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Assessing Business Impacts of Agility Criterion and Order Allocation Strategy in Multi-Criteria Supplier Selection

Jaehun Lee, Hyunbo Cho, Yong Seog Kim

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To appear in: Expert Systems with Applications

Please cite this article as: Lee, J., Cho, H., Kim, Y.S., Assessing Business Impacts of Agility Criterion and Order Allocation Strategy in Multi-Criteria Supplier Selection, Expert Systems with Applications (2014), doi: http:// dx.doi.org/10.1016/j.eswa.2014.08.041

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Assessing Business Impacts of Agility Criterion and Order Allocation Strategy in Multi-Criteria Supplier Selection

Jaehun Lee, Hyunbo ChoDepartment of Industrial and Management Engineering

Pohang University of Science & TechnologySan 31 Hyoja, Pohang 790-784, Republic of Korea

Yong Seog KimManagement Information Systems Department

Jon M. Huntsman School of Business3515 Old Main Hill

Utah State UniversityLogan, UT 84322-3515, USA

ABSTRACT

This paper formulates supplier evaluation and selection as a multi-criteria decision-making

(MCDM) problem with subjective and fuzzy preferences of decision makers over evaluation criteria. As

an outcome, this paper provides decision makers with a decision support system that presents the Pareto

fronts, a set of best possible high-quality suppliers and optimized business operation levels from such

suppliers. In addition, this paper quantifies the importance of the agility criterion and its sub-criteria in

the process of evaluating and selecting agile suppliers by measuring the magnitude of bullwhip effect

and inventory costs. The proposed system uses a fuzzy analytic hierarchy process (fuzzy AHP) and

fuzzy technique for order of preference by similarity to ideal solution (fuzzy TOPSIS) to successfully

determine the priority weights of multiple criteria and selects the fittest suppliers by taking the

vagueness and imprecision of human assessments into consideration. More importantly, it presents

approximated Pareto fronts of the resulting supplier chains for varying priority weights of the agility

criterion and its sub-criteria. Finally, we compare business costs of agile and non-agile supply chains

before and after reconfigurations of original supply chains in response to unexpected disruptions under

two order allocation strategies, a skewed order allocation (SOA) strategy and an even order allocation

(EOA) strategy.

1

KEYWORDS

Supplier selection; Agile supply chain; Pareto fronts, Bullwhip effect; Fuzzy AHP; Fuzzy TOPSIS;

Multi-criteria decision-making (MCDM)

1. INTRODUCTION

Due to increasing reliance on outsourcing of many complex services and products, evaluating

and selecting qualified suppliers becomes an essential part of building a successful supply chain (Araz et

al., 2007). Often, the supplier evaluation and selection problem is formulated as a multi-criteria

decision-making (MCDM) problem with various quantitative and qualitative evaluation criteria. In this

approach, the ultimate goal is to present the decision maker with a set of high-quality suppliers from

which to choose and approximate Pareto front that represents the optimized business operation levels

from chosen suppliers.

Various methods to select the best-fit suppliers have been proposed from diverse disciplines

(Araz et al., 2007; Bottani and Rizzi, 2008; Chan et al., 2008; Chen et al., 2006; Ha and Krishnan, 2008).

In particular, turbulent and volatile markets enforce organizations to restructure their supply chains to be

more responsive to customer needs through a high level of maneuverability. Naturally, agility defined as

the ability to respond rapidly to change in demand volume and variety becomes one of the most critical

evaluation criteria for supplier evaluation and selection (Christopher, 2000). Note that change in demand

may come from several different sources such as marketplace, competition, customer desire, technology

and social factors (Lin et al., 2006). Therefore, agility in these days is regarded as a business-wide

capability that embraces organizational structures, information systems, logistics processes and mindsets

(Christopher, 2000). This implies that it is imperative for organizations to cooperate and leverage

complementary competencies along the up- and down-stream of their supply chains (Yusuf, 2004).

Based on these observations, this study intends to quantify the importance of agility criterion in

the process of evaluating suppliers and estimate the business impact of resulting supply chains. To this

end, we measure the magnitude of bullwhip effect and inventory cost of agile supply chain that is

supposed to rapidly respond to change in demand and supply shortage, and hence is less likely to suffer

from high bullwhip effect or high inventory cost. Note that bullwhip effect is a phenomenon in which

variance of demand information is amplified when moving upstream in supply chains (Chen et al., 2000;

Lee et al., 1997; Luong, 2007) due to the invisibility of end demand, order batching, supply shortage, or

other behavioral causes (Chen and Lee, 2012; Croson and Donohue, 2006; Klein and Rai, 2009; Yao

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and Zhu, 2012). We also consider other criteria such as general management capability, manufacturing

capability and collaboration capability to evaluate candidate suppliers from an MCDM perspective.

To quantify subjective and vague preferences of decision makers over multiple criteria with

linguistic assessments, we calculate the prior weights of decision criteria with a fuzzy analytic hierarchy

process (AHP) method (Chan et al., 2008). Then we determine the rankings of candidate suppliers using

another fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) (Chen et al.,

2006) and select the fittest suppliers. By successfully integrating AHP and TOPSIS based on the fuzzy

theory, we not only consider the imprecision of human assessments but also reflect the subjective

preferences of decision makers, making the presented model generalizable to the cases of decision

makers with different preferences.

More importantly, we intend to visualize the importance of agile criterion by comparing

differences of bullwhip effect and inventory cost from two supply chains: an agile supply chain with the

suppliers chosen considering agility and other criteria, and a non-agile supply chain built without

considering agility. In particular, we approximate the Pareto fronts of agile and non-agile supplier chain

as we vary the relative importance of agility criterion in the evaluation process of candidate suppliers.

This way, decision makers easily identify a set of high-quality suppliers from which to choose as their

strategic preferences over agility criterion change.

After validating our concepts in a simple supply chain consisting of one buyer and one supplier,

we expand our simple supply chain into a more realistic supply chain consisting of multiple suppliers. In

particular, we compare business costs of agile and non-agile supply chains before and after

reconfigurations of original supply chains in response to unexpected disruptions. For example, we

imagine that when the fittest supplier in the current supply chain cannot serve as a business partner, the

buyer replaces it with new suppliers. If the buyer allocates most of order to the fittest supplier and the

remaining orders to the other suppliers in the supply chain (i.e., taking a skewed order allocation (SOA)

strategy), its reconfiguration business impacts could be serious. In contrast, if it evenly allocates order

among suppliers in the supply chain (i.e., taking an even order allocation (EOA) strategy), the

reconfiguration impact could be tolerable. In this study, we intend to present the Pareto fronts of original

and reconfigured supply chains associated with SOA and EOA strategy, and compare changes in

bullwhip effect for both agile and non-agile supply chains before and after disruption.

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The remainder of this paper is organized as follows. In Section 2, we provide a literature review

on agile supply chain, supplier evaluation and selection with fuzzy multi-criteria decision making and

bullwhip effect of supply chain. Then we describe the framework of the proposed decision support

system (DSS) that helps decision makers configure agile supply chains by evaluating and selecting

candidate suppliers based on fuzzy multi-criteria in Section 3. Business impacts of agile and non-agile

supply chains are assessed by measuring the magnitude of the bullwhip effect and inventory cost in

Sections 4 and 5, respectively. In Section 6, a simple supply chain is expanded into a more complex

supply chain consisting of multiple suppliers which is used to compare business impacts of agile and

non-agile supply chains in response to unexpected disruptions. Finally, we provide concluding remarks

and suggest future research direction in Section 7.

2. LITERATURE REVIEW

This study takes a holistic approach to leverage three closely related domains toward successful

agile supply chain construction. The first relevant domain is agile supply chain management discipline

that recognizes the importance of an agile supply chain that responds rapidly to change in demand both

in terms of volume and variety. Note that it is imperative for companies to cooperate and leverage

complementary competencies because the resources required for agility are often difficult to retain by

single company (Yusuf, 2004). To this regard, many studies have acknowledged that agility is a

business-wide capability that embraces organizational structures, information systems, logistics

processes and mindsets (Krishnamurthy and Yauch, 2007; Power et al., 2001). A number of ways of

streamlining a traditional supply chain into agile supply chain have been presented. For example, Galan

et al. (2007) presented the concept of reconfigurable manufacturing systems (RMSs) that make it

possible to produce any quantity of customized products while allowing mass production. Similarly,

Kristianto et al. (2012) presented the need to incorporate the manufacturing process (e.g., assembly

planning) into logistics design (e.g., demand planning and inventory allocation process) to improve the

agility of a supply chain. While these studies recognize the importance of agility and present an

innovative manufacturing process to enhance the agility, they are limited in a sense that they mainly

focus on the improvement of internal manufacturing process rather than the entire supply chain

management. In addition, these studies do not explicitly consider multiple and often fuzzy criteria in the

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process of supplier evaluation. In particular, none of these studies considered the effects of order

allocation strategies in agile supply chain in respond to unexpected disasters.

The second associated domain is the multi-criteria decision making (MCDM) domain that has

garnered researchers’ interests in marketing, management science, operation management and

engineering disciplines (Bottani and Rizzi, 2008; Kim et al., 2005; Tan et al., 2012; Wallenius et al.,

2008). In fact, several studies already formulated the supplier selection problem as an MCDM problem

(Ho et al., 2010; Hong and Lee, 2013; Jadidi et al., 2014; Ware, 2014). For example, Hong and Lee

(2013) presented a decision support system that helps procure managers identify, assess, mitigate and

monitor supply risk. In addition, several other studies (Arikan, 2013; Labib, 2011; Önüt et al., 2009;

Pitchipoo et al., 2013; Shen and Yu, 2012) presented various fuzzy methods to consider the ambiguity of

evaluating decision alternatives and determining relative weights of multiple criteria. In particular,

analytic hierarchy process (AHP) first introduced by Saaty (1980) has been a popular approach for

supplier evaluation and selection, though it was extended with fuzzy theory to suitably address the

ambiguities involved in the linguistic assessment of the data (Chan et al., 2008). For example, Kar

(2014) applied group decision support theory with fuzzy AHP to the supplier selection problem, and

Deng et al. (2014) extended AHP based on Dempster-Shafer theory to handle uncertainties due to the

inability of human’s subjective judgment. While methods (e.g., fuzzy AHP and fuzzy TOPSIS) from this

domain are adopted for this study without modification, our study is still useful for two reasons. First,

many of these fuzzy MCDM studies did not consider agility as one of evaluation criteria and mainly

focused on developing an evaluation method. However, our study intends to help decision makers

evaluate candidate suppliers based on agility explicitly and understand a trade-off between conflicting

criteria (agility vs. other criteria). Second, this study presents decision makers with a set of high-quality

suppliers from which to choose and approximated Pareto front that visually represents the optimized

business operation levels.

The third domain considered in this study is the mathematical approach (Bray and Mendelson,

2012; Lee et al., 1997; Lee et al., 2000; Ware, 2014) that provides theoretical and analytical foundations

and estimates the sensitivity of internal and external factors of supply chains. For example, Bray and

Mendelson (2012) modeled a specific supply chain mathematically with the martingale model of

forecast evolution (MMFE) demand process (i.e., demand uncertainty resolves gradually) and a

generalized order-up-to policy (GOUTP) to estimate the size of bullwhip effect. Ware (2014) modeled a

dynamic supplier selection problem over multi-periods and solved it using a mixed integer non-linear

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program. While these mathematical models are theoretically valid and provide a simplified framework

to understand complex structures of supply chains, most of these models are limited in a sense that they

do not reflect realistic characteristics of decision making with subjective preferences and ambiguous

assessments of criteria priorities. Rather than focusing on developing a new complex mathematical

model, we define a simple supply chain model for this study in Section 4 to utilize it as an analytical

foundation.

In summary, this study presents an integrated decision support system toward an agile supply

chain that uses a fuzzy MCDM process to select the fittest agile suppliers, estimates business and

economic impacts in terms of the magnitude of the bullwhip effect and inventory cost, and presents

Pareto fronts that help decision makers draw managerial insights. Thus we intend to overcome the

limitations of previous studies that are purely methodological and lack quantitative analyses of business

impacts. In addition, the obtained Pareto fronts help decision makers easily visualize and understand the

business impacts of resulting supply chains as they reconfigure supply chains according to their unique

and subjective business strategies.

3. FRAMEWORK OF THE PROPOSED AGILE SUPPLY CHAIN DSS

The research framework for agile supply chain DSS consists of the following four major steps:

(1) identification of evaluation criteria and decision hierarchy, (2) identification of evaluation criteria

weights, (3) supplier evaluation and selection using the fuzzy AHP and fuzzy TOPSIS methods, and (4)

business impact assessment of the proposed system. We present the first three steps in the current

section, and business impact assessment of the proposed system in the Sections 4 and 5, respectively.

Finally, a supply chain consisting of multiple suppliers is used to compare business impacts of agile and

non-agile supply chains in response to unexpected disruptions in Section 6.

3.1 Identification of Evaluation Criteria and Decision Hierarchy

We first identify both quantitative and qualitative evaluation criteria to evaluate candidate

suppliers to formulate supplier evaluation and selection problem as an MCDM problem. In particular,

we identify several sub-criteria within in each main criterion and form the decision hierarchy based on

relationships between main and sub-criteria toward the ultimate goal of selecting the fittest suppliers.

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To this end, five managers or assistant managers from a leading Korean automotive company were

interviewed as industry experts to identify and determine the necessary criteria. During this interview,

the critical factors that influence decision-makers with respect to the core requirements of buyers were

identified and synthesized. In addition, we have reviewed the literature to collect the criteria adopted in

previous supplier evaluation problems. Specifically, we searched articles with keywords such as

‘supplier selection’, ‘supplier evaluation’, ‘vendor selection’, ‘partner selection’, and ‘supply chain

design’, resulting in more than 20 studies from leading journals such as Expert Systems with

Applications, European Journal of Operation Research, International Journal of Production Economics,

and Journal of Purchasing. Subsequently, evaluation criteria used in these studies were presented to

industry experts and were grouped and verified by them and authors together in terms of their

significance and attainability. In the end, four main evaluation criteria, namely the general management

capability perspective (GP), manufacturing capability perspective (MP), collaboration capability

perspective (CP), and agility perspective (AP) were categorized. Each criterion includes two to nine sub-

criteria. Table 1 describes the 25 sub-criteria of the four main criteria. Note that some sub-criteria, such

as production facility and capacity, could either be categorized as a type of manufacturing capability or

as a type of agility. In such cases, experts are asked to determine which main criterion is the best fit for

the sub-criteria, and we follow their suggestions. In addition, we also consider the fact that traditional

supply chains without explicit consideration of agility should also respond to the demand change to

some degree and hence assigning such sub-criteria into non-agility main criteria is appropriate.

Table 1. Descriptions of the Main Criteria and Sub-criteria

MainSub-criteria Description

criteria

GP Management and strategy (MS) The degree to which a supplier is in line with the firm’s vision, strategy, and policy

Financial status (FS) The degree to which a supplier is financially stable

Customer relations (CR) The degree to which a supplier has strong customer relationships

Training program (TP) The degree to which a supplier has well-defined HR training programs

Reputation (RE) The degree to which a supplier has a good reputation

History (HI) The degree to which a supplier has a long history in the business

Language (LA) The degree to which a supplier has the ability to communicate in multiple languages

License/Certification/Award (LCA) The degree to which a supplier has certified qualifications

Geographical location (GL) The degree to which a supplier is located nearby

MP Production facility/capacity (PFC) The degree to which a supplier has considerable production capacity

Product diversity (PD) The degree to which a supplier offers diversified products

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R&D capability (RD) The de gre e to whi ch a supplie r put s effort into R& D activities

Safet y re gulations (S R) The de gre e to whi ch a supplie r ob eys safe ty regul ation s

Environm ent al regula tion s (E R) The de gre e to whi ch a supplie r is e nviron mentally friendly

Q uality control ( QC) The de gre e to whi ch a supplie r co nduc ts quali ty c ontr ol actively

Produ ct price (PP ) The de gre e to whi ch a supplie r offers a cheape r price

C P A fter-sale s se rvice (A S) The de gre e to whi ch a supplie r pro vid es g ood after-sales service

D elivery relia bility ( DR) The de gre e to whi ch a supplie r meets deli very req uire ments

A P D elivery spee d ( DS) The de gre e to whi ch a supplie r meets deli very speed r equirements

D elivery flexibility ( DF) The de gre e to whi ch a supplie r can respond to change s in delivery requirements

M ake fle xibility ( MF) The de gre e to whi ch a supplie r can respond to change s in production requirements

Sourc e fl exibility (SF ) The de gre e to whi ch a supplie r can respond to change s in source requirements

A gile customer re sponsivene ss ( ACR ) The de gre e to whi ch a supplie r can respond to change s in customer requirements

Collabora tion with pa rtne rs ( CPB ) The de gre e to whi ch a supplie r can col lab orate across each partner’s core business

I T inf rastructure (IT) The de gre e to whi ch a supplie r ad opts a practi cal IT sy stem

O nce the s upp lier e val uat ion criteria were i den tified, the decision hier arc hy for supplier selection a

t f our le vel s was str uct ured as s how n in Figure 1. The t op level of the hierarchy represents the ultimate g oal

o f se lec ting t he best s upp lier. T he secon d lev el i s g roupe d u nde r crite rion o f GP, MP, CP, and AP.

At the third level, various s ub-criteria that measure th e can did ate s upp liers in detail are presented.

Fin ally , t he bot tom level of th e hierarch y p re sents the can di dat e su pplier s.

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Figure 1. Decision Hierarchy of Supplier Selection

3.2 Identification of Evaluation Criteria Weights

After forming the decision hierarchy, we calculated the weights of the evaluation criteria using the fuzzy AHP. To this end, we first briefly review the AHP method (Saaty, 1980) introduced to solve various qualitative and quantitative MCDM problems involving subjective judgments such as determining the importance of factors in product design and selecting the best product concept (Raharjo

et al., 2008). Technically, AHP determines the relative priority (wi) of the ith criterion by exploiting a multi-level hierarchical structure of decision-making problems. Given a set of decision criteria {1,…,n},

the AHP method starts to construct a pairwise comparison matrix A(n×n) whose element aij (≠0)

represents the relative importance of the ith criterion compared with the jth criterion by using pre-defined numerical comparison scale scores S={1, 2, 3, 4, 5, 6, 7, 8, 9}, 1 for equally preferred and 9 for absolutely preferred, by carrying out full pairwise comparisons of n decision criteria. By definition, the

values of aii and aji are set to 1 and 1/aij, respectively. The relative normalized weight of the ith decision

criterion is then calculated by calculating the geometric mean of the ith row of a pairwise comparison matrix A, resulting in a normalized comparison matrix R. The final weights for each criterion are calculated from this final normalized comparison matrix R by calculating the average of the elements of each rows.

However, the requirement of obtaining full pairwise comparisons of evaluation criteria based on

pre-defined numerical comparison scale scores of AHP (i.e., S={1, 2, 3, 4, 5, 6, 7, 8, 9}) cannot suitably

address the uncertainties and ambiguities involved in the assessment of evaluation criteria with the

linguistic variables more frequently adopted by decision makers. That is, decision makers often prefer

using linguistic variables such as “(the ith criterion is) Equally (preferred to the jth criterion), Weakly,

Fairly Strongly, Very Strongly, Absolutely” to using numerical comparison scale scores in the pairwise

comparison process. Therefore, it is necessary to transform evaluation inputs based on linguistic

variables into numerical numbers for each criterion using triangular fuzzy numbers that allows partial

membership (or truth) of linguistic variables to numerical numbers (Chan et al., 2008; Chang, 1992).

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Table 2. Priority Weights for Evaluation Criteria

Main criteria Priority weights Sub-criteria (Priority weights)

GP 0.12 MS (0.15) HI (0.07)

FS (0.16) LA (0.00)

CR (0.17) LCA (0.14)

TP (0.00) GL (0.10)

RE (0.21)

MP 0.41 PFC (0.22) ER (0.00)

PD (0.00) QC (0.31)

RD (0.13) PP (0.34)

SR (0.01)

CP 0.10 AS (0.54) DR (0.46)

AP 0.38 DS (0.00) ACR (0.27)

DF (0.09) CPB (0.10)

MF (0.19) IT (0.33)

SF (0.02)

We present calculated priority weights of main criteria and sub-criteria in

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Table 2 based on a geometric mean method. The detailed calculation procedure is explained in

Appendix A. The industry experts considered MP (0.41) the most important main criterion in the

process of selecting the best supplier. Also notable is the fact that they estimate the importance of AP to

be 38% in the automotive industry. This is significant considering the fact that experts were not

informed of or influenced by any member of research teams to weight this new criterion more, but were

simply advised to determine the priority weights of the four criteria to “select the best supplier” in their

business domain.

3.3 Supplier Evaluation and Selection

Once the relative weights of each evaluation criterion of candidate suppliers were determined by

fuzzy AHP, fuzzy TOPSIS was then used to rank candidate suppliers. The TOPSIS (Hwang and Yoon,

1981) is based on the concept that the chosen supplier should have the shortest geometric distance from

the positive ideal solution and the longest geometric distance from the negative ideal solution. Note that

the positive ideal solution consists of all of best values attainable of criteria, whereas the negative ideal

solution is composed of all worst values attainable of criteria. To this end, decision makers provide their

valuable inputs in regard to how ideal each candidate supplier is for each criterion using a set of

numerical scale scores. Once a normalized numerical value for each criterion over a set of candidate

suppliers is obtained, the geometric distance between each supplier and the ideal supplier with the best

score in each criterion is computed to determine rank among suppliers over multi-criteria.

In fuzzy TOPSIS (Chen et al., 2006), the fitness (or utility) of the candidate suppliers with

respect to each criterion is represented by a fuzzy number using linguistic variables and, hence, the

ranking of the suppliers is based on the comparison of their corresponding fuzzy utilities. Following the

concept of TOPSIS, the fuzzy positive ideal solution (FPIS) and the fuzzy negative ideal solution (FNIS)

are defined and the distance of each supplier from FPIS (D+) and FNIS (D-) calculated. Finally, the

closeness coefficient (CC) value of each supplier is calculated and the ranking order of all candidate

suppliers is determined to select the best one from a set of candidate suppliers.

For our study, we artificially generated a number of suppliers with well distributed scores over

main criteria and sub-criteria. Specifically, we simulated 100 candidate suppliers’ information (CS1–

CS100) along with virtual experts’ judgment of each candidate supplier for the individual criterion using

the linguistic variables and their corresponding fuzzy numbers: (0,1,3)-very poor, (1,3,5)-poor, (3,5,7)-

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fair, (5,7,9)-good, and (7,9,10)-very good. Note also that we maintain positive relationships between judgment values of sub-criteria within the same criterion with approximately 20% noise level so that a

supplier si with the highest value for a criterion ci does not necessarily receives the highest value for

other criteria cj while the value of cj is likely to be high. Then, it becomes straightforward to determine the ranking order of all candidate suppliers by following the steps illustrated in Chen et al. (2006). Rankings of exemplar suppliers are described in Table 3.

Table 3. Fuzzy TOPSIS Results and Rankings

w/ considering AP (agile supply chain) w/o considering AP (non-agile supply chain)D+ D- CC Ranking D+ D- CC Ranking

CS1 0.180 0.841 0.824 1 0.165 0.474 0.742 3

CS2 0.246 0.779 0.760 4 0.203 0.438 0.683 13

CS3 0.409 0.625 0.605 25 0.191 0.450 0.702 8

CS4 0.379 0.654 0.633 21 0.083 0.554 0.870 1

Note that we present two different outcomes of fuzzy TOPSIS in Table 3: one considers all four

main criteria and their associated sub-criteria, and the other considers only three main criteria,

eliminating AP. We denote the resulting supply chain based on the first outcome as the agile supply

chain, whereas the resulting supply chain based on the second outcome as non-agile supply chain mainly

because it does not explicitly consider AP criterion.

In Table 3, the ranking orders of the candidate suppliers are very different depending whether or not AP criterion was considered as an input of fuzzy TOPSIS. For example, CS1 was chosen as the best supplier when AP was considered, while CS4 was the best when AP was not considered. In addition,

while CS1 was a top ranked supplier in either case (i.e., 1st with AP and 3rd without AP), rankings of

many other suppliers were significantly different (e.g., CS3 was ranked 25 th with AP, but 8th without

AP). This in turn implies that the resulting agile supply chain and non-agile supply chain will be very different in their nature of meeting the business requirements. In the following section, we compare the business impacts of the two resulting supply chains in a very simple but generalizable configuration.

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4. BULLWHIP EFFECT CHANGE IN AGILE SUPPLY CHAIN WITH A SINGLE SUPPLIER

4.1 Simple Supply Chain Configuration

The business impact of the proposed agile supply chain DSS is quantified by comparing the

magnitude of the bullwhip effect of the resulting agile supply chain with that of the legacy supply chain

systems that are partially agile or not agile at all. Again, the bullwhip effect is the phenomenon in which

variance of demand information is amplified when moving upstream in supply chains (Lee et al., 1997).

To quantify the magnitude of bullwhip effect of agile and non-agile supply chains, we imagine a very

simple supply chain consisting of one buyer and one supplier in Section 4 and 5.

In this simple supply chain, the customer demand is assumed to follow the AR(1) autoregressive

model while order lead time is considered to be fixed. We also assume that the buyer employs a simple

order-up-to inventory policy with the forecasted demand based on either minimizing mean-squared

forecast error technique or moving average forecasting method. We adopt the following set of notations

to describe this simple supply chain.

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demand of period t

qt order quantity at the beginning of period t

St order-up-to level at the beginning of period t

φ the first-order autocorrelation coefficient

δ the constant of the autoregressive model

μd mean of the autoregressive process which is used to describe the demand

process σd2 variance of demand

L order lead time

DtL lead-time demand

ˆ L

lead-time demand forecastDt

σˆtL standard deviation of lead-time demand forecast error

εt forecast error for period t , i.i.d. from N(0,σ2)

z the constant chosen to meet a desired service level

Note that St , the inventory position at the beginning of period t after the order has been placed, is

ˆ Lˆ

L

calculated as St = Dt after considering the lead-time demand forecast of period t to support the+ zσt

desired service level in accordance to the business strategy. Once the value of St is determined, the

order quantity, qt , at the beginning of period t is determined as follows: qt = St − St −1 +Dt−1. Since we

assume that the customer demand follows the AR(1) autoregressive model, it is modeled by

δ 2 σ 2

φ, and it is trivial to show that

E ( Dt ) = μ d = 1 − φand

V a r ( Dt ) = σ d =. Now, if the

1 − φ 2

buyer forecast demand by minimizing the expected mean squares of error, lead time demand forecast

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and its variance can be determined by ˆ L

= μ d ( L −φ (1 − φ L )

) +φ (1 − φ L ) and

D t1 − φ 1 − φ

Dt −1

L 2 σ d2 (1 + φ ) L i 2 , respectively. Then, order quantity is obtained by

(σ t ) = ∑ (1 − φ )

ˆ

1 − φ i =1

q t =1 − φ L +1 D

t − 1 −φ (1 − φ L ) D

t − 2 , (1)1 − φ 1 − φ

and variance of order quantity is calculated (Luong, 2007) as shown in Equation (2)

V A R ( qt ) =(1 + φ )(1 − 2 φ L + 1 ) + 2φ 2 L + 2

σ d2 .

(2)1 − φ

Finally, the magnitude of the bullwhip effect (B) can be determined by taking the ratio of the variance of

order quantity and the variance of demand as shown in Equation (3) (Chen et al., 2000; Luong, 2007).

B =

Var ( q )

=

(1 + φ )(1 − 2φ L +1 ) + 2φ 2 L+ 2t

(3)σ d

2 1− φ

On the other hand, if demand is predicted with moving average forecasting of p observations, the

order quantity is obtained by

q t = (1 +L

) D t − 1 − (L )

D

t − p − 1 +

z

L ( S t − St −1 ) (4)p p

p

p

2

D

∑ˆ

) ∑ t − i( Dt − i − μ t

where i = 1 and ˆ i =1 . The magnitude of the bullwhip effect can be calculated as

S t =p − 1

μ t =p

a lower bound form (Chen et al., 2000) as shown in Equation (5):

B =Var ( qt )

≥ 1 + (2 L

+2L2 + z 2 L

)(1 − φ p ) (5)

σ d2 p p2

4.2 Bullwhip Effect with Autocorrelation Coefficient and Desired Service Level

We compare the magnitude of the bullwhip effect of the agile supply chain with that of the

legacy (or non-agile) supply chain system. In this section, we are particularly interested in estimating the

magnitude of the bullwhip effect that changes as the first-order autocorrelation coefficient of the

customer demand and desired service level change. By definition, with higher values of autocorrelation

15

coefficient, the demand of the current time is more dependent on the demand of the last time, and the

demand line fluctuates more violently due to the increasing variance. Therefore, it is easy to conjecture

that the magnitude of bullwhip effect of two supply chains increases as the value of autocorrelation

coefficient increases. However, since the agile supply chain should be able to adapt much swiftly to

unexpected customer demand than non-agile supply chain, we expect the difference in the magnitude of

the bullwhip effect of two supply chains to become larger as the value of autocorrelation coefficient

increases.

We show the magnitude of bullwhip effect of agile and non-agile supply chains in Figure 2(a),

where x-axis and y-axis represents the first-order autocorrelation coefficient in demand (φ ) and the

magnitude of the bullwhip effect (B), respectively. As expected, the magnitude of the bullwhip effect

from the agile supply chain is much smaller than that of non-agile supply chain although the differences

in B values of two supply chains are greatly affected by φ . First of all, we note that the maximum

magnitude of bullwhip effect of agile supply chain does not exceed three, indicating that the variance of

order quantity is less than three times that of demand. However, in the non-agile supply chain, the

maximum value of B is greater than nine, reflecting much greater fluctuation in variance of order

quantity over variance of demand. Also, our simple lead time analysis from data sets (i.e., the lead time

of agile and non-agile supply chain is one and nine days) confirms the significant difference in B values

of the two supply chains. Secondly, we also note that the difference of B values of the two supply chains

is not noticeable until φ = 0.3, but afterward the difference becomes very obvious with higher values of

φ . This implies that keeping the supply chain agile becomes even more critical when demands are highly

correlated to minimize unexpected risks estimated through B values. Interestingly, the B values of two

supply chains start to decrease after φ reaches a certain point (i.e., φ = 0.7 and φ = 0.9 for agile and non-

agile supply chain, respectively) partly because it is relatively easy for the buyer to forecast highly

correlated demand. Overall, these observations imply that a non-agile supply chain is likely to suffer

from a much larger bullwhip effect. In our following analyses, we limit our discussion to the specific

value of autocorrelation coefficient (φ = 0.8) for both supply chains where both supply chains suffer

from near maximum risks.

16

( a) Au toc orr ela tion C oeffic ien t (b) Desire d Service Lev el

Figur e 2 . B ullwhip Effect Trend s with Auto co rrelati on and S erv ice Level

Simi larly, we ill ust rate the relatio nship between the va lu e o f B and d esi red se rvi ce lev el ( z ) in

Fig ure 2(b). No te tha t service le vel used in calculati ng order-up- to-level is s trategically deter min ed by the

de cision ma ke r a nd it ulti mately determi nes sto ckout (or o ut- of-s toc k) rate. S in ce fre quent sto cko uts

c ause lost sales, dis satisfi ed sh opp ers, and dimi nis hed store lo ya lty, it is im porta nt to maint ain an

a pprop riate s er vic e level w hile av oi din g e xtr em ely hig h inv ent ory costs inc ur red fro m ov erstoc ks. In our

s imple supply c ha in, when z= 0 , stoc kou t r ate is

estimated to be 15.8 %, a nd w hen z ≥ 3 , stoc kout r ate

is l ess th an 0.1% (Peterson , 198 5). Note that Equ atio n ( 3) does not in clude des ired serv ice level as an

inp ut parameter and hence th e value of B do es not ch ange ev en if the de sired ser vic e l ev el varies.

The refore , we use Equ ation (5) to det erm in e t he lo wer boun d of B as sum ing that the no rm ally

d istributed dem an d is fo rec ast ed with a m ov ing a ver age of p = 5 o bserva tions. A ccording to Fig ure 3,

the B v alu es of bot h a gile and no n-agil e su pply chains ste adily increa se as the buyer seeks high er

serv ice leve ls mainly b ec ause i t in cre as es bot h orde r-u p-to-leve l and order qu antity. H ow ever,

th e tren d of B v al ues of the ag ile supply chai n is m uch m ore stable in respon d to th e serv ice level

th an t hat of the non-a gile sup ply chain. W hile the B val ue s of a gile su pply cha in do no t cha nge si

gnific antl y over vari ous s erv ice levels, the B val ues of non-agile s upp ly ch ain chang e sign ifi

cantly fro m nin e whe n s er vic e level is zero to clo se to 14 when service le vel is fo ur.

17

4.3 The Pareto Fronts with Various Weights of Agility Criterion

Figure 3 illustrates the Pareto fronts of the two supply chains. The Pareto front of the agile supply chain (shown as the solid line) represents the B values of agile supply chain constructed with a

set of 1st ranked suppliers as we vary the weight of the AP between 0 and 1 while maintaining the same

relative weight ratios of the other main criteria and sub-criteria as in

18

Table 2. That is, it simply displays the minimum B values of agile supply chain associated with

1st ranked suppliers that naturally vary as we increase or decrease the weight of AP. For example, when

AP weight is set at 0.4 in the process of selecting the best supplier, we evaluate all candidate suppliers

using fuzzy TOPSIS method explained in Section 3.3. Assuming that CS1 is chosen as the best supplier

out of all candidate suppliers, we identify its lead time (1.65) from the database. Then, the minimum

magnitude (2.1) of bullwhip effect of the agile supply chain is calculated based on Equation (3). We

repeat this routine until we calculate the magnitudes of bullwhip effect for all possible weights of AP.

Note, however, that the B values of the non-agile supply chain do not change even if we vary the weight

of AP because, by definition, non-agile supply chain is constructed with 1st ranked supplier chosen

without considering AP criterion. Therefore, the same supplier will be always chosen and, hence, the

Pareto front of non-agile supply chain should be represented as a straight line. In order to obtain a

dynamically changing Pareto front of non-agile supply chain without sacrificing the applicability of the

proposed model and the generalizability of managerial insights, we first compute the ratio of lead time

of agile to non-agile supply chains for a chosen weight of AP criterion. Since 1st ranked supplier and the

corresponding lead time of agile supply chain varies as the weight of the AP criterion varies, this ratio

dynamically changes as the weight of the AP criterion varies. Specifically, the ratio is supposed to

increase at a decreasing rate as the weight of AP criterion increases because the lead time of the agile

supply chain with higher agility decreases. Once we obtain the ratio of lead time over various weights of

AP criterion, we multiply it with the original fixed lead time of the 1st ranked supplier of the non-agile

supply chain, and calculate B values from the lead time to obtain the dynamically adjusted Pareto front

of the non-agile supply chain. The dotted line in Figure 3 represents such a Pareto front of the non-agile

supply chain. While it is more appropriate to denote it as a lead time ratio between agile and non-agile

supply chain, we simply name it a Pareto front of the non-agile supply chain for notational convenience.

The Pareto fronts intersect at the point where AP weight is set to zero.

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Figure 3. The Pareto Fro nts of Bu llw hi p Effect

A s e xpe cte d, the Pa reto fron t o f t he agile supply c hai n s ho ws the tre nd of decreasing B values b ecause

sup pliers with m ore a gility are chosen as 1st r anked su ppl iers as th e w eig ht of AP in cre ases. O ne ma nageri al

implic atio n o bt ain ed fro m the Par eto fr ont of ag ile sup ply ch ai n is th at it p ote ntially pr ovides the list of best s

uppli ers as well as corresponding B va lu es o f the sup ply ch ai n th at the buyer ca n c hoose b as ed on her u nique

an d s ubjective bu sin ess strat egy. For ex am ple, when th e buyer do es not consider

a gility as a critical cr iterio n f or configuri ng her su pply chain, B values that her best con figure d s upply c

hain faces wil l foll ow th e Pareto front of the n on-agile sup pl y chain. However, if sh e review s and

restructures her supply chain into an agile su ppl y c hai n to effec tively re spond to une xpected de ma nd and

mar ket fl uct uations, B values will fo llow the Paret o fron t of agile su pply chain. Th eref or e, i f we assume

that the buy er rec onfigures h er su pply c hain from no n-a gile s upp ly chain to ag ile su pply ch ain by s ign

ifican tly in cre asi ng the we ig hts of AP fr om 0 to 0 .4, th e B value of her a gile su pply chain drops 4.5 to 2 .1

(i.e ., 53 % d ec rea se) fo llo wing the pat h of the Paret o fr ont o f a gile su pply cha in. H ow ever, t his

ma gnitude of positive busines s imp act is regarde d as an o ve rly conserva tive esti ma te c onsideri ng the

fact that i f she do es not re con figure her supply chain into an agile sup ply c hai n, h er su pply chain will

s uff er from greater b ull whip e ffect along the Pa reto fron t of th e non-ag ile supply c hain. In suc h a ca se,

the B v alu e that her non-agi le supply ch ain will face in cr eas es f ro m 4.5 to 6 .2 (i.e ., 3 8% in cr eas e). Ta ken

a ll t ogether, the total impac t of re confi guring supply c hain by increasing t he r ela tive w ei ght of agility in

20

supplier selection is the sum of improvement due to the increased agility (53%) and the nature of the

new agile supply chain (38%).

Another important managerial implication that decision makers obtain from Figure 3 is that she

can determine an appropriate weight of agility in her supply chain configuration. That is, while it is

tempting to make her supply chain extremely agile, the positive business impact due to decreased B

values increases at a decreasing rate. For example, even if the buyer decides to increase the weight of

AP from 0.4 to 1.0, B values only marginally change and hence she may not enjoy any considerable

business impacts. In contrast, the buyer may enjoy great business impact by increasing the weight of AP

from 0.2 to 0.4 easily. This way, decision makers can make informed judgments to determine an

appropriate level of agility in her supply chain configuration.

4.4 The Pareto Fronts with Various Weights of Agility Sub-Criteria

We present in Figure 4 outcomes of sensitivity analyses of a sub-criterion within AP while

maintaining the priority weight of AP at 0.38 and the same weight ratios among other sub-criteria within

AP as in

21

Table 2.

22

(a) I T in fra structure ( b) Agi le Cu sto me r Responsiv eness

(c) So ur ce Fle xibilit y (d) Deliv ery Fle xi bility

Figure 4. Imp ac ts of A gility Sub-c rit eria on Bull whi p E ffe ct

Fo r e xa mple, Fig ur e 4 (a) illu strates t he Pareto fr ont of agile sup pl y c hai n as w e v ar y th e weight

o f IT infrastructure ( IT) within A P from zer o t o 1 witho ut ch anging weight ratios of oth er su b-c riteria.

We im me dia tely n ote th at the im pact of t he IT sub-crit erio n on the B val ue is marginal (but neg ative)

e ven w ith it s g reatest po ssi ble weight (1. 0) consideri ng the fact that IT ( weight 0. 33) is consi dered the

mo st important sub-c rit erio nby ex per ts. Th e Pareto front of the ag ile supply c hain based on adjusted

weights of deli ver y s peed (DS) also sh ow s a very s imilar pa ttern of I T criteri on and he nce is no t sho wn.

Fig ure 4( b) shows th at the typical Pareto fro nt o f t hree other s ub-cri teria: agil e c ustom er respo nsi veness

(AC R), m ake flexibi lity (M F), and co llab or atio n wit h partners ( CPB) tha t all s how simila r d ecreasing

tren ds of B v alu es as their weights beco me greater than cert ain val ue s (e .g., 0.2 f or ACR, 0.1 for M F and

23

CPB). Finally, Figure 4(c) and (d) show Pareto fronts of agile supply chains based on varying weights of

source flexibility (SF) and delivery flexibility (DF), increasing trends of B values as weights of the

criteria increase. All these trends in Figure 4(a) ~ (d) result from the fact that a different supplier is

selected as the weight of a chosen sub-criterion varies. One interesting managerial insight gained from

Figure 4 is that as priority weights of sub-criteria with minimal weights in

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Table 2 deviate farther from weights pre-determined by industry experts, B values greatly

increase. For example, as priority weights of DF and SF increase from (0.09 to 0.6) and (0.02 to 0.6), B

values of agile supply chains significantly increase from 2.1 to 4.5 (114%), implying that decision

makers should not try to significantly vary priority weights of sub-criteria within AP from the suggested

weight values by industry experts. Rather, they are strongly advised to maximize the positive impact on

their supply chains by increasing the weight of AP while maintaining similar relative weights of sub-

criteria within AP as shown in

25

Table 2. In the following section, we compare economic impacts of two resulting supply chains

with the same assumptions.

5. INVENTORY COST CHANGE IN AGILE SUPPLY CHAIN WITH A SINGLE SUPPLIER

5.1 Inventory Cost Change with Autocorrelation Coefficient and Desired Service Level

To estimate the economic impact of agile and non-agile supply chains, we calculate inventory

cost by running simulation under the same assumptions as in Section 4. It is noted that inventory cost is

composed of order cost, holding cost, and shortage cost. In this study, we ignore shortage cost since

most suppliers pursue high service level to avoid stockout. While we admit that it is very subjective to

estimate these costs, we try to avoid such criticism by following a well-defined cost classification

scheme, AIAG’s materials off-shore sourcing (MOSS) project (2009), in the automotive industry.

According to this scheme, we estimate the cost of the single most important part (engine and

transmission) to be US$3,000, while ordering cost and holding cost to be US$18.3 and US$438.

We show the economic impact of agile and non-agile supply chains in Figure 5(a), where the x-

axis and y-axis represent the first-order autocorrelation coefficient in demand (φ ) and the inventory cost

in US million dollars (US$M) computed by sum of order cost and holding cost, respectively. As

expected, the economic impact (measured by inventory cost) of the agile supply chain is much smaller

than that of the non-agile supply chain although differences are greatly affected by φ . Specifically, we

find that the maximum inventory cost of agile supply chain is near US$160 M while that of the non-

agile supply chain is greater than US$370 M. We attribute the higher inventory cost of the non-agile

supply chain to the fact that it should hold more safety stocks because of its inability to respond to

changes of demand appropriately According to our simulation results presented in Figure 5(a), the agile

supply chain can save from US$70 M to US$210 M in inventory costs via reducing holding stocks

depending on the autocorrelation strength of market demand.

26

(a) Autocorrelatio n Coefficient (b ) Desired Se rvice Le vel

F ig ure 5. Ec onomic I mp act Tr end s w ith Autocor relati on and Se rvice Le vel

W e also obse rv e t hre e diff ere nt regions o f how i nve nto ry costs of b oth ag ile an d non -a gile

s upply chains cha nge in res pond to cha nges in a ut ocorrelation streng th of marke t deman d: i) in se nsitive

regi on ( φ ≤ 0. 5), ii) sensitiv e region (0.5 ≤ φ ≤ 0. 8), and iii) hig hl y sens iti ve region ( φ ≥ 0.8). In

p art icu lar, w e observ e that sh ar ply increasi ng pat terns of inv entor y costs in a rang e of φ (≥ 0.8) are

c om pl etel y opposite to sharply decr ea sin g patte rn s of B value s a s sho wn in Fi gure 2(a), i mplyin g that

e ffo rts to re duce the bullwhip effect d o not nec ess arily reduce in ve ntory cost. This is p oss ible b ecause

the differenc e b et wee n dem an d and order quantity ca n be lar ger as th e v alue of φ beco me s large r. For

e xample, unde r our mo del s pecifi ed in Se ctio n 4.1, t he dai ly average gap a t e ac h p eriod betw een

d em and a nd order q uantity in cre as es as φ inc reases: 130 (= 2500 – 23 70 when φ = 0.6),

1 40 (= 3 333 – 3190 wh en φ = 0.7), 1 55 (= 5000 – 484 5 at whe n φ = 0. 8), and 170 (= 10 000 – 9 830

whe nφ = 0.9). Th is mean s th at ord er quantity wi ll nev er me et marke t d em and w hile bullwh ip eff ect

c om puted by taking a ra tio of the varia nce of or der quantity an d th e v arian ce o f d em and is redu ced.

In order to id enti fy the relation shi p betw ee n t he inventory co st and de sired service l evel ( z ), we

o bt ain ed ann ual in ventory cos ts from 1,0 00 sim ul atio n runs w ith the foll owi ng param eter setting s: δ =

1 000, φ = 0.8, and (f or t he ini tial desi red servi ce level, 99.0% ). We present

relationsh ips between the in ventory cos t a nd desired service le vel of agile a nd non-a gile supp ly ch ain s in

Fig ure 5(b). As ex pe cte d, the inv entor y c ost of the ag ile supp ly c hain is muc h low er in res pon se to the s

erv ice level than that of non-agi le sup pl y c hai n. For example, w hen t he desired service le vel is set at

27

99.0% ( z = 2.33 ), the inventory cost of the agile supply chain is estimated to be US$90 M but that of

the non-agile supply chain is estimated to be about three times higher (US$250 M). When a higher

service level (99.9%, z = 3.10 ) is targeted, a wider gap of inventory costs between agile and non-agile

supply chains is revealed (US$ 120 M vs. US$300 M).

5.2 The Inventory Cost Pareto Fronts with Various Weights of Agility Criterion

Figure 6 illustrates the Pareto fronts of the two supply chains focusing on inventory costs. The Pareto front of the agile supply chain (shown as the solid line) represents the trend of inventory costs of

agile supply chain constructed with a set of 1st ranked suppliers for varying values of agility criterion.

Because the same suppliers are chosen as 1st ranked supplier for a specific value of agility criterion, the Pareto fronts of the two supply chains in Figure 6 takes the exactly same shape as those in Figure 3 except that the y-axis represent inventory cost instead of the magnitude of bullwhip effect.

As expected, the inventory cost Pareto front of the agile supply chain shows the trend of decreasing

inventory costs with the same reason of decreasing B values in Figure 3. One of managerial implications

obtained from the Pareto front of the agile supply chain is that it potentially provides the trade-off

relationship between weight of agile perspective and inventory cost. For example, if we assume that the

buyer reconfigures her supply chain from non-agile supply chain to agile supply chain by significantly

increasing the weight of AP from 0 to 0.4, the inventory cost drops US$83 M to US$58 M (i.e., 30%

decrease) following the Pareto front of agile supply chain. However, if she configures non-agile supply

chain, the economic impact of reconfiguring supply chain will increase from US$83 M to US$104 M (i.e.,

25% decrease). Taken all together, the total economic impact of reconfiguring supply chain by increasing

the relative weight of agility in supplier selection is US$46 M composed of the increased agility (US$25

M, 30% decrease) and the nature of the new agile supply chain (US$21 M, 25% decrease). Another

managerial implication that decision makers obtain from Figure 6 is that she can determine an appropriate

weight of agility in her supply chain configuration. That is, decision makers of the buyer can make

informed judgments to determine an appropriate level of agility to minimize inventory cost.

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Fig ure 6. Th e P ar eto Fr onts o f Inve ntory Cos t

6. AS SESS ING RESI LIE N CE O F A GILE S UPPL Y CH AIN WI TH M ULTI PL E S U PPLIE R S

Su pply chain res ili ence c an be de fined as th e abili ty to return to it s origi na l state after being d

isrupted (Christo phe r & Peck , 200 4). In this se ction, in or der to assess resilienc e o f agile s upp ly ch ain, we

co mpare bu sin es s c ost s of agile a nd no n-agil e s upp ly chains befo re an d after reconfigurati ons of

s upply ch ain s in r espon se to u nexp ecte d disr uptio ns i n business env ironm ents. To this end, we

assume that the fittest sup plie r in t he current s upp ly cha in ca nnot s erve as a business partner due to un

ex pected e nvironmental rea sons ( e.g ., a flo od or an ea rth quake in the geogr aphical loca tion o f t he sup

plier) . T hen the bu yer need to replace it with candidate sup plie rs and m ay consider chan ging orde r allo

cati on rat ios a m ong suppl iers f or sup ply quantitie s prov id ed by the to-be- rep la ced supplier .

T he first strat eg y of o rde r a llocation a mo ng su ppl iers is to allocate the entire qua ntity of the

fitte st su pplier to the second fittes t s uppli er that possess th e manufacturing capab ili ty to meet the d em

and. Under this circ um sta nce, the rec onfiguratio n cost of supply c hain is s imply the d iff erence of

b ull wh ip effect magn itu de or in ven tory c os t b etw ee n t he fittest and the sec ond fittest sup plier. Si nce e

stimatin g t he busine ss co st o f suc h s trateg y is tr ivia l, we do no t p res en t th e o ut com e. Th e oth er two s

trategies maintai n a set o f m ultiple supp liers by alloca ting o rd ers am ong the m to minimize business

29

costs from reconfiguration of supply chains. Note that these strategies can result in significantly

different results because of their order allocation proportion among suppliers. For example, SOA

strategy is to allocate most of order demand to the fittest supplier and the remaining orders to the other

suppliers in the supply chain. While SOA strategy takes a full advantage of operational efficiency

including agility of the fittest supplier, its reconfiguration cost may be substantial when the fittest

supplier cannot serve as a business partner for any reasons. In contrast, EOA strategy is to evenly

allocate order demand among multiple suppliers to make the supply chain agile so that it responses

efficiently and effectively to the disruption of the supply chain.

To study the Pareto fronts of original and reconfigured supply chains associated with SOA and

EOA strategy, we assume that both agile- and non-agile supply chains before disruption are composed

of three best suppliers based on multiple criteria and selection methods explained in previous sections.

Specifically, we assume that order allocation for three suppliers under SOA strategy is 60%, 20%, and

20%, respectively, while it is 35%, 35%, and 30% under EOA strategy. Then, assuming that the supplier

with the largest order allocation is not available any longer, the buyer needs to reconfigure its supply

chain with new suppliers so that it seamlessly procure the order quantity of the disrupted supplier. Since

it is almost impossible to simulate all possible different combinations on how many new suppliers

produce how much of the disrupted order allocation, we assume that two new suppliers in reconfigured

supply chain take over the disrupted demand. Specifically, we assume that the buyer allocates 30% of

order to each new supplier in SOA strategy case, and 20% and 15% to each new supplier in EOA

strategy case. We summarize these settings in Table 4.

30

T abl e 4 . Order A llocation wi th SOA and EOA Strategy

B ef ore Re co nfi gurati on After Reconfiguration

Sup plier S1 S2 S3 S4 S5 S1 S2 S3 S4 S5

SOA 60 % 20 % 20 % 0% 0% 0% 20% 20% 30% 30%

EOA 35 % 35 % 30 % 0% 0% 0% 35% 30% 20% 15%

N ote tha t w e adj ust ord er all ocation r atio s amo ng su pplier s after the reconfiguration in both SOA

a nd E OA strategy to be sim ilar s o th at we can compa re b usiness imp acts of supply chains with different

o rd er all oc atio n str ategie s befor e the reco nfigu ration but si milar order allocation after the

rec onfigurat ion. N ote also tha t while multip le criteria for selecting new suppliers for agile- and non-

a gile s upply c hai n are differ ent, both su pply cha ins can be im ple mented with either SOA or EOA

s trategy. Th e m ain differen ce of agile sup ply c hai n fr om n on-agile supply chain is that its B values are

d epend ent on t he deg re e of a gility weight in e val uating an d s ele cting suppliers. In summary, for each

SO A a nd E OA str ategy, there will be tw o agil e s upp ly (i.e ., bef ore and after reconfiguration) and two

n on-ag ile su pply chains (i.e., b efo re an d af ter re con figura tion) as s hown in Figure 7(a) and 7(b).

(a) SO A Strategy (b) EOA Strategy

Figure 7. The B ullwhip Effect Fronts w ith S OA and EOA Strategies

A s e xpe cted in a dvanc e, Figure 7( a) an d 7(b) show that the B values of reconfigured non-agile

s upply chain (i.e., red do tted line) ar e muc h hig her th an t hose of orig inal supply chain (i.e., black dotted

31

line) mainly because the best supplier is replaced with two new but inferior suppliers in terms of three

evaluation criteria. However, we notice that changes of B values from original (i.e., black solid line) to

reconfigured agile supply chain (i.e., red solid line) are strongly dependent on the weight of AP criterion

in relation to three other criteria. For example, when AP is not highly weighted (e.g., a range between

0.1 and 0.3), we find from both SOA and EOA strategies that the Pareto front of the original agile

supply chain shows a much better performance (i.e., lower B values) than that of the reconfigured agile

supply chain. This makes sense because the fittest supplier in the original agile supply chain may not be

the most agile because it is the first ranked based on multiple criteria including AP. Therefore, when

new suppliers that were ranked lower from multiple perspectives than the to-be-replaced supplier but are

better on AP criterion join into the reconfigured supply chain, the agility and hence B values of the

reconfigured supply chain can be improved. However, when the AP criterion is considered highly

important (e.g., AP weight >= 0.4), the reconfigured agile supply chain shows lower B values than the

original agile supply chain mainly because the to-be-replaced supplier is a supplier with a high agility

value.

Figure 8. Change Rates of Bullwhip Effect from Original to Reconfigured Supply Chain

Two additional important findings are also noted from Figure 8. We first find that the difference

of B value between original and reconfigured agile supply chain is much smaller than that of non-agile

32

supply chain. For example, the B value of agile supply chain with SOA strategy increases by 15% on

average, while that of non-agile supply chain increases by 29%. With EOA strategy, we make a similar

observation: it increases by 8% in agile supply chain, while it increases by 23% in non-agile supply

chain. In conclusion, agile supply chain is much less affected by unexpected disruptions than non-agile

supply chain for both order allocation strategies. We also find that supply chains with SOA strategy is

more susceptible to external disruption than those with EOA strategy. For example, agile supply chains

with high AP weight (i.e., AP >= 0.4) with SOA strategy experience significantly higher increases in B

values than agile supply chains with EOA strategy (between 5% and 31% vs. between 1% and 16%).

Similarly, agile supply chains with low AP weight (i.e., AP <= 0.3) under SOA strategy experience

much greater changes in B values than corresponding agile supply chains under EOA strategy (-2% and

-14% vs. -2% and -24%). We also make a similar observation from non-agile supply chain: B values of

non-agile supply chain under SOA strategy increase by 29%, while B values of non-agile supply chain

under EOA strategy increase by 21%.

7. CONCLUSION AND FUTURE RESEARCH

It is critical to transform a current supply chain into an agile supply chain to significantly

improve responsiveness to unexpected demand fluctuations. This study applies fuzzy AHP and fuzzy

TOPSIS to determine relative importance of multi-criteria and assess potential suppliers while

translating the subjective judgments of evaluators based on ambiguous linguistic variables into

quantifiable numeric estimates. In particular, this study presents Pareto fronts of agile and non-agile

supply chains to visualize changes in business efficiency levels measured in the magnitude of bullwhip

effect and inventory cost as the weight of agility criterion varies. These Pareto fronts help decision

makers determine an appropriate level of agility in their supply chains configuration by considering

business efficiency improvement at a decreasing rate as a higher level of agility is sought. In addition,

findings from various Pareto fronts of sub-criteria in agility criterion suggest that decision makers

should understand relative impacts of sub-criteria and should not significantly vary priority weights of

sub-criteria from values suggested by industry experts. Finally, Pareto fronts help decision makers

quantify business benefits from reconfiguring non-agile supply chain into agile supply chain and from

adding more agility to the current agile supply chain.

33

Our findings in this study also offer theoretical contributions to supply chain research

community. According to our experimental results, configuring and maintaining an agile supply chain

becomes more important when the current demand is highly correlated with past demand patterns and/or

high service level is strategically pursued. For example, assuming that the normally distributed demand

is forecasted with a moving average of five observations, the bullwhip effect trend of the agile supply

chain is much more stable in respond to varying service levels than that of the non-agile supply chain. At

the same time, we also note that bullwhip effects of agile and non-agile supply chains are not

significantly different when demand autocorrelation coefficient is low, but they become significantly

different as the current demand is highly correlated with past demand patterns. Another important

theoretical contribution of this study is in regard to the evaluation of two order allocation strategies, SOA

and EOA, in the reconfigurations process of original supply chains in response to unexpected

disruptions. According to our experiments, agile supply chain is much less affected by unexpected

disruptions than non-agile supply chain under both order allocation strategies. However, we find that

supply chains with SOA strategy is more susceptible to external disruption than those with EOA strategy.

For example, regardless of agility levels, supply chains with SOA strategy result in significantly greater

changes in bullwhip effect values than supply chains with EOA strategy.

While this study greatly helps decision makers visualize and estimate business impacts of agile

supply chain and order allocation strategies, it is far from complete. The findings of this study should

serve as a good starting point for assessing impacts of agility in more realistic and complicated supply

chains. For example, the simple supply chain model may be expanded into a multi-stage supply chain

model consisting of multiple suppliers and buyers to estimate the magnitude of bullwhip effect at

intermediaries of multiple stages. In addition, decision makers may also be able to estimate the impact of

agility associated with different order allocation strategies in respond to unexpected disruptions. In a

more complex situation, the buyer in reality may face a multi-tier structure of suppliers in which the

buyer directly negotiates with top-tier level suppliers only and those contracted suppliers in turn

negotiate with lower-tier level suppliers.

34

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38

APPENDIX A. CALCULATION PROCEDURE FOR PRIORITY WEIGHTS

In this Appendix, we illustrate procedure for calculating priority weights of main criteria and sub-criteria

shown in

39

Table 2 in detail. The first step is to have each expert or decision maker conducted pairwise comparisons

among main criteria and subjectively decide her own preference of one criterion over another

considering the main goal of selecting the best supplier. The geometric means of these values were then

calculated to obtain an agreed pairwise comparison matrix and these values were shown in Table 5.

Then, obtaining the priority weights of main criteria is straightforward by following the fuzzy AHP

method based on Chang's (1992) extent analysis.

Table 5. Pairwise Comparison Matrix among Main Criteria

GP MP CP AP

GP 1.00, 1.00, 1.00 0.15, 0.23, 0.47 0.53, 1.25, 2.63 0.15, 0.21, 0.42

MP 2.14, 4.36, 6.43 1.00, 1.00, 1.00 2.14, 2.81, 3.38 1.00, 1.93, 2.63

CP 0.38, 0.80, 1.90 0.30, 0.36, 0.47 1.00, 1.00, 1.00 0.26, 0.38, 0.80

AP 2.37, 4.67, 6.77 0.38, 0.52, 1.00 1.25, 2.67, 3.88 1.00, 1.00, 1.00

First, the fuzzy synthetic extent values of criterion i, Si, were calculated using the following

m n m −1

formula: S i = ∑ M gij ⊗ ∑ ∑ M gi

j , where Mgij represents i-th triangular fuzzy number with regard to

j =1 i =1 j =1

m

each criterion j for m criteria. To obtain ∑ M gij , we performed the fuzzy addition operation for a

j =1

m

particular matrix such that ∑ M gij

j =1

m m m

= (∑ l j ,∑ mj ,∑ u j ) where l, m, u represent the triangular fuzzyj =1 j =1 j=1

n m −1 n m −1 1 1 1

values. Also, ∑ ∑ M gij can be obtained using the formula : ∑ ∑ M gi

j = , , .n n n

i =1 j=1 i =1 j=1∑

ui ∑

mi ∑

li

i =1 i =1 i=1

Please, note that the operational law for two triangular fuzzy numbers is as follows:

M1 ⊗ M2 = (l1l2 , m1 m2 , u1u2 ) .

Based on the information in Table 5, the fuzzy synthetic extent values of main criteria were obtained as

follows:

SGP = (1.83, 2.69, 4.52) ⊗ (15.04, 24.17, 34.77) −1 = (0.05, 0.11, 0.30)

40

SMP = (6.28,10.10,13.44) ⊗ (15.04, 24.17, 34.77) −1 = (0.18, 0.42,

0.89) SCP = (1.94, 2.53, 4.17) ⊗ (15.04, 24.17, 34.77) −1 = (0.06,

0.11, 0.28) −

Next, the degree of possibility of Sj over Si , V ( S j ≥ Si ) , was calculated using a following formula:

1, if m j ≥ mi ,

V (S j ≥ S i 0, if li ≥ u j ,) =

li − u j

, otherwise,(m − u ) − (m

j j

− l )i i

These values are shown as follows:

V (S GP ≥ SMP ) = [0.18 − 0.30] [(0.11− 0.30) − (0.42 − 0.18)] = 0.28

V (S GP ≥ SCP ) = 1

V (S GP ≥ SAP ) = [0.14 − 0.30] [(0.11− 0.30) − (0.37 − 0.14)] = 0.38

V (S MP ≥ SGP ) = 1

V (S MP ≥ SCP ) = 1

V (S MP ≥ SAP ) = 1

V (S CP ≥ SGP ) = [0.05 − 0.28] [(0.11− 0.28) − (0.11− 0.05)] = 0.97

V (S CP ≥ SMP ) = [0.18 − 0.28] [(0.11− 0.28) − (0.42 − 0.18)] = 0.24

V (S CP ≥ SAP ) = [0.14 − 0.28] [(0.11− 0.28) − (0.37 − 0.14)] = 0.34

V (S AP ≥ SGP ) = 1

V (S AP ≥ SMP ) = [0.18 − 0.84] [(0.37 − 0.84) − (0.42 − 0.18)] = 0.93

41

V ( S AP ≥ SCP ) = 1

Then, the minimum degree of possibility for each criterion was obtained as follows:

d '(GP) = min(0.28,1, 0.38) = 0.28

d '( MP) = min(1,1,1) = 1

d '(CP) = min(0.97, 0.24, 0.34) = 0.24

d '( AP) = min(1, 0.93,1) = 0.93

Finally, the priority weights of main criteria, W′, were constructed as a set of the minimum degree of

possibility for each criterion such as W ' = (0.28,1, 0.24, 0.93) . Often, the normalized weights, W, could

be derived from W′, such as W = (0.12,0.41,0.10,0.38)T . Based on either W or W′, two most important

main criteria for supplier evaluation were found to be manufacturing capability (GP) and agility (AP).

The priority weights of sub-criteria for a chosen main criterion could be calculated in the same manner.

42

Highlights

Formulate the supplier selection problem as a multi-criteria decision-making

(MCDM) problem

Help decision makers to select the fittest suppliers for varying priority weights of multi-

criteria

Quantify the importance of the agility criterion by measuring the magnitude of bullwhip

effect

Visualize the operational and economic impacts of the agility criterion using the Pareto

fronts

Compare resilience of agile and non-agile supply chains before and after

unexpected disruptions

43