

0,027 0,232 0,042 0,095

cost of material (L: 0,133) product quality (L: 0,429) transport distance (L: 0,133) delivery time (L: 0,306)

0,072 0,116 0,012 0,036

cost of material (L: 0,133) product quality (L: 0,429) transport distance (L: 0,133) delivery time (L: 0,306))

0,016 0,116 0,072 0,165

Percent Poland

23,6

Percent

Slovenia

36,9

V.

Conclusion

Today, procurement logistics plays a very important role in the supply chain, so its optimization enables a significant effect on the entire logistics system. When it comes to the import of the required components, it is necessary to take into account a large number of criteria which may affect the formation of the final price of the product and the position that the company establishes in the market. Thanks to the multi-criteria analysis methods, primarily fuzzy approach that has lately been more and more represented in a simple way, we may optimize the above mentioned system. Application of the fuzzy analytical hierarchy process for evaluation of criteria puts the emphasis on the most important criteria, which in this case are: material price, quality, transport distance and time of delivery, while the criteria product portfolio and method of payment are of little importance and do not affect the supplier’s decision-making. On the basis of the four criteria selected by applying classic analytic hierarchy process, we reach the optimal solution which is the supplier located in the territory of Italy.

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