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INTERDISCIPLINARY J OURNAL O F C ONTEMPORARY R ESEARCH IN BUSINESS

COPY R IGHT 2012 Institute of Interdisciplinary Business Research 655

J ANUARY 2012 V OL 3, N O 9

Application of fuzzy TOPSIS method for the selection ofWarehouse Location: A Case Study

Maysam Ashrafzadeh* Department of Industrial Engineering

Najafabad Branch, Islamic Azad University, Isfahan, Iran

Postal Code: 81647-76574, Unit 3, No 289, East Kakh Saadatabad St, Mir Ave, Isfahan, Iran

Farimah Mokhatab Rafiei Department of Industrial Engineering

Isfahan University of Technology, Isfahan, Iran, 84156-83111

Naser Mollaverdi Isfahani Department of Industrial Engineering

Isfahan University of Technology, Isfahan, Iran, 84156-83111

Zahra Zare Department of Industrial Engineering

Najafabad Branch, Islamic Azad University, Isfahan, Iran

Abstract

Warehouse location selection is a multi-criteria decision problem including bothquantitative and qualitative criteria and has a strategic importance for many companies.The conventional approaches to warehouse location selection problem tend to be lesseffective in dealing with the imprecise or vague nature of the linguistic assessment.Under many situations, the values of the qualitative criteria are often impreciselydefined for the decision-makers. To overcome this difficulty, fuzzy multi-criteriadecision-making methods are proposed. In this paper, we present a multi-criteriadecision making approach for selecting warehouse location under partial or incompleteinformation (uncertainty). The proposed approach comprises of two steps. In step 1, weidentify the criteria for warehouse location selection. In step 2, experts providelinguistic ratings to the potential alternatives against the selected criteria. FuzzyTOPSIS is used to generate aggregate scores selection of best alternative. This papershows a successful application of fuzzy TOPSIS to a real warehouse location selection

problem of a big company in Iran. Keywords: Warehouse location; Multi criteria decision making; Fuzzy TOPSIS

1. Introduction

Warehouses are a key aspect of modern supply chains and play a vital role in thesuccess, or failure of businesses today [24]. A warehouse is a commercial building for

buffering and storing goods. Warehouses are utilized by manufacturers, importers,

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warehouses and from warehouses to markets. The problem is to choose a set of pointswhere warehouses are located so that the sum of warehouse location costs andtransportation costs are minimized. In their study they consider different formulationstyles due to Geoffrion and Graves [25] and Sharma [44] for the multistage warehouselocation problem; and cast them in the formulation style of Sharma and Sharma [46] toobtain a variety of formulations of the problem SSCWLP. A public warehousesselection support system (PWSS) software has been built by Colson and Dorigo [17] togive the opportunity to industrial users of exploiting a classical data base on publicwarehouses, where several items of information are given on each warehouse located ina given country. Their software public warehouses selection support has two purposes:to select public warehouses according to several criteria and to exploit a database whensome data are missing. They use multiple-criteria selections and rankings with a mixtureof classical true continuous criteria and Boolean ones from a methodological point ofview. Michel and Hentenryck [40] present a very simple tabu-search algorithm which

performs amazingly well on the uncapacitated warehouse location problem. Thealgorithm uses a linear neighborhood. Drezner et al. [20] concern themselves with theoptimal location of a central warehouse, when the possible locations and the number ofwarehouses are known. They solve the problem sequentially. First, for any given centralwarehouse location, the problem is a pure inventory problem. They find the optimal

policy for the inventory problem. They express the total inventory and transportationcosts as a function of the central warehouse location. The next step is to optimize thistotal cost function over all possible central warehouse locations. Partovi [42] explains anew analytic model for facility location that takes into account both external andinternal criteria that sustain competitive advantage. Partovis model, which is based onquality function deployment (QFD), also includes the analytic hierarchy process (AHP)

and the analytic network process (ANP) concepts to determine the best location for afacility. The most well- known general heuristic methods for facility location problemsare Tabu Search (TS), Simulated Annealing (SA), and Genetic Algorithms (GA).Arostegui et al. [2] compare the relative performance of TS, SA, and GA on variousfacilities location problems. Hidaka and Okano [26] propose a simulation-basedapproach to the large-scale incapacitated warehouse/facility location problems,including a heuristic algorithm named Balloon Search. Tzeng and Chen [50] proposea location model based on a fuzzy multi objective approach. The model helps indetermining the optimal number and sites of fire stations at an international airport, andalso assists the relevant authorities in drawing up optimal locations for fire stations.Because of the combinatorial complexity of their model, a genetic algorithm isemployed and compared with the enumeration method. Kuo et al. [35] develop adecision support system using the fuzzy sets theory integrated with analytic hierarchy

process for locating a new convenience store. Chen [9] proposes a new multiple criteriadecision-making method to solve the distribution center location selection problemunder a fuzzy environment. In the proposed method, the ratings of each alternative andthe weight of criterion are described by linguistic variables that can be expressed intriangular fuzzy numbers. The final evaluation value of each distribution centre locationis also expressed in a triangular fuzzy number.

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3. Preliminaries of fuzzy set theory

To deal with vagueness of human thought, Zadeh [54] first introduced the fuzzy settheory, which was oriented to the rationality of uncertainty due to imprecision or

vagueness. A major contribution of fuzzy set theory is its capability of representingvague data. The theory also allows mathematical operators and programming to apply tothe fuzzy domain. A fuzzy set is a class of objects with a continuum of grades ofmembership. Such a set is characterized by a membership (characteristic) function,which assigns to each object a grade of membership ranging between zero and one.With different daily decision making problems of diverse intensity, the results can bemisleading if the fuzziness of human decision making is not taken into account [49].Fuzzy sets theory providing a more widely frame than classic sets theory, has beencontributing to capability of reflecting real world [23]. Fuzzy sets and fuzzy logic are

powerful mathematical tools for modeling: uncertain systems in industry, nature andhumanity; and facilitators for common-sense reasoning in decision making in theabsence of complete and precise information. Their role is significant when applied tocomplex phenomena not easily described by traditional mathematical methods,especially when the goal is to find a good approximate solution [5]. Fuzzy set theory isa better means for modeling imprecision arising from mental phenomena which areneither random nor stochastic. Human beings are heavily involved in the process ofdecision analysis. A rational approach toward decision making should take into accounthuman subjectivity, rather than employing only objective probability measures. Thisattitude, towards imprecision of human behavior led to study of a new decision analysisfiled fuzzy decision making [37].A tilde ~ will be placed above a symbol if the symbol represents a fuzzy set. Some related definitions offuzzy set theory adapted from (Buckley [7], Dubois and Prade [21], Kaufmann and Gupta [31], Klir andYuan [34], Pedrycz [43], Zadeh [54], Zimmermann [55]) are presented as follows:

Definition 1. A fuzzy set M ~

in a universe of discourse X is characterized by a membershipfunction )(~ x M that maps each element x in X to a real number in the interval [0, 1]. The function value

)(~ x M is termed the grade of membership of x in M ~

. The nearer the value of )(~ x M to unity, the higherthe grade of membership of x in M

~.

Definition 2. A triangular fuzzy number (TFN), M ~

is shown in Fig.1. A triangular fuzzy number isdenoted simply as ( l / m , m / u ) or ( l , m , u ). The parameters l , m and u , respectively, denote thesmallest possible value, the most promising value and the largest possible value that describe a fuzzyevent.

Each triangular fuzzy number has linear representations on its left and right side such that its membershipfunction can be defined as:

( ) ( )( ) ( )

>

>>> . Therefore, alternative Isfahan )(

1 A is recommended as warehouse

location.

ConclusionA warehouse location selection is a multi-criteria decision-making problem including

both quantitative and qualitative. In this paper, we present a multi-criteria decisionmaking approach for warehouse location selection under fuzzy environment. The

proposed approach comprises of two steps. In step 1, the criteria for warehouse locationselection are identified. These criteria are labor costs, transportation costs, handlingcosts, land cost, skilled labor, availability of labor force, land availability, climate,existence of modes of transportation, telecommunication systems, quality and reliability

of modes of transportation, quality and reliability of utilities, proximity to Customers, proximity to producer, lead times and responsiveness. In step 2, the experts providelinguistic ratings to the criteria and the alternatives. Fuzzy TOPSIS is used to aggregatethe ratings and generate an overall performance score for measuring each alternative.The alternative with the highest score is selected as the best warehouse locationselection. The warehouse location selection problem in this paper can be solved byfuzzy AHP and the obtained results can be compared for further research.

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Tables and Figures

Table 1: Warehouse selection criteria.

Criteria SymbolLabor costs C 1 Transportation costs C 2 Handling costs C 3 Land cost C 4 Skilled labor C 5 Availability of labor force C 6 Land availability C 7 Climate C 8 Existence of modes of transportation C 9 Telecommunication systems C 10 Quality and reliability of modes of transportation C 11 Quality and reliability of utilities C 12 Proximity to Customers C 13 Proximity to producer C 14 Lead Times and responsiveness C 15

Table 2: Linguistic terms for alternative ratings.

Linguistic term Membership functionVery Poor (VP) (0,0,1)Poor (0,1,3)Medium Poor (MP) (1,3,5)Fair (F) (3,5,7)Medium Good (MG) (5,7,9)Good (G) (7,9,10)Very good (VG) (9,10,10)

Figure 1. A triangular fuzzy number, M ~

M ~

u

)( yr M

M m

)( yl M

l

1

0

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Table 3 : Linguistic terms for criteria ratings.

Linguistic term Membership functionVery Low (VL) (0,0,1)Low (L) (0,1,3)Medium Low (ML) (1,3,5)Medium (M) (3,5,7)Medium High (MH) (5,7,9)High (H) (7,9,10)Very High (VH) (9,10,10)

Table 4: Linguistic assessments for the 15 criteria.

Criteria Decision makers

D1 D2 D3 D4 D5

C1 ML MH MH ML MC2 H VH VH H HC3 H MH H H MHC4 MH H MH MH MC5 MH MH MH M MHC6 ML M M ML MLC7 MH H MH MH MHC8 ML ML ML M MLC9 MH H MH MH MHC10 M H M H HC11 VH VH VH VH VHC

12 ML MH M M ML

C13 H H VH H VHC14 VH VH H H HC15 VH H H H VH

Table 6: Aggregate fuzzy criteria weight

Criteria Weight C1 (1,5,9)C2 (5,8.8,10)C3 (3,6.2,9)C

4 (3,7.4,10)

C5 (5,8.8,10)C6 (1,5.4,9)C7 (1,4.6,9)C8 (5,8.2,10)C9 (7,9.4,10)C10 (7,9.4,10)C11 (3,5.8,9)C12 (3,6.6,9)C13 (5,8.8,10)C14 (3,7.4,10)C15 (3,7.4,10)C16 (3,7,10)

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C 1 5

C 1 4

C 1 3

C 1 2

C 1 1

C 1 0

C 9

C 8

C 7

C 6

C 5

C 4

C 3

C 2

C 1 Criteria

V G

V G

G G M G

M G

G G G G G MP

G G G D1

V G

V G

M G

M G

G F V G

M G

G G G F M G

M G

M G

D2

G G G M G

G M G

G G G M G

M G

MP

M G

M G

G D 3

G V G

G G G M G

G G M G

G G MP

G G G D4

G G G G G M G

V G

M G

M G

M G

V G

MP

G G G D 5

A1

G G M G

M G

M G

F M G

M G

F M G

M G

F M G

F F D1

M

G

M

G

M

G

M

G

M

G

F M

G

M

G

F M

G

M

G

F F M

G

F D2

M G

M G

M G

M G

M G

M G

M G

G F M G

F MP

F F M G

D 3

M G

G M G

M G

M G

M G

M G

G M G

M G

M G

F M G

M G

M G

D4

M G

M G

F M G

G F G M G

F M G

G F M G

M G

F D 5

A2

M G

M G

M G

F M G

F M G

M G

F F M G

MP

M G

F F D1

F F F F F F F M G

M G

F F MP

F F F D2

M

G

M

G

M

G

M

G

M

G

F M

G

M

G

M

G

F F F F F M

G

D 3

G M G

G M G

F F F M G

M G

M G

M G

F M G

M G

M G

D4

F F F F M G

F M G

F F M G

M G

F M G

F F D 5

A 3

M G

M G

M G

M G

M G

F M G

F M G

F M G

MP

M G

F F D1

F F F M G

F F F M G

F M G

F MP

M G

M G

F D2

G F G F M G

F M G

F M G

M G

F F F M G

M G

D 3

M G

F M G

F M G

M G

M G

M G

M G

M G

M G

F M G

M G

M G

D4

F F F F F F F F F M G

F F M G

F F D 5

A4

G M G

G M G

M G

F M G

M G

M G

M G

M G

MP

M G

M G

M G

D1

G F G M G

M G

F G M G

M G

M G

M G

F M G

M G

M G

D2

M G

F M G

F M G

F M G

M G

M G

M G

F F F M G

M G

D 3

G F G M G

M G

M G

M G

M G

M G

M G

M G

F M G

M G

G D4

M G

F M G

M G

M G

F M G

F F M G

M G

F M G

F F D 5

A 5

Al t e r n

a t i v e

T a b l e

5

: L i n g ui s t i c

a s s e s s m e n t s f or

t h e t h r e e a l t e r n a t i v e s .

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COPY R IGHT 2012 I tit t f I t di i li B i R h671


Table 7: Aggregate fuzzy decision matrix

Criteria Alternative

A1 A2 A3 A4 A5C1 (5,8.6,10) (3,5.8,9) (3,5.8,9) (3,5.8,9) (3,7,10)C2 (5,8.2,10) (3,6.2,9) (3,5.4,9) (3,6.2,9) (3,6.6,9)C3 (5,8.2,10) (3,6.2,9) (3,6.2,9) (3,6.6,9) (3,6.6,9)C4 (1,3.4,7) (1,4.6,7) (1,4.2,7) (1,4.2,7) (1,4.6,7)C5 (5,8.8,10) (3,7,10) (3,6.2,9) (3,5.8,9) (3,6.6,9)C6 (5,8.2,10) (5,7,9) (3,5.8,9) (3,6.6,9) (5,7,9)C7 (5,8.2,10) (3,5.4,9) (3,6.2,9) (3,6.2,9) (3,6.6,9)C8 (5,8.2,10) (5,7.8,10) (3,6.6,9) (3,5.8,9) (3,6.6,9)C9 (7,9.4,10) (5,7.4,10) (3,6.2,9) (3,6.2,9) (5,7.4,10)C10 (3,6.6,9) (3,5.8,9) (3,5,7) (3,5.4,9) (3,5.4,9)C11 (5,8.6,10) (5,7.4,10) (3,6.2,9) (3,6.2,9) (5,7,9)C12 (5,8.2,10) (5,7,9) (3,5.8,9) (3,5.8,9) (3,6.6,9)C13 (5,8.6,10) (3,6.6,9) (3,6.6,10) (3,6.6,10) (5,8.2,10)C14 (7,9.6,10) (5,7.8,10) (3,6.2,9) (3,5.4,9) (3,5.4,9)C15 (7,9.4,10) (5,7.4,10) (3,6.6,10) (3,6.6,10) (5,8.2,10)

Table 8: Distance ),( 1 A Ad v

and ),( 1 A Ad v for alternatives.

Criteria d + d - A1 A2 A3 A4 A5 A1 A2 A3 A4 A5

C1 5.608 6.157 6.157 6.157 5.943 5.53 4.747 4.747 4.747 5.352C2 3.979 5.19 5.405 5.19 5.093 5.652 4.528 4.338 4.528 4.635C3 4.725 5.698 5.698 5.607 5.607 5.789 4.799 4.799 4.884 4.884C4 6.712 6.345 6.461 6.461 6.345 5.786 6.028 5.94 5.94 6.028C5 4.706 5.316 5.493 5.573 5.416 5.479 5.146 4.547 4.488 4.611C6 4.372 4.53 4.774 4.675 4.53 4.198 3.724 3.634 3.691 3.724C7 4.889 6.036 5.846 5.846 5.757 5.601 4.564 4.683 4.683 4.75C8 4.472 4.515 4.761 4.853 4.761 4.128 4.101 3.641 3.596 3.641C9 4.144 5.057 5.846 5.846 5.057 5.945 5.449 4.683 4.683 5.449C10 5.829 6.01 6.341 6.108 6.108 5.791 5.633 4.306 5.563 5.563C11 3.277 3.512 4.786 4.786 3.663 5.518 5.119 4.161 4.161 4.525C12 5.761 5.957 6.234 6.234 6.112 5.409 4.81 4.706 4.706 4.772C13 3.912 5.093 5.06 5.06 3.979 5.779 4.635 5.14 5.14 5.652C14 2.998 4.057 5.19 5.405 5.405 6.277 5.53 4.528 4.338 4.338C15 3.02 4.144 5.06 5.06 3.979 6.208 5.415 5.14 5.14 5.652

Table 9 : Closeness coefficient )( iCC of the three alternatives

A1 A2 A3 A4 A5

id 68.404 77.618 83.115 82.863 77.754id 83.088 74.228 68.993 70.287 73.576

iCC 0.5485 0.4888 0.4536 0.4589 0.4862

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