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Novel approach for manufacturing supply chain risk analysis using fuzzy supply inoperability input-output model
Accepted Manuscript Letters Novel approach for manufacturing supply chain risk analysis using fuzzy supply inoperability input-output model Mary Eloise Brosas, Michelle Abigail Kilantang, Noreen Bless Li, Lanndon Ocampo, Michael Angelo Promentilla, Krista Danielle Yu PII: DOI: Reference:
S2213-8463(17)30005-6 http://dx.doi.org/10.1016/j.mfglet.2017.03.001 MFGLET 88
To appear in:
Manufacturing Letters
Received Date: Revised Date: Accepted Date:
5 October 2016 24 January 2017 5 March 2017
Please cite this article as: M.E. Brosas, M.A. Kilantang, N.B. Li, L. Ocampo, M.A. Promentilla, K.D. Yu, Novel approach for manufacturing supply chain risk analysis using fuzzy supply inoperability input-output model, Manufacturing Letters (2017), doi: http://dx.doi.org/10.1016/j.mfglet.2017.03.001
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Novel approach for manufacturing supply chain risk analysis using fuzzy supply inoperability input-output model 1
1
1
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Mary Eloise Brosas , Michelle Abigail Kilantang , Noreen Bless Li , Lanndon Ocampo *, Michael Angelo 3 4 Promentilla , Krista Danielle Yu 1
Department of Industrial Engineering, University of San Carlos, 6000 Cebu City, Philippines 2 School of Management, University of the Philippines Cebu, 6000 Cebu City, Philippines 3 Department of Chemical Engineering, De La Salle University, 2401 Taft Avenue, 1004 Manila, Philippines 4 School of Economics, De La Salle University, 2401 Taft Avenue, 1004 Manila, Philippines *corresponding author: [email protected]
Abstract Aside from becoming more complex and dynamic, manufacturing supply chains must be capable in adapting to disruptive events caused by natural and man-made disasters. Risk analysis is an aid in developing mitigation policies to achieve a resilient manufacturing supply chain. However, the uncertainty and vagueness of information along the supply chain pose a challenge to risk analysis. Previous approaches on the analysis of supply chain risks have been proposed but have drawbacks that may provide counterintuitive results. Thus, this study attempts to develop a methodological approach based on supply-driven inputoutput analysis with fuzzy parameters in order to address supply chain risk analysis. The motivation behind the adoption of such approach lies in the strength of I-O analysis in addressing interdependent systems and its ability to address uncertainty of information shared among members. The proposed approach was applied to an herbal manufacturing supply chain to illustrate the methodology. Keywords: supply chain, risk analysis, fuzzy set theory, input-output model, inoperability 1. Introduction Due to the current highly competitive environment, individual firms no longer compete as individual entities, but rather as supply chains to supply chains (Lambert & Cooper, 2000). The goal of any supply chain, in particular manufacturing supply chain, is to improve operational efficiency, effectiveness, profitability and competitive advantage of its members and partners (Min & Zhou, 2002). In order to achieve this goal, several issues must be addressed especially on managing manufacturing supply chain risks. Negative impacts can occur in a manufacturing supply chain due to the existence of risk events which can cause unanticipated changes in material flows along the supply chain. Such risks include international terrorism (Sheffi, 2002), economic crises and wars (Lim, 2010), and natural calamities such as fires, earthquakes and typhoons (Wiengarten et al., 2015) among others. Several works have addressed supply chain risks using different approaches (Aqlan and Lam, 2016; Sarkar & Mohapatra, 2009; Blos and Miyagi, 2015). Despite of the increase of works focusing on this topic for the last two decades, there is still an inadequate use of quantitative models (Kirilmaz & Erol, 2016) in systematically assessing and analysing risks. Due to the complex behaviour of the manufacturing supply chain such as the interactions among its members, its interdependent components must not be analysed simultaneously, not individually. Haimes and Jiang (2001) and Santos and Haimes (2004) made an excellent
contribution by adopting the Leontief input-output (I-O) model (Leontief, 1936) in analysing risks of interdependent systems, e.g. supply chain, which was previously used in analysing economic sectors (Miller and Blair, 2009). Haimes and Jiang (2001) proposed the inoperability input-output model (IIM) which analyses the “ripple effects” of sector perturbation in interdependent economic systems. It is widely used to capture the changes in demand (Miller & Blair, 2009) when perturbation in one or more sectors occur (Baghersa & Zobel, 2015). The perturbation is represented by a real number in [0,1]; 0 being the undisrupted state of the system and 1 being the total system failure (Santos & Haimes, 2004). In contrast to the Leontief I-O model, Ambica Ghosh developed a total opposite approach which is the supply-driven input-output model in 1958 (Ghosh, 1958). While the Leontief I-O model is demand-driven, the Ghosh I-O model focuses on allocating the outputs, wherein output value is dependent on the value added vector (Reyes & Mendoza, 2013). Extensions of the Ghosh model were also done to analyse risks due to supply perturbation. Leung et al. (2007) introduced the supply driven inoperability model (SIIM), a counterpart of the previously developed IIM. Omega et al. (2016) and Ocampo et al. (2016) identified certain system characteristics where SIIM is more appropriate than the IIM: (1) when majority if not all of system components have no exogenous final demand, (2) demand is fixed and can rarely change, e.g. due to contracts, and (3) increase of prices of outputs due to increase in prices of value-added inputs is more relevant for decision-making. Ocampo et al. (2016) demonstrated the application of IIM in manufacturing systems. One interesting note pointed out by Omega et al. (2016) is the application of SIIM in analysing supply chain risks. SIIM is more applicable in evaluating the risks in a supply chain due to the presence of valueadded inputs such as procurement of raw materials, labor, inbound and outbound logistics, marketing and sales, and technological development that pose vulnerability to disruption. Manufacturing supply chain risks are not only difficult to manage but are highly unpredictable and uncertain as well (Helbing et al., 2006). Uncertainty in supply chains are currently addressed in literature, e.g. Giri and Chakraborty (2016) on vendor-buyer coordination with stochastic demand and uncertain yield and Setak et al. (2016) on pickup and delivery supply chain network. Incorporating uncertainty in risk analysis is a new approach to move forward so that risks can be represented with higher level of accuracy. Developing quantitative approach that represents uncertainty in risk analysis is thus required for better decision support (Ghadge et al., 2012; Tang & Nurmaya Musa, 2011). A well-established mathematical framework, such as fuzzy set theory can measure uncertainty that is caused by vague and perception-based situations, is a plausible method in addressing this gap (Tan et al., 2015; Zadeh, 1965). Various works in literature have linked fuzzy set theory to the input-output model, e.g. fuzzy input-output analysis (Buckley, 1989), fuzzy dynamic input-output inoperability in critical Italian infrastructures (Oliva et al., 2011) and in strategic risk management in global production networks (Niknejad and Petrovic, 2016) and the fuzzy inoperability input-output model in assessing risks on implementing mandatory biodiesel blending programs in the Philippines (Aviso et al., 2015), among others. In response to the need pointed out by Omega et al (2016), this paper attempts to develop a manufacturing supply chain risk analysis approach based on supply driven IIM with fuzzy parameters in order to holistically quantify risks. The motivation behind the adoption of fuzzy set theory in supply driven IIM is to take into account the uncertainties associated with transactions data of supply chain members which might be due to loss of certain information and poor data recording, among others. This aids decision-makers and
policy-makers in developing mitigation policies to improve resiliency of manufacturing supply chains. Methodologically, the approach lends itself with the fuzzy input-output table proposed by Panchal et al (2014) but the computational approaches differ significantly with the Gauss-Seidel algorithm of Panchal et al (2014). The contribution of this work is the proposed fuzzy supply inoperability input-output model in carrying out manufacturing supply chain risk analysis with uncertain data. 2. Proposed mathematical approach 2.1. Fuzzy set theory Definition 1: Let be a universal set and is a standard fuzzy set. In a standard fuzzy set A, each element is mapped to the closed interval by the membership function . The set of pairs is called fuzzy set, where and is the membership value of . Definition 2: A fuzzy number is said to be a triangular fuzzy number (TFN) if its membership function is characterized as follows:
(1)
Theorem 1: (Arithmetic operations of TFNs) Let and TFNs. The arithmetic operations are as follows (Kauffman and Gupta, 1985):
be two
(2) (3) (4) (5) (6) (7) Eq. (3) is based on the interval arithmetic or extension principle. 2.2. Fuzzy supply-driven input-output model Derived from the award winning input-output model of Wassily Leontief (1936), the traditional input-output Ghosh model was developed and expressed as: (8)
where
is a total input column vector of all components is a column vector of value-added inputs and
, is
the supply coefficient matrix obtained from the Leontief coefficient matrix . In the proposed fuzzy supply-driven input-output model, where is a fuzzy Leontief coefficient matrix and each element is a TFN. Similarly, is a fuzzy value-added input vector where each is a TFN. To compute for the fuzzy total input column vector with , and , obtain . Consider and
,
,
and
and . Then the following
can be obtained through routine computation: (9) (10) (11)
2.3. Fuzzy supply-driven inoperability input-output model The supply-driven IIM (SIIM) derived from the Ghosh model was developed by Leung et al. (2007) which can represented as (12) wherein
is a column vector of the cost change in output of components due to value-added perturbation, is described as the interdependency matrix obtained from the systems I-O table, and is the initial supply perturbation vector whose elements represent the difference between the perturbed valueadded and the planned value-added divided by the nominal production which is equivalent to the increase of value-added as a proportion of total planned input. Symbolically, (13) (14) In the proposed fuzzy SIIM, the entries in the nominal production vector and are computed using (9)-(12). Using (6), then . From these constructions, denote and
as well as
,
and
are TFNs and , . The
entries in the initial perturbation vector with , and is also a TFN and are exogenously determined as estimates of the increase of value-added inputs due to supply perturbation. From the fuzzy interdependency matrix
denoted as
, construct and
,
. Then the following can be established (15) (16) (17)
Finally, to compute for the fuzzy final perturbation vector ,
and
with
, the following can be computed (18) (19) (20)
3. Case Study A case study in an herbal food supplement manufacturing supply chain with plausible data is presented here to elucidate the proposed approach. The topology of the supply chain is presented in Figure 1. Firm F pioneers four main product lines, having CHRO-Plus Herbal Dietary Supplement as its best-selling product. In producing Firm F’s main product, it has five different suppliers for its raw materials (Firm E, Firm A, Firm B, Firm D, Firm C). A third party manufacturer (Firm G) is also involved in this supply chain, which is responsible for the loading and packaging of the product. The final outputs are then sent back to Firm F ready for distribution to different pharmacies, groceries and merchandisers, which are lastly sold to final consumers. The transactions table in TFNs is presented in Table 1.
Figure 1: Topology of the herbal food supplement manufacturing supply chain The Philippines is an archipelago that is known to be most exposed to tropical typhoons, with an estimated average of around 20 storms per year (Philippines Typhoons: Facts and Figures, 2014). Suppose that a typhoon has struck the geographical area of the malunggay seeds supplier of Firm F, the damage from the typhoon can cause a shortage in supply which can affect its intermediate demands within the supply chain. Due to the supply disruption, a 10 % increase in the price of the malunggay seeds is assumed to be initially perturbing the firm supplying the seeds (Firm B), i.e. . The effect on Firm F brought about by this change in price of the malunggay seeds can be investigated with the use of the proposed approach. Using Eqs. (9)-(11) and (15)-(20) along with the arithmetic operations represented by Eqs. (2)-(7), Table 2 shows the result of the fuzzy SIIM specifically the valueadded perturbation caused by an increase in the price of malunggay seeds.
Table 1. Fuzzy Input-Output Table Firm F
Firm E
Firm A
Firm B
Firm D
Firm C
Firm G
Firm H
Firm I
Firm J
Exogenous Final Demand (c)
Required Production (x)
Firm F
(47.50,50.00,52.50)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(9.50,10.00,10.50)
(23.75,25.00,26.25)
(19.00,20.00,21.00)
(9.50,10.00,10.50)
(9.5,10.00,10.50)
(118.75,125.00,131.25)
Firm E
(0.24,0.25,0.26)
(0.19,0.20,0.21)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.95,1.00,1.05)
(0.48,0.50,0.53)
(0.52,0.55,0.58)
(2.38,2.50,2.63)
Firm A
(0.48,0.50,0.53)
(0.00,0.00,0.00)
(2.85,3.00,3.15)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(4.75,5.00,5.25)
(0.48,0.50,0.53)
(0.95,1.00,1.05)
(9.50,10.00,10.50)
Firm B
(0.86,0.90,0.95)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(1.90,2.00,2.10)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.24,0.25,0.26)
(0.71,0.75,0.79)
(1.04,1.10,1.16)
(4.75,5.00,5.25)
Firm D
(0.19,0.20,0.21)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(1.38,1.45,1.52)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.14,0.15,0.16)
(0.29,0.30,0.32)
(0.86,0.90,0.95)
(2.85,3.00,3.15)
Firm C
(0.38,0.40,0.42)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(2.85,3.00,3.15)
(0.00,0.00,0.00)
(0.19,0.20,0.21)
(0.00,0.00,0.00)
(3.80,4.00,4.20)
(0.38,0.40,0.42)
(7.60,8.00,8.40)
Firm G
(57.00,60.00,63.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(418.00,440.00,462.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(475.00,500.00,525.00)
Firm H
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(95.00,100.00,105.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
Firm I
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
Firm J
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
Value Added Inputs
(12.11,12.75,13.39)
(2.19,2.30,2.42)
(6.65,7.00,7.35)
(2.85,3.00,3.15)
(1.47,1.55,1.63)
(4.75,5.00,5.25)
(47.50,50.00,52.50)
(9.50,10.00,10.50) (4.75,5.00,5.25)
(2.85,3.00,3.15)
(7.60,8.00,8.40)
Total Inputs (x) (118.75,125.00,131.25)
(2.38,2.50,2.63)
(190.00,200.00,210.00) (285.00,300.00,315.00)
(237.50,250.00,262.50) (142.50,150.00,157.50) (190.00,200.00,210.00) (570.00,600.00,630.00) (0.00,0.00,0.00)
(166.06,174.80,183.54) (307.42,323.60,339.78)
(9.98,10.50,11.03)
(180.00,189.50,199.00) (190.00,200.00,210.00)
(22.28,23.45,24.62)
(475.00,500.00,525.00) (285.00,300.00,315.00) (570.00,600.00,630.00) (190.00,200.00,210.00)
Note: all values in the table are in terms of millions (x 1,000,000)
The transactions matrix as shown in Table 1 is composed of TFNs that represent the costs of materials that serve as input from the preceding member firm of the manufacturing supply chain. Due to the uncertainty of transactions data associated with poor recording system among other, the transactions matrix is represented by symmetric TFNs with base of the median data.
Table 2. Value-added perturbation caused by malunggay prices increase scenario Manufacturing supply chain members Firm F
0
(5.396 x 10-5,9.231 x 10-5,9.800 x 10-5)
Firm E
0
(0,0,0)
Firm A
0
(0,0,0)
Firm B
(0.1,0.1,0.1)
(0.149,0.167,0.196)
Firm D
0
(0,0,0)
Firm C
0
(0,0,0) -7
Firm G
0
(7.900 x 10 ,3.846 x 10-6,7.980 x 10-6)
Firm H
0
(2.109 x 10-6,4.808 x 10-6,7.009 x 10-6)
Firm I
0
(1.107 x 10-6,2.091 x 10-6,3.382 x 10-6)
Firm J
0
(1.550 x 10-5,2.450 x 10-5,3.786 x 10-5)
Firm B, the initially perturbed member, has the highest range value of final perturbation. Final perturbation for firms E, A, D & C have zero range values for the reason that it does not get inputs from other members in the supply chain. While initially, firms F, G, H, I and J have no initial perturbation but due to their interdependencies to Firm B, then their output prices would increase with an uncertainty represented by the TFNs in the third column of Table 2. 5. Conclusion This study attempts to develop a fuzzy supply-driven inoperability input-output approach in order to address the lack of systemic, quantitative method in analyzing manufacturing supply chain risks with uncertainty of data. This approach can be applied in actual case studies involving manufacturing supply chains with members within the same geographical location as well as global supply chains. Future application and extensions of this approach can also be developed such as applying dynamic inoperability which involves time variables, and incorporating shock absorption index and vulnerability index in the proposed approach. References Aviso, K., Amalin, D., Promentilla, M., Santos, J., Yu, K. & Tan, R., (2015). Risk assessment of the economic impacts of climate change on the implementation of mandatory biodiesel blending programs: A fuzzy inoperability input-output modeling (IIM) approach. Biomass and Bioenergy, 83, 436-447. Aqlan F., & Lam, S. (2016). Supply chain optimization under risk and uncertainty: A case study for high-end server manufacturing. Computers & Industrial Engineering, 93, 78-87.
Baghersad, M., & Zobel, C. (2015). Economic impact of production bottlenecks caused by disasters impacting interdependent industry sectors. International Journal of Production Economics, 168, 71– 80. Blos, M., & Miyagi, P. (2015). Modeling the Supply Chain Disruptions: A Study based on the Supply Chain Interdependencies. IFAC-PapersOnLine, 48-3, 2053–2058. Buckley, J.J. (1989). Fuzzy input-output analysis. Eur. J. Oper. Res., 39, 54 - 60. Giri, B.C., Chakraborty, A. (2016). Coordinating a vendor-buyer supply chain with stochastic demand and uncertain yield. International Journal of Management Science and Engineering Management, 1-7, DOI: 10.1080/17509653.2016.1141337 Ghadge, A., Dani, S., Kalawsky, R., (2012). Supply chain risk management: present and future scope. Int. J. Logist. Manag. 23 (3), 313–339. Ghosh, A., (1958). Input-Output Approach in an Allocation System. Economica, New Series, 25(97), 58-64. Haimes Y. Y., & Jiang, P. (2001). Leontief-based model of risk in complex interconnected infrastructures. Journal of Infrastructure Systems, 7, 1–12. Helbing, D., Ammoser, H., and Kühnert, C., (2006). Information flows in hierarchical networks and the capability of organizations to successfully respond to failures, crises, and disasters. Physica A, 363, 141-150. Kaufmann, A., & Gupta, M.M. (1985). Introduction to fuzzy arithmetic: theory and applications. New York: Van Nostrand Reinhold Company. Kirilmaz, O. & Erol, S., (2016). A Proactive Approach to Supply Chain Risk Management: Shifting Orders Among Suppliers to Mitigate the Supply Side Risks, http://dx.doi.org/10.1016/j.pursup.2016.04.002. Lambert D., & Cooper M. (2000). Issues in Supply Chain Management. Industrial Marketing Management, 29, 65-83. Leontief, W. (1936). Quantitative Input and Output Relations in the Economic System of the United States, Review of Economic Statistics, XVIII, 105-125. Leung, M., Haimes, Y., and Santos, J. (2007). Supply- and Output-Side Extensions to the Inoperability Input-Output Model for Interdependent Infrastructures. J. Infrastruct. Syst., 10.1061/(ASCE)1076-0342(2007)13:4(299), 299-310. Lim, S. J. (2010). Risk response strategies in the supply chain: Examining attributes of stakeholders and risk attitude. Master thesis, Singapore Management University. Miller, R., & Blair, P. (2009). Input-Output Analysis: Foundations and Extensions. New York, NY: Cambridge University Press. Min H., & Zhou G. (2002). Supply Chain Modeling: Past, Present and Future. Computers & Industrial Engineering, 43, 231-249. Niknejad, A. & Petrovic, D. (2016). A Fuzzy Dynamic Inoperability Input– Output Model for strategic risk management in Global Production Networks. Int. J. Production Economics, 179, 44 – 58. Ocampo, L., Masbad, J., Noel, V. & Omega, R., (2016). Supply-side inoperability input– output model (SIIM) for risk analysisin manufacturing systems. Journal of Manufacturing Systems, 41, 76–85. Oliva, G., Panzieri, S., & Setola, R. (2011). Fuzzy Dynamic Input – Output Inoperability Model. International Journal of Critical Infrastructure Protection, 4, 165 – 175.
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S2213-8463(17)30005-6 http://dx.doi.org/10.1016/j.mfglet.2017.03.001 MFGLET 88
To appear in:
Manufacturing Letters
Received Date: Revised Date: Accepted Date:
5 October 2016 24 January 2017 5 March 2017
Please cite this article as: M.E. Brosas, M.A. Kilantang, N.B. Li, L. Ocampo, M.A. Promentilla, K.D. Yu, Novel approach for manufacturing supply chain risk analysis using fuzzy supply inoperability input-output model, Manufacturing Letters (2017), doi: http://dx.doi.org/10.1016/j.mfglet.2017.03.001
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Novel approach for manufacturing supply chain risk analysis using fuzzy supply inoperability input-output model 1
1
1
2
Mary Eloise Brosas , Michelle Abigail Kilantang , Noreen Bless Li , Lanndon Ocampo *, Michael Angelo 3 4 Promentilla , Krista Danielle Yu 1
Department of Industrial Engineering, University of San Carlos, 6000 Cebu City, Philippines 2 School of Management, University of the Philippines Cebu, 6000 Cebu City, Philippines 3 Department of Chemical Engineering, De La Salle University, 2401 Taft Avenue, 1004 Manila, Philippines 4 School of Economics, De La Salle University, 2401 Taft Avenue, 1004 Manila, Philippines *corresponding author: [email protected]
Abstract Aside from becoming more complex and dynamic, manufacturing supply chains must be capable in adapting to disruptive events caused by natural and man-made disasters. Risk analysis is an aid in developing mitigation policies to achieve a resilient manufacturing supply chain. However, the uncertainty and vagueness of information along the supply chain pose a challenge to risk analysis. Previous approaches on the analysis of supply chain risks have been proposed but have drawbacks that may provide counterintuitive results. Thus, this study attempts to develop a methodological approach based on supply-driven inputoutput analysis with fuzzy parameters in order to address supply chain risk analysis. The motivation behind the adoption of such approach lies in the strength of I-O analysis in addressing interdependent systems and its ability to address uncertainty of information shared among members. The proposed approach was applied to an herbal manufacturing supply chain to illustrate the methodology. Keywords: supply chain, risk analysis, fuzzy set theory, input-output model, inoperability 1. Introduction Due to the current highly competitive environment, individual firms no longer compete as individual entities, but rather as supply chains to supply chains (Lambert & Cooper, 2000). The goal of any supply chain, in particular manufacturing supply chain, is to improve operational efficiency, effectiveness, profitability and competitive advantage of its members and partners (Min & Zhou, 2002). In order to achieve this goal, several issues must be addressed especially on managing manufacturing supply chain risks. Negative impacts can occur in a manufacturing supply chain due to the existence of risk events which can cause unanticipated changes in material flows along the supply chain. Such risks include international terrorism (Sheffi, 2002), economic crises and wars (Lim, 2010), and natural calamities such as fires, earthquakes and typhoons (Wiengarten et al., 2015) among others. Several works have addressed supply chain risks using different approaches (Aqlan and Lam, 2016; Sarkar & Mohapatra, 2009; Blos and Miyagi, 2015). Despite of the increase of works focusing on this topic for the last two decades, there is still an inadequate use of quantitative models (Kirilmaz & Erol, 2016) in systematically assessing and analysing risks. Due to the complex behaviour of the manufacturing supply chain such as the interactions among its members, its interdependent components must not be analysed simultaneously, not individually. Haimes and Jiang (2001) and Santos and Haimes (2004) made an excellent
contribution by adopting the Leontief input-output (I-O) model (Leontief, 1936) in analysing risks of interdependent systems, e.g. supply chain, which was previously used in analysing economic sectors (Miller and Blair, 2009). Haimes and Jiang (2001) proposed the inoperability input-output model (IIM) which analyses the “ripple effects” of sector perturbation in interdependent economic systems. It is widely used to capture the changes in demand (Miller & Blair, 2009) when perturbation in one or more sectors occur (Baghersa & Zobel, 2015). The perturbation is represented by a real number in [0,1]; 0 being the undisrupted state of the system and 1 being the total system failure (Santos & Haimes, 2004). In contrast to the Leontief I-O model, Ambica Ghosh developed a total opposite approach which is the supply-driven input-output model in 1958 (Ghosh, 1958). While the Leontief I-O model is demand-driven, the Ghosh I-O model focuses on allocating the outputs, wherein output value is dependent on the value added vector (Reyes & Mendoza, 2013). Extensions of the Ghosh model were also done to analyse risks due to supply perturbation. Leung et al. (2007) introduced the supply driven inoperability model (SIIM), a counterpart of the previously developed IIM. Omega et al. (2016) and Ocampo et al. (2016) identified certain system characteristics where SIIM is more appropriate than the IIM: (1) when majority if not all of system components have no exogenous final demand, (2) demand is fixed and can rarely change, e.g. due to contracts, and (3) increase of prices of outputs due to increase in prices of value-added inputs is more relevant for decision-making. Ocampo et al. (2016) demonstrated the application of IIM in manufacturing systems. One interesting note pointed out by Omega et al. (2016) is the application of SIIM in analysing supply chain risks. SIIM is more applicable in evaluating the risks in a supply chain due to the presence of valueadded inputs such as procurement of raw materials, labor, inbound and outbound logistics, marketing and sales, and technological development that pose vulnerability to disruption. Manufacturing supply chain risks are not only difficult to manage but are highly unpredictable and uncertain as well (Helbing et al., 2006). Uncertainty in supply chains are currently addressed in literature, e.g. Giri and Chakraborty (2016) on vendor-buyer coordination with stochastic demand and uncertain yield and Setak et al. (2016) on pickup and delivery supply chain network. Incorporating uncertainty in risk analysis is a new approach to move forward so that risks can be represented with higher level of accuracy. Developing quantitative approach that represents uncertainty in risk analysis is thus required for better decision support (Ghadge et al., 2012; Tang & Nurmaya Musa, 2011). A well-established mathematical framework, such as fuzzy set theory can measure uncertainty that is caused by vague and perception-based situations, is a plausible method in addressing this gap (Tan et al., 2015; Zadeh, 1965). Various works in literature have linked fuzzy set theory to the input-output model, e.g. fuzzy input-output analysis (Buckley, 1989), fuzzy dynamic input-output inoperability in critical Italian infrastructures (Oliva et al., 2011) and in strategic risk management in global production networks (Niknejad and Petrovic, 2016) and the fuzzy inoperability input-output model in assessing risks on implementing mandatory biodiesel blending programs in the Philippines (Aviso et al., 2015), among others. In response to the need pointed out by Omega et al (2016), this paper attempts to develop a manufacturing supply chain risk analysis approach based on supply driven IIM with fuzzy parameters in order to holistically quantify risks. The motivation behind the adoption of fuzzy set theory in supply driven IIM is to take into account the uncertainties associated with transactions data of supply chain members which might be due to loss of certain information and poor data recording, among others. This aids decision-makers and
policy-makers in developing mitigation policies to improve resiliency of manufacturing supply chains. Methodologically, the approach lends itself with the fuzzy input-output table proposed by Panchal et al (2014) but the computational approaches differ significantly with the Gauss-Seidel algorithm of Panchal et al (2014). The contribution of this work is the proposed fuzzy supply inoperability input-output model in carrying out manufacturing supply chain risk analysis with uncertain data. 2. Proposed mathematical approach 2.1. Fuzzy set theory Definition 1: Let be a universal set and is a standard fuzzy set. In a standard fuzzy set A, each element is mapped to the closed interval by the membership function . The set of pairs is called fuzzy set, where and is the membership value of . Definition 2: A fuzzy number is said to be a triangular fuzzy number (TFN) if its membership function is characterized as follows:
(1)
Theorem 1: (Arithmetic operations of TFNs) Let and TFNs. The arithmetic operations are as follows (Kauffman and Gupta, 1985):
be two
(2) (3) (4) (5) (6) (7) Eq. (3) is based on the interval arithmetic or extension principle. 2.2. Fuzzy supply-driven input-output model Derived from the award winning input-output model of Wassily Leontief (1936), the traditional input-output Ghosh model was developed and expressed as: (8)
where
is a total input column vector of all components is a column vector of value-added inputs and
, is
the supply coefficient matrix obtained from the Leontief coefficient matrix . In the proposed fuzzy supply-driven input-output model, where is a fuzzy Leontief coefficient matrix and each element is a TFN. Similarly, is a fuzzy value-added input vector where each is a TFN. To compute for the fuzzy total input column vector with , and , obtain . Consider and
,
,
and
and . Then the following
can be obtained through routine computation: (9) (10) (11)
2.3. Fuzzy supply-driven inoperability input-output model The supply-driven IIM (SIIM) derived from the Ghosh model was developed by Leung et al. (2007) which can represented as (12) wherein
is a column vector of the cost change in output of components due to value-added perturbation, is described as the interdependency matrix obtained from the systems I-O table, and is the initial supply perturbation vector whose elements represent the difference between the perturbed valueadded and the planned value-added divided by the nominal production which is equivalent to the increase of value-added as a proportion of total planned input. Symbolically, (13) (14) In the proposed fuzzy SIIM, the entries in the nominal production vector and are computed using (9)-(12). Using (6), then . From these constructions, denote and
as well as
,
and
are TFNs and , . The
entries in the initial perturbation vector with , and is also a TFN and are exogenously determined as estimates of the increase of value-added inputs due to supply perturbation. From the fuzzy interdependency matrix
denoted as
, construct and
,
. Then the following can be established (15) (16) (17)
Finally, to compute for the fuzzy final perturbation vector ,
and
with
, the following can be computed (18) (19) (20)
3. Case Study A case study in an herbal food supplement manufacturing supply chain with plausible data is presented here to elucidate the proposed approach. The topology of the supply chain is presented in Figure 1. Firm F pioneers four main product lines, having CHRO-Plus Herbal Dietary Supplement as its best-selling product. In producing Firm F’s main product, it has five different suppliers for its raw materials (Firm E, Firm A, Firm B, Firm D, Firm C). A third party manufacturer (Firm G) is also involved in this supply chain, which is responsible for the loading and packaging of the product. The final outputs are then sent back to Firm F ready for distribution to different pharmacies, groceries and merchandisers, which are lastly sold to final consumers. The transactions table in TFNs is presented in Table 1.
Figure 1: Topology of the herbal food supplement manufacturing supply chain The Philippines is an archipelago that is known to be most exposed to tropical typhoons, with an estimated average of around 20 storms per year (Philippines Typhoons: Facts and Figures, 2014). Suppose that a typhoon has struck the geographical area of the malunggay seeds supplier of Firm F, the damage from the typhoon can cause a shortage in supply which can affect its intermediate demands within the supply chain. Due to the supply disruption, a 10 % increase in the price of the malunggay seeds is assumed to be initially perturbing the firm supplying the seeds (Firm B), i.e. . The effect on Firm F brought about by this change in price of the malunggay seeds can be investigated with the use of the proposed approach. Using Eqs. (9)-(11) and (15)-(20) along with the arithmetic operations represented by Eqs. (2)-(7), Table 2 shows the result of the fuzzy SIIM specifically the valueadded perturbation caused by an increase in the price of malunggay seeds.
Table 1. Fuzzy Input-Output Table Firm F
Firm E
Firm A
Firm B
Firm D
Firm C
Firm G
Firm H
Firm I
Firm J
Exogenous Final Demand (c)
Required Production (x)
Firm F
(47.50,50.00,52.50)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(9.50,10.00,10.50)
(23.75,25.00,26.25)
(19.00,20.00,21.00)
(9.50,10.00,10.50)
(9.5,10.00,10.50)
(118.75,125.00,131.25)
Firm E
(0.24,0.25,0.26)
(0.19,0.20,0.21)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.95,1.00,1.05)
(0.48,0.50,0.53)
(0.52,0.55,0.58)
(2.38,2.50,2.63)
Firm A
(0.48,0.50,0.53)
(0.00,0.00,0.00)
(2.85,3.00,3.15)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(4.75,5.00,5.25)
(0.48,0.50,0.53)
(0.95,1.00,1.05)
(9.50,10.00,10.50)
Firm B
(0.86,0.90,0.95)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(1.90,2.00,2.10)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.24,0.25,0.26)
(0.71,0.75,0.79)
(1.04,1.10,1.16)
(4.75,5.00,5.25)
Firm D
(0.19,0.20,0.21)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(1.38,1.45,1.52)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.14,0.15,0.16)
(0.29,0.30,0.32)
(0.86,0.90,0.95)
(2.85,3.00,3.15)
Firm C
(0.38,0.40,0.42)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(2.85,3.00,3.15)
(0.00,0.00,0.00)
(0.19,0.20,0.21)
(0.00,0.00,0.00)
(3.80,4.00,4.20)
(0.38,0.40,0.42)
(7.60,8.00,8.40)
Firm G
(57.00,60.00,63.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(418.00,440.00,462.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(475.00,500.00,525.00)
Firm H
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(95.00,100.00,105.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
Firm I
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
Firm J
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
(0.00,0.00,0.00)
Value Added Inputs
(12.11,12.75,13.39)
(2.19,2.30,2.42)
(6.65,7.00,7.35)
(2.85,3.00,3.15)
(1.47,1.55,1.63)
(4.75,5.00,5.25)
(47.50,50.00,52.50)
(9.50,10.00,10.50) (4.75,5.00,5.25)
(2.85,3.00,3.15)
(7.60,8.00,8.40)
Total Inputs (x) (118.75,125.00,131.25)
(2.38,2.50,2.63)
(190.00,200.00,210.00) (285.00,300.00,315.00)
(237.50,250.00,262.50) (142.50,150.00,157.50) (190.00,200.00,210.00) (570.00,600.00,630.00) (0.00,0.00,0.00)
(166.06,174.80,183.54) (307.42,323.60,339.78)
(9.98,10.50,11.03)
(180.00,189.50,199.00) (190.00,200.00,210.00)
(22.28,23.45,24.62)
(475.00,500.00,525.00) (285.00,300.00,315.00) (570.00,600.00,630.00) (190.00,200.00,210.00)
Note: all values in the table are in terms of millions (x 1,000,000)
The transactions matrix as shown in Table 1 is composed of TFNs that represent the costs of materials that serve as input from the preceding member firm of the manufacturing supply chain. Due to the uncertainty of transactions data associated with poor recording system among other, the transactions matrix is represented by symmetric TFNs with base of the median data.
Table 2. Value-added perturbation caused by malunggay prices increase scenario Manufacturing supply chain members Firm F
0
(5.396 x 10-5,9.231 x 10-5,9.800 x 10-5)
Firm E
0
(0,0,0)
Firm A
0
(0,0,0)
Firm B
(0.1,0.1,0.1)
(0.149,0.167,0.196)
Firm D
0
(0,0,0)
Firm C
0
(0,0,0) -7
Firm G
0
(7.900 x 10 ,3.846 x 10-6,7.980 x 10-6)
Firm H
0
(2.109 x 10-6,4.808 x 10-6,7.009 x 10-6)
Firm I
0
(1.107 x 10-6,2.091 x 10-6,3.382 x 10-6)
Firm J
0
(1.550 x 10-5,2.450 x 10-5,3.786 x 10-5)
Firm B, the initially perturbed member, has the highest range value of final perturbation. Final perturbation for firms E, A, D & C have zero range values for the reason that it does not get inputs from other members in the supply chain. While initially, firms F, G, H, I and J have no initial perturbation but due to their interdependencies to Firm B, then their output prices would increase with an uncertainty represented by the TFNs in the third column of Table 2. 5. Conclusion This study attempts to develop a fuzzy supply-driven inoperability input-output approach in order to address the lack of systemic, quantitative method in analyzing manufacturing supply chain risks with uncertainty of data. This approach can be applied in actual case studies involving manufacturing supply chains with members within the same geographical location as well as global supply chains. Future application and extensions of this approach can also be developed such as applying dynamic inoperability which involves time variables, and incorporating shock absorption index and vulnerability index in the proposed approach. References Aviso, K., Amalin, D., Promentilla, M., Santos, J., Yu, K. & Tan, R., (2015). Risk assessment of the economic impacts of climate change on the implementation of mandatory biodiesel blending programs: A fuzzy inoperability input-output modeling (IIM) approach. Biomass and Bioenergy, 83, 436-447. Aqlan F., & Lam, S. (2016). Supply chain optimization under risk and uncertainty: A case study for high-end server manufacturing. Computers & Industrial Engineering, 93, 78-87.
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