The article presents a methodology for measuring the metallurgical supply chain resilience, which enables the ascertainment
of key resilience capabilities and measurable criteria, and determining a level of the resilience. The
methodology is based on Analytic Network Process (ANP), which is used to solve the complex decision-making
problems, whose structures can be mapped as non-linear networks. Since ambiguous pairwise comparisons expressed
by fuzzy sets are considered, the Fuzzy Analytic Network Process (FANP) is applied. The methodology is
verified on the generalised model of a metallurgical supply chain. The SuperDecisions software was used for the
application. The experiments performed demonstrate the high level of suitability of the FANP approach for measuring
metallurgical supply chain resilience.Web of Science55478678

Lenort, Radim

Staš, David

Wicher, Pavel

Zapletal, František

DSpace at VSB Technical University of Ostrava

783METALURGIJA 55 (2016) 4, 783-786 P. WICHER, F. ZAPLETAL, R. LENORT, D. STAŠMEASURING THE METALLURGICAL SUPPLY CHAIN RESILIENCE USING FUZZY ANALYTIC NETWORK PROCESSReceived – Prispjelo: 2015-11-06Accepted – Prihvaćeno: 2016-04-25Preliminary Note – Prethodno priopćenjeP. Wicher, F. Zapletal, R. Lenort, VŠB – Technical University of Ostrava, Czech Republic, D. Staš, ŠKODA AUTO University, Czech Re publicThe article presents a methodology for measuring the metallurgical supply chain resilience, which enables the as-certainment of key resilience capabilities and measurable criteria, and determining a level of the resilience. The methodology is based on Analytic Network Process (ANP), which is used to solve the complex decision-making problems, whose structures can be mapped as non-linear networks. Since ambiguous pairwise comparisons ex-pressed by fuzzy sets are considered, the Fuzzy Analytic Network Process (FANP) is applied. The methodology is verified on the generalised model of a metallurgical supply chain. The SuperDecisions software was used for the application. The experiments performed demonstrate the high level of suitability of the FANP approach for measur-ing metallurgical supply chain resilience.Key words: metallurgy, methodology, supply chain resilience, Analytic Network Process, fuzzy setsINTRODUCTIONToday’s metallurgical supply chains face a turbulent environment, in which a wide spectrum of factors can result in supply chain disruption. For this reason, the authors of the article have developed a new methodol-ogy for assessing and measuring the metallurgical sup-ply chain (MSC) resilience [1]. The methodology is based on the Analytic Hierarchy Process (AHP). The basic stages of the methodology include: I) Analysis of resilience skills; II) Draft of resilience indicators; III) Creation of a hierarchical system of resilience indica-tors; IV) Evaluation of the MSC resilience, and V) In-terpretation of obtained results. However, the AHP method has two serious weaknesses: a) it does not take complex interdependencies between used criteria into consideration and b) it does not reflect the uncertainty of the managerial decision making process. The aim of the article is to apply and prove the feasibility of the Fuzzy Analytic Network Process (FANP) in the de-signed methodology.ANALYTIC NETWORK PROCESSThe Analytic Network Process (ANP), developed by Saaty, is a multistage decomposition method used to solve decision-making problems involving more than one criterion of optimality [2]. The main principle be-hind ANP is to view decisions as based on a framework of interconnected factors and evaluate the given factors in relationship to each other. These evaluations are rep-ISSN 0543-5846METABK 55(4) 783-786 (2016)UDC – UDK 669.011:001.8:516.5/.9=111resented by weights, which are determined on the basis of pair comparisons.ANP is performed on the basis of three basic steps (modified according to [2-4]):1) Model construction. A decision-making problem is analysed by researchers and transformed into a net-work structure. This network contains elements, clus-ters and connections. The elements symbolise funda-mental building blocks of the network. They represent both criteria and alternatives. Clusters are groupings of elements, which are logically related factors of the deci-sion. Connections determine interdependence among elements.2) Pairwise comparison matrices and local priority vectors. The determination of weights is based on node pairwise comparisons when one element depends on two or more different elements from one cluster and on cluster pairwise comparisons when elements (one or more) from one cluster depend on two or more elements from other clusters. The relative importance values are determined using Saaty’s 1 - 9 scale. Pairwise compari-sons are performed in the framework of node and clus-ter matrices, and local priority vectors are derived as estimates of the relative importance associated with the elements or clusters being compared.3) Supermatrix construction. In the first step, the un-weighted supermatrix is created directly from all local priority vectors. In the second step, the weighted super-matrix is calculated by multiplying the values of the un-weighted supermatrix with their affiliated cluster weights. By normalizing the weighted supermatrix, it is made column-stochastic. In the third and final step, the limit supermatrix is processed by raising the entire su-permatrix to powers until it converges in terms of lines. 784 P. WICHER et al.: MEASURING THE METALLURGICAL SUPPLY CHAIN RESILIENCE USING FUZZY ANALYTIC METALURGIJA 55 (2016) 4, 783-786Limit priority values within this supermatrix indicate the flow of influence of an individual element towards the overall goal. Since the decision alternatives are ele-ments of an original cluster of the network, their limit priorities are synonymous with their contributions to the goal and are used for the ranking of alternatives, be-ing normalized within the cluster [5].FUZZY ANPDue to the ambiguity latent in pairwise compari-sons, the fuzzy extension of the ANP is considered (FANP). Two possible approaches to deal with fuzzi-ness exist – either fuzzy extensions of valued relations (see e.g. [6-8]) or defuzzification of the fuzzy quantities by some appropriate metric (e.g. a possibilistic mean, see [9]) could be used. In the authors’ humble opinion, the first possibility is more suitable. It reflects the un-certainty in a better way because it does not use one real number to represent the whole fuzzy quantity.Deviation of the FANP from the ANP is in Step 2) of the method. That is why only fuzzy pairwise compari-son will be described more deeply in this section. Let us express the preference relationships given by triangular fuzzy numbers (TFNs) and linguistic description as fol-lows (based on Saaty [10]): (1,1,1) – identity, (1,1,2) – weak importance, (1,2,3) – moderate importance, (2,3,4) – moderate plus, (3,4,5) – strong importance, (4,5,6) – strong plus, (5,6,7) – very strong, (7,8,9) – al-most absolute importance, (8,8,9) – absolute impor-tance, where  is a triangular fuzzy num-ber with the core  and the support  (see Fig-ure 1).  (1)  (2)  (3)  (4)for i = 1, 2, …, n; where a and b are TFN’s (al, am, au) and (bl, bm, bu), respectively.2) Use of fuzzy valued relations to calculate weights of criteria. In this step, fuzzy synthetic extensions are defuzzified by using the min fuzzy extension of the val-ued relation “≤” given by (5) and weights Wi are calcu-lated, for more details (see e.g. Fiedler et al. [11]).   (5)for i, j = 1, 2, …, n3) Standardization of the weights. In order to obtain the sum of weights within one matrix equal to 1, final weights wi are calculated using (6).   (6)for i, j = 1, 2, …, n.4) A check of a Saaty’s matrix consistency. In the line with [6], a consistency of the matrix is sufficient if inequality (7) holds.  (7)where  stands for the arithmetic mean of the maximum real eigenvalues of the matrices  for i, j = 1, 2, …, n is the size of the Saaty’s matrix) and RI denotes a random index whose value depends on n [6].EXPERIMENTS AND RESULTSA generalised model of a global MSC was used to apply and confirm the developed methodology (see In-troduction) using FANP. The model includes 5 mines (ore and coal suppliers), 15 metallurgical plants, 50 steel wholesalers, and 500 direct consumers. The MSC operates on four continents with a relatively wide met-allurgical assortment. A large part of the MSC has a holding structure. The holding company controls metal-lurgical plants and their suppliers. With this structure the supplier part of the chain features a large degree of mutual interdependence and financial interconnected-ness.The first two stages of the designed methodology are described in [1] in details. As key resilience skills were determined (stage I): S1 Cooperation, S2 Flexibil-ity, S3 Visibility, S4 Capacity, and S5 Financial Strength (see Figure 2 and Table 1). For each skill appropriate measurable indicators (stage II) SI11 - SI51 were se-lected (for details see Table 2). It was appropriate to modify and merge the third stage (creating a hierarchi-cal system of resilience indicators) and fourth stage (evaluation of the MSC resilience) into one new stage: Figure 1  General triangular fuzzy number denoting a preference levelInverse elements aji expressing the non-preference are expressed also by a TFN: . Deriv-ing the weights of criteria from the fuzzy Saaty’s matrix can be divided into the following steps [8]:1) Fuzzy synthetic extension calculation. Fuzzy ele-ments of Saaty’s matrix have to be converted into TFNs called fuzzy synthetic extensions  using (1)-(4) [6].785 P. WICHER et al.: MEASURING THE METALLURGICAL SUPPLY CHAIN RESILIENCE USING FUZZY ANALYTICMETALURGIJA 55 (2016) 4, 783-786creating and evaluating a fuzzy network system of resil-ience indicators, which respects the ANP and FANP principles. This stage has three steps according to ANP methodology:1) Model construction. When using the ANP meth-od, it is possible to express not only hierarchical de-pendencies among indicators (see solid arrows in Fig-ure 2) but non-hierarchical ones too (see dashed arrows in Figure 2).2) Pairwise comparison matrices and local prior-ity vectors. First, it is necessary to create and complete six matrices for the analysed network structure using the FANP approach described above. The local priority vectors of the resilience skills and indicators are ob-tained in this way. This part is computationally exten-sive, thus only results are shown in Table 1. Second, four alternatives are specified: Minimum, Threshold, Optimum, and Real. Values of these alternatives for each indicator are determined in Table 2 (for more de-tails see [1]).These alternatives are incorporated into the created network structure as a subnetwork of each indicator. Local priority vectors of the alternatives are calculated on the basis of pairwise comparison matrices using the deterministic values of the alternatives.3) Supermatrix construction. This step was carried out using the SuperDecisions software. Global priority vectors of the resilience indicators and alternatives, shown in Tables 3 and 4, represent the final results.The final stage of the developed methodology Inter-pretation of obtained results remained the same. The Threshold Alternative represents the lowest acceptable value and the Optimum represents a target resilience level based on the strategic plans of the MSC. From that point of view, it can be stated that the actual resilience of the investigated MSC (Real Alternative) is very close to the Threshold Alternative and thus very insufficient (see the column FANP in Table 4).Figure 2 Model of the MSC resilience networkTable 2 Description and values of measurable criteriaIndicatorName UnitMinimumThresholdOptimumRealSI11 Number of cooperating partners in the MSC Number of enterprises weighted by the size of material fl ow0 30 45 30SI12 Investment in cooperation development in the MSC Mil. € per year 0 10 30 3,33SI21 Width of portfolio of the MSC The number of groups in the classifi cation of NACE 1 3 9 5SI22 Alternative options to ensure production in the MSC Percentage of own capacities 0 20 40 15SI31 Number of enterprises sharing basic information in the MSCNumber of enterprises weighted by the size of material fl ow0 30 45 20SI32 Number of enterprises using an integrated ERP system in the MSCNumber of enterprises weighted by the size of material fl ow0 30 45 15SI41 Reserve capacity of the MSC Percentage of own capacities 0 10 15 20SI51 Creditworthiness index of the MSC Kralicek´s Quick Test scale 5 3 1 2,75Table 1 Local weights of skills and indicators Concerning MSC Resilience Concerning S1 and S2S1 0,2528 SI11/SI21 0,5S2 0,2578 SI12/SI22 0,5S3 0,0725 With respect to S3S4 0,1520 SI31 0,2927S5 0,3169 SI32 0,7073With respect to S1 With respect to S3S1 0,5 S1 0,5663S5 0,5 S3 0,4337786 P. WICHER et al.: MEASURING THE METALLURGICAL SUPPLY CHAIN RESILIENCE USING FUZZY ANALYTIC METALURGIJA 55 (2016) 4, 783-786Table 4 Global weights of alternativesAlternative AHP / % FANP / %Minimum 8,12 10,04Threshold 45,97 40,59Optimum 100 100Real 49,33 41,6Table 3 Global weights of resilience indicatorsIndicator AHP / % FANP / %SI11 12,11 7,25SI12 12,11 20,22SI21 9,16 5,48SI22 9,16 5,48SI31 2,38 2,86SI32 7,15 4,29SI41 13,84 8,29SI51 34,09 46,13To increase the MSC resilience it is necessary to fo-cus on indicators and skills with the highest weight. From the column FANP in Table 3 it is obvious that the most important is to increase the Financial strength skill measured by the SI51 indicator. Its Real Value is lower than its Threshold one (see Table 2).CONCLUSIONThe presented experimental work has demonstrated that using the FANP approach is crucial for the devel-oped methodology. If the AHP were to be used, the re-sults would be significantly different. From the com-parison of results in Table 4, it is obvious that the AHP gives a more optimistic evaluation of the MSC resil-ience than the FANP. It is caused by different weights acquired from using both approaches (see Table 3). The main reason is that the AHP is unable to take non-hier-archical dependencies among the resilience indicators into consideration (see Figure 2).AcknowledgementThe work was supported by the specific university research of the Ministry of Education, Youth and Sports of the Czech Republic in VSB – Technical University of Ostrava No. SP2016/107 and by the grant No. GA 16-01298S of the Czech Science Foundation.REFERENCES[1] P. Wicher, R. Lenort, M. Čech, Measurement of Metallur-gical Supply Chain Resilience - Case Study, Proceeding, METAL 2015: 24th International Conference on Metallurgy and Materials, Ostrava, 2015, TANGER, pp. 2125-2130.[2] T. L. Saaty, L. G. Vargas, Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks, Springer, New York, 2013.[3] T. L. Saaty, Fundamentals of the analytic network pro-cess—multiple networks with benefits, costs, opportuni-ties and risks, Journal of Systems Science and Systems Engineering 13 (2004) 3, 348-379.[4] T. L. Saaty, Fundamentals of the analytic network pro-cess—Dependence and feedback in decision-making with a single network, Journal of Systems Science and Systems Engineering 13 (2004) 2, 129-157.[5] B. Wolfslehner, H. Vacik, M. J. Lexer, Application of the analytic network process in multi-criteria analysis of su-stainable forest management, Forest Ecology and Manage-ment 207 (2005) 1, 157-170.[6] Y. C. Tang, T. W. Lin, Application of the fuzzy analytic hierarchy process to the lead-free equipment selection de-cision, International Journal of Business and Systems Re-search 5 (2011) 1, 35-56.[7] P. Srichetta, W. Thirachon, Applying Fuzzy Analytic Hie-rarchy Process to Evaluate and Select Product of Notebook Computers, International Journal of Modeling and Optimi-zation 2 (2012) 2, 168-173.[8] K. J. Zhu, Y. Jing, D. Y. Chang, A discussion on extent analysis method and applications of fuzzy AHP, European Journal of Operational Research 116 (1999) 2, 450-456.[9] M. B. Ayhan, A Fuzzy AHP Approach for Supplier Selec-tion Problem: A Case study in a Gearmotor Company, In-ternational Journal of Managing Value and Supply Chains 4 (2013) 3, 11-23.[10] T. L. Saaty, Decision making with the analytic hierarchy process, International Journal of Services Sciences 1 (2008) 1, 83-98.[11] M. Fiedler, J. Nedoma, J. Ramik, J. Rohn, K. Zimmer-mann, Linear Optimization Problems with Inexact Data, Springer, London, 2006.Note:  The responsible translator for English language is Ryan Scott (Mladá Boleslav, Czech Republic)

Measuring the metallurgical supply chain resilience using fuzzy analytic network process

The article presents a methodology for measuring the metallurgical supply chain resilience, which enables the ascertainment of key resilience capabilities and measurable criteria, and determining a level of the resilience. The methodology is based on Analytic Network Process (ANP), which is used to solve the complex decision-making problems, whose structures can be mapped as non-linear networks. Since ambiguous pairwise comparisons expressed by fuzzy sets are considered, the Fuzzy Analytic Network Process (FANP) is applied. The methodology is verified on the generalised model of a metallurgical supply chain. The SuperDecisions software was used for the application. The experiments performed demonstrate the high level of suitability of the FANP approach for measuring metallurgical supply chain resilience

Measuring the metallurgical supply chain resilience using fuzzy analytic network process

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