doi: 10.3934/jimo.2018074

An integrated Principal Component Analysis and multi-objective mathematical programming approach to agile supply chain network design under uncertainty

1. 

School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

2. 

Faculty of Engineering, Urmia University, Urmia, West Azerbaijan Province, Iran

* Corresponding author: Tel.: +98 441 2972854; Fax: +98 441 2773591, Email address: r.babazadeh@urmia.ac.ir

Received  January 2018 Revised  January 2018 Published  June 2018

Fund Project: The authors are supported by INSF grant (Iran National Science Foundation)

The design of agile supply chain networks has attracted more attention in recent years according to the competitive business environment. Further, due to high degree of uncertainty in agile supply chains (SCs), developing robust and efficient decision making tools are of interest. In this study, an integrated approach based on principal component analysis (PCA) and multi-objective possibilistic mixed integer programming (MOPMIP) approaches is proposed to optimally design agile supply chain network under uncertainty. The PCA method is used for ranking and filtering the suppliers, constituting the first layer of the supply chain, based on agility criteria. The proposed MOPMIP model is employed to construct the agile supply chain network under uncertainty. In the proposed MOPMIP model, three objective functions including 1) total costs minimization, 2) total delivery time minimization and 3) maximization of flexibility are considered. An interactive fuzzy solution approach is used to solve the proposed MOPMILP model. Two numerical examples, is conducted to evaluate the performance and efficiency of the proposed integrated approach for agile supply chain network design under uncertainty.

Citation: Azam Moradi, Jafar Razmi, Reza Babazadeh, Ali Sabbaghnia. An integrated Principal Component Analysis and multi-objective mathematical programming approach to agile supply chain network design under uncertainty. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018074
References:
[1]

H. Abdi and L. J. Williams, Principal component analysis, Wiley Interdisciplinary Reviews: Computational Statistics, 2 (2010), 433-459. doi: 10.1002/wics.101.

[2]

R. Abratt and N. Kleyn, Corporate identity, corporate branding and corporate reputations: Reconciliation and integration, European Journal of Marketing, 46 (2012), 1048-1063.

[3]

I. M. Ambe, Agile supply chain: Strategy for competitive advantage, Journal of Global Strategic Management, 4 (2010), 5-17. doi: 10.20460/JGSM.2010415835.

[4]

Y. Aït-Sahalia and D. Xiu, Principal component analysis of high frequency data, Journal of the American Statistical Association, 2017.

[5]

R. Babazadeh, J. Razmi and R. Ghodsi, Supply chain network design problem for a new market opportunity in an agile manufacturing system Journal of Industrial Engineering International, 8 (2012), 19pp. doi: 10.1186/2251-712X-8-19.

[6]

R. Babazadeh and J. Razmi, A robust stochastic programming approach for agile and responsive logistics under operational and disruption risks, International Journal of Logistics Systems and Management, 13 (2012), 458-482. doi: 10.1504/IJLSM.2012.050158.

[7]

M. Bachlaus, M. K. Pandey, C. Mahajan, R. Shankar and M. K. Tiwari, Designing an integrated multi-echelon agile supply chain network: A hybrid taguchi-particle swarm optimization approach Journal of Intelligent Manufacturing, 9 (2008), p747. doi: 10.1007/s10845-008-0125-1.

[8]

B. W. Bolch and C. Huang, Multivariate Statistical Methods for Business and Economics, Prentice-Hall, 1973.

[9]

M. J. Braunscheidel and N. C. Suresh, The organizational antecedents of a firm's supply chain agility for risk mitigation and response, Journal of Operations Management, 27 (2009), 119-140. doi: 10.1016/j.jom.2008.09.006.

[10]

T. A. Brown, Confirmatory Factor Analysis for Applied Research, Guilford Publications, 2014.

[11]

H. CarvalhoS. G. Azevedo and V. Cruz-Machado, Agile and resilient approaches to supply chain management: Influence on performance and competitiveness, Logistics Research, 4 (2012), 49-62. doi: 10.1007/s12159-012-0064-2.

[12]

J. ChaiJ. N. Liu and E. W. Ngai, Application of decision-making techniques in supplier selection: A systematic review of literature, Expert Systems with Applications, 40 (2013), 3872-3885. doi: 10.1016/j.eswa.2012.12.040.

[13]

A. T. ChanE. W. Ngai and K. K. Moon, The effects of strategic and manufacturing flexibilities and supply chain agility on firm performance in the fashion industry, European Journal of Operational Research, 259 (2017), 486-499. doi: 10.1016/j.ejor.2016.11.006.

[14]

M. ChristopherR. Lowson and H. Peck, Creating agile supply chains in the fashion industry, International Journal of Retail & Distribution Management, 32 (2004), 367-376.

[15]

M. Christopher, The agile supply chain: Competing in volatile markets, Industrial Marketing Management, 29 (2000), 37-44. doi: 10.1016/S0019-8501(99)00110-8.

[16]

M. Christopher, A. Harrison and R. van Hoek, Creating the agile supply chain: Issues and challenges, in Developments in Logistics and Supply Chain Management, Springer, (2016), 61–68.

[17]

N. CostantinoM. DotoliM. FalagarioM. P. Fanti and A. M. Mangini, A model for supply management of agile manufacturing supply chains, International Journal of Production Economics, 135 (2012), 451-457. doi: 10.1016/j.ijpe.2011.08.021.

[18]

L. De BoerE. Labro and P. Morlacchi, A review of methods supporting supplier selection, European Journal of Purchasing & Supply Management, 7 (2001), 75-89.

[19]

G. W. Dickson, An analysis of vendor selection systems and decisions, European Journal of Marketing, 2 (1996), 5-17. doi: 10.1111/j.1745-493X.1966.tb00818.x.

[20]

D. Dubois and H. Prade, The mean value of a fuzzy number, Fuzzy Sets and Systems, 24 (1987), 279-300. doi: 10.1016/0165-0114(87)90028-5.

[21]

D. Dubois, E. Kerre, R. Mesiar and H. Prade, Fuzzy interval analysis, in Fundamentals of Fuzzy Sets, Springer, 2000, 483–558.

[22]

E. A. Elsayed, A. Shaik Dawood and R. Karthikeyan, Evaluating alternatives through the application of topsis method with entropy weight International Journal of Engineering Trends and Technology (IJETT), 46 (2017). doi: 10.14445/22315381/IJETT-V46P211.

[23]

H. Fargani, W. M. Cheung and R. Hasan, Ranking of factors that underlay the drivers of sustainable manufacturing based on their variation in a sample of UK manufacturing plants, International Journal of Manufacturing Technology and Management (IJMTM), (2017).

[24]

S. FayeziA. Zutshi and A. O'Loughlin, Understanding and development of supply chain agility and flexibility: A structured literature review, International Journal of Management Reviews, 19 (2017), 379-407. doi: 10.1111/ijmr.12096.

[25]

M. Fazli-KhalafA. Mirzazadeh and M. S. Pishvaee, A robust fuzzy stochastic programming model for the design of a reliable green closed-loop supply chain network, Human and Ecological Risk Assessment: An International Journal, 23 (2017), 2119-2149. doi: 10.1080/10807039.2017.1367644.

[26]

P. Fortemps and M. Roubens, Ranking and defuzzification methods based on area compensation, Fuzzy Sets and Systems, 82 (1996), 319-330. doi: 10.1016/0165-0114(95)00273-1.

[27]

A. GangulyR. Nilchiani and J. V. Farr, Evaluating agility in corporate enterprises, International Journal of Production Economics, 118 (2009), 410-423. doi: 10.1016/j.ijpe.2008.12.009.

[28]

S. H. Ghodsypour and C. O'Brien, A decision support system for supplier selection using an integrated analytic hierarchy process and linear programming, International Journal of Production Economics, 56/57 (1998), 199-212. doi: 10.1016/S0925-5273(97)00009-1.

[29]

N. GholamianI. MahdaviR. Tavakkoli-Moghaddam and N. Mahdavi-Amiri, Comprehensive fuzzy multi-objective multi-product multi-site aggregate production planning decisions in a supply chain under uncertainty, Applied Soft Computing, 37 (2015), 585-607. doi: 10.1016/j.asoc.2015.08.041.

[30]

D. M. Gligor and M. C. Holcomb, Understanding the role of logistics capabilities in achieving supply chain agility: A systematic literature review, Supply Chain Management: An International Journal, 17 (2012), 438-453. doi: 10.1108/13598541211246594.

[31]

A. González, A study of the ranking function approach through mean values, Fuzzy Sets and Systems, 35 (1990), 29-41. doi: 10.1016/0165-0114(90)90016-Y.

[32]

D. Harrington, Confirmatory Factor Analysis, Oxford University Press, 2009. doi: 10.1093/acprof:oso/9780195339888.001.0001.

[33]

M. A. HasanJ. Sarkis and R. Shankarr, Agility and production flow layouts: An analytical decision analysis, Computers & Industrial Engineering, 62 (2012), 898-907. doi: 10.1016/j.cie.2011.12.011.

[34]

A. HasaniS. H. Zegordi and E. Nikbakhsh, Robust closed-loop supply chain network design for perishable goods in agile manufacturing under uncertainty, International Journal of Production Research, 50 (2012), 4649-4669. doi: 10.1080/00207543.2011.625051.

[35]

S. Heilpern, The expected value of a fuzzy number, Fuzzy Sets and Systems, 47 (1992), 81-86. doi: 10.1016/0165-0114(92)90062-9.

[36]

F. R. Jacobs, R. B. Chase and R. R. Lummus, Operations and Supply Chain Management, McGraw-Hill/Irwin New York, 2014.

[37]

M. JiménezM. ArenasA. Bilbao and M. V. Rodríguez, Linear programming with fuzzy parameters: An interactive method resolution, European Journal of Operational Research, 177 (2007), 1599-1609. doi: 10.1016/j.ejor.2005.10.002.

[38]

M. Jiménez, Ranking fuzzy numbers through the comparison of its expected intervals, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 4 (1996), 379-388. doi: 10.1142/S0218488596000226.

[39]

T. Jitpaiboon, The Roles of Information Systems Integration in the Supply Chain Integration Context-Firm Perspective, Ph. D thesis, University of Toledo, 2005.

[40]

I. T. Jolliffe and J. Cadima, Principal component analysis: A review and recent developments, Phil. Trans. R. Soc. A, 374 (2016), 20150202.

[41]

D. Kannan, Role of multiple stakeholders and the critical success factor theory for the sustainable supplier selection process, International Journal of Production Economics, 195 (2018), 391-418. doi: 10.1016/j.ijpe.2017.02.020.

[42]

K. C. LamR. Tao and M. C. K. Lam, A material supplier selection model for property developers using fuzzy principal component analysis, Automation in Construction, 19 (2010), 608-618. doi: 10.1016/j.autcon.2010.02.007.

[43]

T. Mak and F. Nebebe, Factor analysis and methods of supplier selection, International Journal of Supply Chain Management, 5 (2016), 1-9.

[44]

A. W. Min and K. G. Shin, Exploiting multi-channel diversity in spectrum-agile networks, The 27th Conference on Computer Communications, IEEE, (2008), 1921–1929. doi: 10.1109/INFOCOM.2008.256.

[45]

K. Mukherjee, Modeling and optimization of traditional supplier selection, in Supplier Selection, Springer, 2017, 31–58. doi: 10.1007/978-81-322-3700-6_2.

[46]

D. J. Olive, Principal component analysis, in Robust Multivariate Analysis, Springer, 2017, 189–217. doi: 10.1007/978-3-319-68253-2_6.

[47]

F. Pan and R. Nagi, Robust supply chain design under uncertain demand in agile manufacturing, Computers & Industrial Engineering, 37 (2010), 668-683. doi: 10.1016/j.cor.2009.06.017.

[48]

F. Pan and R. Nagi, Multi-echelon supply chain network design in agile manufacturing, Omega, 41 (2013), 969-983. doi: 10.1016/j.omega.2012.12.004.

[49]

M. A. ParraA. B. TerolB. P. Gladish and M. V. R. Uría, Solving a multiobjective possibilistic problem through compromise programming, European Journal of Operational Research, 164 (2005), 748-759. doi: 10.1016/j.ejor.2003.11.028.

[50]

D. PeidroJ. MulaM. Jiménez and M. del Mar Botella, A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment, European Journal of Operational Research, 205 (2010), 65-80. doi: 10.1016/j.ejor.2009.11.031.

[51]

A. Petroni and M. Braglia, Vendor selection using principal component analysis, Journal of Supply Chain Management, 36 (2000), 63-69. doi: 10.1111/j.1745-493X.2000.tb00078.x.

[52]

M. S. Pishvaee and J. Razmi, Environmental supply chain network design using multi-objective fuzzy mathematical programming, Applied Mathematical Modelling, 36 (2012), 3433-3446. doi: 10.1016/j.apm.2011.10.007.

[53]

M. S. Pishvaee and S. A. Torabi, A possibilistic programming approach for closed-loop supply chain network design under uncertainty, Fuzzy Sets and Systems, 161 (2010), 2668-2683. doi: 10.1016/j.fss.2010.04.010.

[54]

L. L. Portes and L. A. Aguirre, Matrix formulation and singular-value decomposition algorithm for structured varimax rotation in multivariate singular spectrum analysis, Physical Review E, 93 (2016), 052216. doi: 10.1103/PhysRevE.93.052216.

[55]

J. RazmiM. Seifoory and M. S. Pishvaee, A fuzzy multi-attribute decision making model for selecting the best supply chain strategy: Lean, agile or leagile, Journal of Industrial Engineering, 45 (2011), 127-142.

[56]

J. Razmi and A. Sabbaghnia, Tracing the impact of non-uniform forecasting methods on the severity of the bullwhip effect in two-and three-level supply chains, International Journal of Management Science and Engineering Management, 10 (2015), 297-304. doi: 10.1080/17509653.2015.1016132.

[57]

P. RolaD. Kuchta and D. Kopczyk, Conceptual model of working space for agile (scrum) project team, Journal of Systems and Software, 118 (2016), 49-63. doi: 10.1016/j.jss.2016.04.071.

[58]

C. Rolland-Debord, S. Fry, J. Giovannelli, C. Langlois, N. Bricout, B. Aguilaniu, A. Bellocq, O. Le Rouzic, S. Dominique, A. Delobbe and G. François, Physiologic determinants of exercise capacity in pulmonary langerhans cell histiocytosis: A multidimensional analysis, PloS one, 12 (2017), e0170035.

[59]

M. R. G. Samani, S. A. Torabi and S. M. Hosseini-Motlagh, Integrated blood supply chain planning for disaster relief, International Journal of Disaster Risk Reduction, (2017).

[60]

J. Sarkis and S. Talluri, A model for strategic supplier selection, Journal of Supply Chain Management, 38 (2002), 18-28. doi: 10.1111/j.1745-493X.2002.tb00117.x.

[61]

M. R. ShaharudinK. GovindanS. ZailaniK. C. Tan and M. Iranmanesh, Product return management: Linking product returns, closed-loop supply chain activities and the effectiveness of the reverse supply chains, Journal of Cleaner Production, 149 (2017), 1144-1156. doi: 10.1016/j.jclepro.2017.02.133.

[62]

T. P. Shri and N. Sriraam, Comparison of t-test ranking with PCA and SEPCOR feature selection for wake and stage 1 sleep pattern recognition in multichannel electroencephalograms, Biomedical Signal Processing and Control, 31 (2017), 499-512.

[63]

Z. A. Sohi and S. A. Torabi, Integrated home video content procurement and distribution planning under uncertainty, Computers & Industrial Engineering, 106 (2017), 329-337.

[64]

H. Stadtler, Supply chain management: An overview in Supply Chain Management and Advanced Planning, Springer, Berlin, Heidelberg, 2015, 3–28.

[65]

S. Subhash, Applied Multivariate Techniques, John Wily & Sons Inc., Canada, 1996.

[66]

R. Suri, QRM and POLCA: A winning combination for manufacturing enterprises in the 21st century, Citeseer, 32 (2003).

[67]

D. R. Towill, Engineering the agile supply chain, Logistics Systems Dynamics Group, (2001), 377-396. doi: 10.1016/B978-008043567-1/50020-6.

[68]

C. A. Weber, J. R. Current and W. Bentonn, Vendor selection criteria and methods, European Journal of Operational Research, The 27th Conference on Computer Communications, 50 (1991), 2–18. doi: 10.1016/0377-2217(91)90033-R.

[69]

C. Wu and D. Barnes, Formulating partner selection criteria for agile supply chains: A Dempster-Shafer belief acceptability optimisation approach, International Journal of Production Economics, 125 (2010), 284-293. doi: 10.1016/j.ijpe.2010.02.010.

[70]

R. R. Yager, A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24 (1981), 143-161. doi: 10.1016/0020-0255(81)90017-7.

[71]

C. A. Yauch, Measuring agility as a performance outcome, Journal of Manufacturing Technology Management, 22 (2011), 384-404. doi: 10.1108/17410381111112738.

[72]

F. You and I. E. Grossmann, Design of responsive supply chains under demand uncertainty, Computers & Industrial Engineering, 32 (2008), 3090-3111. doi: 10.1016/j.compchemeng.2008.05.004.

[73]

Y. Y. YusufA. GunasekaranE. Adeleye and K. Sivayoganathan, Agile supply chain capabilities: Determinants of competitive objectives, European Journal of Operational Research, 159 (2004), 379-392. doi: 10.1016/j.ejor.2003.08.022.

show all references

References:
[1]

H. Abdi and L. J. Williams, Principal component analysis, Wiley Interdisciplinary Reviews: Computational Statistics, 2 (2010), 433-459. doi: 10.1002/wics.101.

[2]

R. Abratt and N. Kleyn, Corporate identity, corporate branding and corporate reputations: Reconciliation and integration, European Journal of Marketing, 46 (2012), 1048-1063.

[3]

I. M. Ambe, Agile supply chain: Strategy for competitive advantage, Journal of Global Strategic Management, 4 (2010), 5-17. doi: 10.20460/JGSM.2010415835.

[4]

Y. Aït-Sahalia and D. Xiu, Principal component analysis of high frequency data, Journal of the American Statistical Association, 2017.

[5]

R. Babazadeh, J. Razmi and R. Ghodsi, Supply chain network design problem for a new market opportunity in an agile manufacturing system Journal of Industrial Engineering International, 8 (2012), 19pp. doi: 10.1186/2251-712X-8-19.

[6]

R. Babazadeh and J. Razmi, A robust stochastic programming approach for agile and responsive logistics under operational and disruption risks, International Journal of Logistics Systems and Management, 13 (2012), 458-482. doi: 10.1504/IJLSM.2012.050158.

[7]

M. Bachlaus, M. K. Pandey, C. Mahajan, R. Shankar and M. K. Tiwari, Designing an integrated multi-echelon agile supply chain network: A hybrid taguchi-particle swarm optimization approach Journal of Intelligent Manufacturing, 9 (2008), p747. doi: 10.1007/s10845-008-0125-1.

[8]

B. W. Bolch and C. Huang, Multivariate Statistical Methods for Business and Economics, Prentice-Hall, 1973.

[9]

M. J. Braunscheidel and N. C. Suresh, The organizational antecedents of a firm's supply chain agility for risk mitigation and response, Journal of Operations Management, 27 (2009), 119-140. doi: 10.1016/j.jom.2008.09.006.

[10]

T. A. Brown, Confirmatory Factor Analysis for Applied Research, Guilford Publications, 2014.

[11]

H. CarvalhoS. G. Azevedo and V. Cruz-Machado, Agile and resilient approaches to supply chain management: Influence on performance and competitiveness, Logistics Research, 4 (2012), 49-62. doi: 10.1007/s12159-012-0064-2.

[12]

J. ChaiJ. N. Liu and E. W. Ngai, Application of decision-making techniques in supplier selection: A systematic review of literature, Expert Systems with Applications, 40 (2013), 3872-3885. doi: 10.1016/j.eswa.2012.12.040.

[13]

A. T. ChanE. W. Ngai and K. K. Moon, The effects of strategic and manufacturing flexibilities and supply chain agility on firm performance in the fashion industry, European Journal of Operational Research, 259 (2017), 486-499. doi: 10.1016/j.ejor.2016.11.006.

[14]

M. ChristopherR. Lowson and H. Peck, Creating agile supply chains in the fashion industry, International Journal of Retail & Distribution Management, 32 (2004), 367-376.

[15]

M. Christopher, The agile supply chain: Competing in volatile markets, Industrial Marketing Management, 29 (2000), 37-44. doi: 10.1016/S0019-8501(99)00110-8.

[16]

M. Christopher, A. Harrison and R. van Hoek, Creating the agile supply chain: Issues and challenges, in Developments in Logistics and Supply Chain Management, Springer, (2016), 61–68.

[17]

N. CostantinoM. DotoliM. FalagarioM. P. Fanti and A. M. Mangini, A model for supply management of agile manufacturing supply chains, International Journal of Production Economics, 135 (2012), 451-457. doi: 10.1016/j.ijpe.2011.08.021.

[18]

L. De BoerE. Labro and P. Morlacchi, A review of methods supporting supplier selection, European Journal of Purchasing & Supply Management, 7 (2001), 75-89.

[19]

G. W. Dickson, An analysis of vendor selection systems and decisions, European Journal of Marketing, 2 (1996), 5-17. doi: 10.1111/j.1745-493X.1966.tb00818.x.

[20]

D. Dubois and H. Prade, The mean value of a fuzzy number, Fuzzy Sets and Systems, 24 (1987), 279-300. doi: 10.1016/0165-0114(87)90028-5.

[21]

D. Dubois, E. Kerre, R. Mesiar and H. Prade, Fuzzy interval analysis, in Fundamentals of Fuzzy Sets, Springer, 2000, 483–558.

[22]

E. A. Elsayed, A. Shaik Dawood and R. Karthikeyan, Evaluating alternatives through the application of topsis method with entropy weight International Journal of Engineering Trends and Technology (IJETT), 46 (2017). doi: 10.14445/22315381/IJETT-V46P211.

[23]

H. Fargani, W. M. Cheung and R. Hasan, Ranking of factors that underlay the drivers of sustainable manufacturing based on their variation in a sample of UK manufacturing plants, International Journal of Manufacturing Technology and Management (IJMTM), (2017).

[24]

S. FayeziA. Zutshi and A. O'Loughlin, Understanding and development of supply chain agility and flexibility: A structured literature review, International Journal of Management Reviews, 19 (2017), 379-407. doi: 10.1111/ijmr.12096.

[25]

M. Fazli-KhalafA. Mirzazadeh and M. S. Pishvaee, A robust fuzzy stochastic programming model for the design of a reliable green closed-loop supply chain network, Human and Ecological Risk Assessment: An International Journal, 23 (2017), 2119-2149. doi: 10.1080/10807039.2017.1367644.

[26]

P. Fortemps and M. Roubens, Ranking and defuzzification methods based on area compensation, Fuzzy Sets and Systems, 82 (1996), 319-330. doi: 10.1016/0165-0114(95)00273-1.

[27]

A. GangulyR. Nilchiani and J. V. Farr, Evaluating agility in corporate enterprises, International Journal of Production Economics, 118 (2009), 410-423. doi: 10.1016/j.ijpe.2008.12.009.

[28]

S. H. Ghodsypour and C. O'Brien, A decision support system for supplier selection using an integrated analytic hierarchy process and linear programming, International Journal of Production Economics, 56/57 (1998), 199-212. doi: 10.1016/S0925-5273(97)00009-1.

[29]

N. GholamianI. MahdaviR. Tavakkoli-Moghaddam and N. Mahdavi-Amiri, Comprehensive fuzzy multi-objective multi-product multi-site aggregate production planning decisions in a supply chain under uncertainty, Applied Soft Computing, 37 (2015), 585-607. doi: 10.1016/j.asoc.2015.08.041.

[30]

D. M. Gligor and M. C. Holcomb, Understanding the role of logistics capabilities in achieving supply chain agility: A systematic literature review, Supply Chain Management: An International Journal, 17 (2012), 438-453. doi: 10.1108/13598541211246594.

[31]

A. González, A study of the ranking function approach through mean values, Fuzzy Sets and Systems, 35 (1990), 29-41. doi: 10.1016/0165-0114(90)90016-Y.

[32]

D. Harrington, Confirmatory Factor Analysis, Oxford University Press, 2009. doi: 10.1093/acprof:oso/9780195339888.001.0001.

[33]

M. A. HasanJ. Sarkis and R. Shankarr, Agility and production flow layouts: An analytical decision analysis, Computers & Industrial Engineering, 62 (2012), 898-907. doi: 10.1016/j.cie.2011.12.011.

[34]

A. HasaniS. H. Zegordi and E. Nikbakhsh, Robust closed-loop supply chain network design for perishable goods in agile manufacturing under uncertainty, International Journal of Production Research, 50 (2012), 4649-4669. doi: 10.1080/00207543.2011.625051.

[35]

S. Heilpern, The expected value of a fuzzy number, Fuzzy Sets and Systems, 47 (1992), 81-86. doi: 10.1016/0165-0114(92)90062-9.

[36]

F. R. Jacobs, R. B. Chase and R. R. Lummus, Operations and Supply Chain Management, McGraw-Hill/Irwin New York, 2014.

[37]

M. JiménezM. ArenasA. Bilbao and M. V. Rodríguez, Linear programming with fuzzy parameters: An interactive method resolution, European Journal of Operational Research, 177 (2007), 1599-1609. doi: 10.1016/j.ejor.2005.10.002.

[38]

M. Jiménez, Ranking fuzzy numbers through the comparison of its expected intervals, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 4 (1996), 379-388. doi: 10.1142/S0218488596000226.

[39]

T. Jitpaiboon, The Roles of Information Systems Integration in the Supply Chain Integration Context-Firm Perspective, Ph. D thesis, University of Toledo, 2005.

[40]

I. T. Jolliffe and J. Cadima, Principal component analysis: A review and recent developments, Phil. Trans. R. Soc. A, 374 (2016), 20150202.

[41]

D. Kannan, Role of multiple stakeholders and the critical success factor theory for the sustainable supplier selection process, International Journal of Production Economics, 195 (2018), 391-418. doi: 10.1016/j.ijpe.2017.02.020.

[42]

K. C. LamR. Tao and M. C. K. Lam, A material supplier selection model for property developers using fuzzy principal component analysis, Automation in Construction, 19 (2010), 608-618. doi: 10.1016/j.autcon.2010.02.007.

[43]

T. Mak and F. Nebebe, Factor analysis and methods of supplier selection, International Journal of Supply Chain Management, 5 (2016), 1-9.

[44]

A. W. Min and K. G. Shin, Exploiting multi-channel diversity in spectrum-agile networks, The 27th Conference on Computer Communications, IEEE, (2008), 1921–1929. doi: 10.1109/INFOCOM.2008.256.

[45]

K. Mukherjee, Modeling and optimization of traditional supplier selection, in Supplier Selection, Springer, 2017, 31–58. doi: 10.1007/978-81-322-3700-6_2.

[46]

D. J. Olive, Principal component analysis, in Robust Multivariate Analysis, Springer, 2017, 189–217. doi: 10.1007/978-3-319-68253-2_6.

[47]

F. Pan and R. Nagi, Robust supply chain design under uncertain demand in agile manufacturing, Computers & Industrial Engineering, 37 (2010), 668-683. doi: 10.1016/j.cor.2009.06.017.

[48]

F. Pan and R. Nagi, Multi-echelon supply chain network design in agile manufacturing, Omega, 41 (2013), 969-983. doi: 10.1016/j.omega.2012.12.004.

[49]

M. A. ParraA. B. TerolB. P. Gladish and M. V. R. Uría, Solving a multiobjective possibilistic problem through compromise programming, European Journal of Operational Research, 164 (2005), 748-759. doi: 10.1016/j.ejor.2003.11.028.

[50]

D. PeidroJ. MulaM. Jiménez and M. del Mar Botella, A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment, European Journal of Operational Research, 205 (2010), 65-80. doi: 10.1016/j.ejor.2009.11.031.

[51]

A. Petroni and M. Braglia, Vendor selection using principal component analysis, Journal of Supply Chain Management, 36 (2000), 63-69. doi: 10.1111/j.1745-493X.2000.tb00078.x.

[52]

M. S. Pishvaee and J. Razmi, Environmental supply chain network design using multi-objective fuzzy mathematical programming, Applied Mathematical Modelling, 36 (2012), 3433-3446. doi: 10.1016/j.apm.2011.10.007.

[53]

M. S. Pishvaee and S. A. Torabi, A possibilistic programming approach for closed-loop supply chain network design under uncertainty, Fuzzy Sets and Systems, 161 (2010), 2668-2683. doi: 10.1016/j.fss.2010.04.010.

[54]

L. L. Portes and L. A. Aguirre, Matrix formulation and singular-value decomposition algorithm for structured varimax rotation in multivariate singular spectrum analysis, Physical Review E, 93 (2016), 052216. doi: 10.1103/PhysRevE.93.052216.

[55]

J. RazmiM. Seifoory and M. S. Pishvaee, A fuzzy multi-attribute decision making model for selecting the best supply chain strategy: Lean, agile or leagile, Journal of Industrial Engineering, 45 (2011), 127-142.

[56]

J. Razmi and A. Sabbaghnia, Tracing the impact of non-uniform forecasting methods on the severity of the bullwhip effect in two-and three-level supply chains, International Journal of Management Science and Engineering Management, 10 (2015), 297-304. doi: 10.1080/17509653.2015.1016132.

[57]

P. RolaD. Kuchta and D. Kopczyk, Conceptual model of working space for agile (scrum) project team, Journal of Systems and Software, 118 (2016), 49-63. doi: 10.1016/j.jss.2016.04.071.

[58]

C. Rolland-Debord, S. Fry, J. Giovannelli, C. Langlois, N. Bricout, B. Aguilaniu, A. Bellocq, O. Le Rouzic, S. Dominique, A. Delobbe and G. François, Physiologic determinants of exercise capacity in pulmonary langerhans cell histiocytosis: A multidimensional analysis, PloS one, 12 (2017), e0170035.

[59]

M. R. G. Samani, S. A. Torabi and S. M. Hosseini-Motlagh, Integrated blood supply chain planning for disaster relief, International Journal of Disaster Risk Reduction, (2017).

[60]

J. Sarkis and S. Talluri, A model for strategic supplier selection, Journal of Supply Chain Management, 38 (2002), 18-28. doi: 10.1111/j.1745-493X.2002.tb00117.x.

[61]

M. R. ShaharudinK. GovindanS. ZailaniK. C. Tan and M. Iranmanesh, Product return management: Linking product returns, closed-loop supply chain activities and the effectiveness of the reverse supply chains, Journal of Cleaner Production, 149 (2017), 1144-1156. doi: 10.1016/j.jclepro.2017.02.133.

[62]

T. P. Shri and N. Sriraam, Comparison of t-test ranking with PCA and SEPCOR feature selection for wake and stage 1 sleep pattern recognition in multichannel electroencephalograms, Biomedical Signal Processing and Control, 31 (2017), 499-512.

[63]

Z. A. Sohi and S. A. Torabi, Integrated home video content procurement and distribution planning under uncertainty, Computers & Industrial Engineering, 106 (2017), 329-337.

[64]

H. Stadtler, Supply chain management: An overview in Supply Chain Management and Advanced Planning, Springer, Berlin, Heidelberg, 2015, 3–28.

[65]

S. Subhash, Applied Multivariate Techniques, John Wily & Sons Inc., Canada, 1996.

[66]

R. Suri, QRM and POLCA: A winning combination for manufacturing enterprises in the 21st century, Citeseer, 32 (2003).

[67]

D. R. Towill, Engineering the agile supply chain, Logistics Systems Dynamics Group, (2001), 377-396. doi: 10.1016/B978-008043567-1/50020-6.

[68]

C. A. Weber, J. R. Current and W. Bentonn, Vendor selection criteria and methods, European Journal of Operational Research, The 27th Conference on Computer Communications, 50 (1991), 2–18. doi: 10.1016/0377-2217(91)90033-R.

[69]

C. Wu and D. Barnes, Formulating partner selection criteria for agile supply chains: A Dempster-Shafer belief acceptability optimisation approach, International Journal of Production Economics, 125 (2010), 284-293. doi: 10.1016/j.ijpe.2010.02.010.

[70]

R. R. Yager, A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24 (1981), 143-161. doi: 10.1016/0020-0255(81)90017-7.

[71]

C. A. Yauch, Measuring agility as a performance outcome, Journal of Manufacturing Technology Management, 22 (2011), 384-404. doi: 10.1108/17410381111112738.

[72]

F. You and I. E. Grossmann, Design of responsive supply chains under demand uncertainty, Computers & Industrial Engineering, 32 (2008), 3090-3111. doi: 10.1016/j.compchemeng.2008.05.004.

[73]

Y. Y. YusufA. GunasekaranE. Adeleye and K. Sivayoganathan, Agile supply chain capabilities: Determinants of competitive objectives, European Journal of Operational Research, 159 (2004), 379-392. doi: 10.1016/j.ejor.2003.08.022.

Figure 1.  Here is the Caption of your figure
Figure 2.  Eigenvalue scree plot
Figure 3.  The Pareto optimal solutions for normalized values of first test problem
Table 1.  The primary defined input attributes for suppliers selection
RowInput attributeRowInput attribute
1Number of facilities21Working hours
2Staff training22Bureaucratic
3Education managers23Defective products
4Standard simple mentation in organizations24Material requirements planning
5In Stock25Distribution plan
6Product price26The geographical location of the factory
7Product variety27The geographical area covered
8Transportation28The political situation in the regions covered
9Waste29Infrastructure
10Market share30After Sales Service
11Career Opportunities31Technical Support
12The use of new technology32Management
13Production Volume33Response to Customer Request
14Automation34E-commerce Capability
15Communication System35JIT
16Delivery36Packing Ability
17Time of preparation37Position in the industry
18Lot Size38Product appearance
19Work in process (WIP)39Quality
20Specialist operators
RowInput attributeRowInput attribute
1Number of facilities21Working hours
2Staff training22Bureaucratic
3Education managers23Defective products
4Standard simple mentation in organizations24Material requirements planning
5In Stock25Distribution plan
6Product price26The geographical location of the factory
7Product variety27The geographical area covered
8Transportation28The political situation in the regions covered
9Waste29Infrastructure
10Market share30After Sales Service
11Career Opportunities31Technical Support
12The use of new technology32Management
13Production Volume33Response to Customer Request
14Automation34E-commerce Capability
15Communication System35JIT
16Delivery36Packing Ability
17Time of preparation37Position in the industry
18Lot Size38Product appearance
19Work in process (WIP)39Quality
20Specialist operators
Table 2.  The most important agility criteria filtered through conducting brain storming meeting
Input indicatorsRow
1Specialist operators
2The use of new technology
3Material requirements planning
4Distribution plan
5Response to Customer Request
6Technical Support
7E-commerce Capability
8Product variety
9Production Volume
10Transportation
11After Sales Service
12Automation
13Communication System
14JIT
15Quality
16The geographical area covered
Input indicatorsRow
1Specialist operators
2The use of new technology
3Material requirements planning
4Distribution plan
5Response to Customer Request
6Technical Support
7E-commerce Capability
8Product variety
9Production Volume
10Transportation
11After Sales Service
12Automation
13Communication System
14JIT
15Quality
16The geographical area covered
Table 3.  The performance indicators of suppliers
Output indicatorsRow
1Product price
2Bureaucratic
3Delivery time
4Work in Process (WIP)
Output indicatorsRow
1Product price
2Bureaucratic
3Delivery time
4Work in Process (WIP)
Table 4.  Total Variance of components
ComponentInitial Eigenvalue
TotalPercentage of VarianceCumulative Percentage
12.07412.96512.965
21.80311.26724.232
31.5759.84334.075
41.3808.62542.700
51.3348.33651.036
61.1817.38358.419
71.0276.41864.836
80.9355.84170.677
90.8845.52376.200
100.7934.95981.159
110.7204.49885.656
120.6243.89889.554
130.5803.62493.178
140.4232.64295.820
150.3622.26598.086
160.3061.914100.000
ComponentInitial Eigenvalue
TotalPercentage of VarianceCumulative Percentage
12.07412.96512.965
21.80311.26724.232
31.5759.84334.075
41.3808.62542.700
51.3348.33651.036
61.1817.38358.419
71.0276.41864.836
80.9355.84170.677
90.8845.52376.200
100.7934.95981.159
110.7204.49885.656
120.6243.89889.554
130.5803.62493.178
140.4232.64295.820
150.3622.26598.086
160.3061.914100.000
Table 5.  Total Variance of components
ComponentExtraction Sums of Squared LoadingsRotation Sums of Squared Loadings
TotalPercentage of VarianceCumulative PercentageTotalPercentage of VarianceCumulative Percentage
12.07412.96512.9651.5489.6759.675
21.80311.26724.2321.5479.67219.347
31.5759.84334.0751.5109.44028.787
41.3808.62542.7001.5069.41038.197
51.3348.33651.0361.4609.12647.324
61.1817.38358.4191.4018.75756.081
71.0276.41864.8361.4018.75564.836
ComponentExtraction Sums of Squared LoadingsRotation Sums of Squared Loadings
TotalPercentage of VarianceCumulative PercentageTotalPercentage of VarianceCumulative Percentage
12.07412.96512.9651.5489.6759.675
21.80311.26724.2321.5479.67219.347
31.5759.84334.0751.5109.44028.787
41.3808.62542.7001.5069.41038.197
51.3348.33651.0361.4609.12647.324
61.1817.38358.4191.4018.75756.081
71.0276.41864.8361.4018.75564.836
Table 6.  Rotated components
VariablesComponents
1234567
X10.042-0.1920.615-0.2110.159-0.273-0.029
X2-0.1750.176-0.015-0.065-0.709-0.101-0.061
X3-0.083-0.096-0.1450.479-0.4400.219-0.067
X40.1200.177-0.2200.6090.221-0.251-0.108
X5-0.208-0.8270.0650.1390.0480.2630.109
X6-0.2230.571-0.2070.0990.2560.1820.418
X70.133-0.1340.2050.753-0.0700.0730.037
X8-0.0730.004-0.090-0.018-0.016-0.729-0.123
X90.8410.0350.1350.0220.083-0.0110.014
X100.551-0.016-0.1000.309-0.0350.370-0.010
X11-0.1100.2280.6950.2210.1900.141-0.097
X12-0.2580.5410.1550.034-0.2830.2920.244
X130.175-0.166-0.147-0.2810.1510.506-0.591
X14-0.1770.115-0.6370.0140.262-0.176-0.120
X15-0.4640.1590.031-0.0860.629-0.029-0.048
X160.1110.005-0.030-0.1630.0720.1910.861
VariablesComponents
1234567
X10.042-0.1920.615-0.2110.159-0.273-0.029
X2-0.1750.176-0.015-0.065-0.709-0.101-0.061
X3-0.083-0.096-0.1450.479-0.4400.219-0.067
X40.1200.177-0.2200.6090.221-0.251-0.108
X5-0.208-0.8270.0650.1390.0480.2630.109
X6-0.2230.571-0.2070.0990.2560.1820.418
X70.133-0.1340.2050.753-0.0700.0730.037
X8-0.0730.004-0.090-0.018-0.016-0.729-0.123
X90.8410.0350.1350.0220.083-0.0110.014
X100.551-0.016-0.1000.309-0.0350.370-0.010
X11-0.1100.2280.6950.2210.1900.141-0.097
X12-0.2580.5410.1550.034-0.2830.2920.244
X130.175-0.166-0.147-0.2810.1510.506-0.591
X14-0.1770.115-0.6370.0140.262-0.176-0.120
X15-0.4640.1590.031-0.0860.629-0.029-0.048
X160.1110.005-0.030-0.1630.0720.1910.861
Table 7.  Suppliers scores driven out via PCA approach
SupplierScoreSupplierScoreSupplierScoreSupplierScore
1-0.4414316-0.4509331-0.70673460.22046
2-0.3994817-0.16193320.52357470.646209
30.079517180.41908330.57433948-0.2407
4-0.0185419-0.05046340.054961490.430716
50.06819200.01026435-0.3108500.175306
6-0.1633921-0.2980536-0.2968151-0.12202
7-0.47472220.283236370.379933520.065461
8-0.2640923-0.10214380.08338653-0.80726
90.35943424-0.387439-0.1178554-0.19505
10-0.48728250.278027400.092893550.258526
110.044161260.19624741-0.19233560.570286
120.50004270.194767420.121639570.265066
131.064131280.00978343-0.39538580.098087
14-0.7230529-0.08439440.67646459-0.50213
15-0.19635300.26665345-0.0272160-0.39293
SupplierScoreSupplierScoreSupplierScoreSupplierScore
1-0.4414316-0.4509331-0.70673460.22046
2-0.3994817-0.16193320.52357470.646209
30.079517180.41908330.57433948-0.2407
4-0.0185419-0.05046340.054961490.430716
50.06819200.01026435-0.3108500.175306
6-0.1633921-0.2980536-0.2968151-0.12202
7-0.47472220.283236370.379933520.065461
8-0.2640923-0.10214380.08338653-0.80726
90.35943424-0.387439-0.1178554-0.19505
10-0.48728250.278027400.092893550.258526
110.044161260.19624741-0.19233560.570286
120.50004270.194767420.121639570.265066
131.064131280.00978343-0.39538580.098087
14-0.7230529-0.08439440.67646459-0.50213
15-0.19635300.26665345-0.0272160-0.39293
Table 8.  The sources of random generation of the most likely values
ParameterValueParameterValue
$\tilde fs_{st}$ $ \sim Uniform(1800000, 4300000)$$\tilde Tr4_{idclt}$ $ \sim Uniform(80, 100)$
$\tilde fp_{pt}$$ \sim Uniform(1700000, 4000000)$$\tilde Cost_{mspt}$$ \sim Uniform(20, 40)$
$\tilde fd_{dt}$$ \sim Uniform(1600000, 3000000)$$\tilde MI_{id}$$ \sim Uniform(100, 120)$
$\tilde fse_{st}$$ \sim Uniform(180000, 480000)$$\tilde CPA1_{pft}$$ \sim Uniform(50000, 60000)$
$\tilde fpe_{pt}$$ \sim Uniform(170000, 400000)$$\tilde CPA2_{djt}$$ \sim Uniform(30000, 35000)$
$\tilde fde_{dt}$$ \sim Uniform(160000, 300000)$$\tilde CPA_{pdt}$$ \sim Uniform(60000, 70000)$
$\tilde de_{ict}$$ \sim Uniform(100, 200)$$\tilde td_{pclt}$$ \sim Uniform(16, 20)$
$\tilde vp_{ipt}$$ \sim Uniform(120, 150)$$\tilde tc_{dclt}$$ \sim Uniform(2, 4)$
$\tilde Hd_{idt}$$ \sim Uniform(10, 30)$$\tilde te_{pdlt}$$ \sim Uniform(10, 16)$
$\tilde Hp_{ipt}$$ \sim Uniform(15, 40)$$\tilde dis1_{pcl}$$ \sim Uniform(200, 600)$
$\tilde Tr1_{isplt}$$ \sim Uniform(80, 100)$$\tilde dis2_{dcl}$$ \sim Uniform(300, 500)$
$\tilde Tr2_{ipdlt}$$ \sim Uniform(40, 60)$$\tilde dis3_{pdl}$$ \sim Uniform(100, 200)$
$\tilde Tr3_{ipclt}$$ \sim Uniform(110, 200)$
ParameterValueParameterValue
$\tilde fs_{st}$ $ \sim Uniform(1800000, 4300000)$$\tilde Tr4_{idclt}$ $ \sim Uniform(80, 100)$
$\tilde fp_{pt}$$ \sim Uniform(1700000, 4000000)$$\tilde Cost_{mspt}$$ \sim Uniform(20, 40)$
$\tilde fd_{dt}$$ \sim Uniform(1600000, 3000000)$$\tilde MI_{id}$$ \sim Uniform(100, 120)$
$\tilde fse_{st}$$ \sim Uniform(180000, 480000)$$\tilde CPA1_{pft}$$ \sim Uniform(50000, 60000)$
$\tilde fpe_{pt}$$ \sim Uniform(170000, 400000)$$\tilde CPA2_{djt}$$ \sim Uniform(30000, 35000)$
$\tilde fde_{dt}$$ \sim Uniform(160000, 300000)$$\tilde CPA_{pdt}$$ \sim Uniform(60000, 70000)$
$\tilde de_{ict}$$ \sim Uniform(100, 200)$$\tilde td_{pclt}$$ \sim Uniform(16, 20)$
$\tilde vp_{ipt}$$ \sim Uniform(120, 150)$$\tilde tc_{dclt}$$ \sim Uniform(2, 4)$
$\tilde Hd_{idt}$$ \sim Uniform(10, 30)$$\tilde te_{pdlt}$$ \sim Uniform(10, 16)$
$\tilde Hp_{ipt}$$ \sim Uniform(15, 40)$$\tilde dis1_{pcl}$$ \sim Uniform(200, 600)$
$\tilde Tr1_{isplt}$$ \sim Uniform(80, 100)$$\tilde dis2_{dcl}$$ \sim Uniform(300, 500)$
$\tilde Tr2_{ipdlt}$$ \sim Uniform(40, 60)$$\tilde dis3_{pdl}$$ \sim Uniform(100, 200)$
$\tilde Tr3_{ipclt}$$ \sim Uniform(110, 200)$
Table 9.  The Pareto optimal solution for different values of importance coefficients
r1r2r3Problem No.Obj1Obj2Obj3CPU time (Sec)
10013.69E+111.38E+080.00E+00134
23.82E+121.26E+090.00E+00646
01016.61E+122.44E+070.00E+00164
22.50E+152.53E+080.00E+00655
00116.61E+121.38E+087.46E+07132
22.50E+151.26E+093.74E+11692
0.450.450.113.39E+127.89E+071.42E+07210
21.13E+156.58E+088.33E+10512
0.350.350.313.99E+129.30E+072.76E+07167
21.30E+157.29E+081.46E+11472
0.250.250.514.55E+121.06E+084.70E+07173
21.58E+159.41E+082.31E+11627
0.150.150.715.50E+121.16E+085.67E+07159
21.80E+159.91E+083.07E+11679
0.050.050.916.20E+121.25E+087.02E+07134
22.25E+151.13E+093.48E+11646
0.20.30.515.20E+129.83E+074.78E+07164
21.68E+158.90E+082.25E+11655
0.20.50.314.93E+127.21E+072.76E+07132
21.70E+156.48E+081.23E+11690
0.30.20.514.38E+121.13E+084.63E+07210
21.53E+159.81E+082.31E+11512
0.30.50.214.24E+126.65E+071.72E+07167
21.53E+156.38E+088.61E+10472
0.50.20.313.12E+121.08E+082.84E+07173
29.27E+149.84E+081.12E+11627
0.50.30.212.93E+129.59E+071.79E+07159
29.47E+148.90E+089.36E+10679
r1r2r3Problem No.Obj1Obj2Obj3CPU time (Sec)
10013.69E+111.38E+080.00E+00134
23.82E+121.26E+090.00E+00646
01016.61E+122.44E+070.00E+00164
22.50E+152.53E+080.00E+00655
00116.61E+121.38E+087.46E+07132
22.50E+151.26E+093.74E+11692
0.450.450.113.39E+127.89E+071.42E+07210
21.13E+156.58E+088.33E+10512
0.350.350.313.99E+129.30E+072.76E+07167
21.30E+157.29E+081.46E+11472
0.250.250.514.55E+121.06E+084.70E+07173
21.58E+159.41E+082.31E+11627
0.150.150.715.50E+121.16E+085.67E+07159
21.80E+159.91E+083.07E+11679
0.050.050.916.20E+121.25E+087.02E+07134
22.25E+151.13E+093.48E+11646
0.20.30.515.20E+129.83E+074.78E+07164
21.68E+158.90E+082.25E+11655
0.20.50.314.93E+127.21E+072.76E+07132
21.70E+156.48E+081.23E+11690
0.30.20.514.38E+121.13E+084.63E+07210
21.53E+159.81E+082.31E+11512
0.30.50.214.24E+126.65E+071.72E+07167
21.53E+156.38E+088.61E+10472
0.50.20.313.12E+121.08E+082.84E+07173
29.27E+149.84E+081.12E+11627
0.50.30.212.93E+129.59E+071.79E+07159
29.47E+148.90E+089.36E+10679
Table 10.  The studies mentioning the agility indicators in the literature
IndexRazmi et al. (2011)Yauch (2011)Ghodsypour and O'Brien (1998)Min and Shin (2008)Weber et al. (1991)Abratt and Kleyn (2012)Dickson (1996)Prater et al. (2001)Kassaee et al. (2014)Dahmardeh et al. (2010)Kumar et al. (2011)Aktepe et al. (1999)Lin (2009)Chan and Thong (2009)This study
1**********
2*********
3*********
4*********
5****
6*************
7*********
8****
9*********
10********
11********
12**********
13*********
14*********
15************
16**********
17********
18*********
19*********
20********
21********
22*********
23*********
24*********
25***
26*******
27*******
28****
29*
30************
31************
32********
33********
34********
35
36*********
37************
38*********
39*************
IndexRazmi et al. (2011)Yauch (2011)Ghodsypour and O'Brien (1998)Min and Shin (2008)Weber et al. (1991)Abratt and Kleyn (2012)Dickson (1996)Prater et al. (2001)Kassaee et al. (2014)Dahmardeh et al. (2010)Kumar et al. (2011)Aktepe et al. (1999)Lin (2009)Chan and Thong (2009)This study
1**********
2*********
3*********
4*********
5****
6*************
7*********
8****
9*********
10********
11********
12**********
13*********
14*********
15************
16**********
17********
18*********
19*********
20********
21********
22*********
23*********
24*********
25***
26*******
27*******
28****
29*
30************
31************
32********
33********
34********
35
36*********
37************
38*********
39*************
Table 11.  Agile suppliers attributes
No.In1In2In3In4In5In6In7In8In9In10In11In12In13In14In15In16
10.540.820.50.620.750.450.620.640.710.60.50.570.520.350.230.6
20.50.040.630.630.950.460.60.760.40.770.50.60.80.530.380.47
30.270.660.720.970.930.480.780.120.370.780.680.630.80.350.120.33
40.430.340.710.750.920.560.720.440.530.680.640.680.720.370.320.3
50.720.130.540.730.680.50.520.650.710.790.620.610.540.550.190.35
60.710.450.810.520.90.520.550.020.310.720.70.650.70.340.10.34
70.50.430.890.940.850.410.580.50.580.610.630.530.760.520.760.34
80.340.770.740.550.740.420.70.060.80.760.40.630.790.440.240.49
90.520.290.860.570.730.620.590.310.710.710.650.650.770.460.740.69
100.390.580.650.760.670.660.620.40.210.610.420.60.520.560.940.36
110.40.530.970.810.960.470.760.170.690.770.420.740.670.240.240.51
120.580.070.750.540.650.60.530.10.860.720.630.740.70.30.060.55
130.40.120.620.870.620.70.730.040.620.790.60.80.790.210.590.64
140.340.810.870.860.630.670.520.940.20.730.490.520.770.50.220.32
150.80.730.890.50.80.590.580.940.260.740.650.620.570.10.440.52
160.620.270.570.891.000.440.70.670.20.620.440.560.590.410.860.65
170.260.010.860.710.910.510.540.610.370.80.420.640.650.290.370.66
180.330.630.960.930.610.650.730.230.440.710.70.640.540.520.170.63
190.50.540.910.860.860.530.740.610.650.710.570.610.740.550.940.48
210.330.890.680.620.810.590.510.380.510.750.510.770.790.410.860.35
220.610.40.560.540.830.70.530.370.630.70.560.640.580.330.970.67
230.680.840.980.90.880.440.690.030.60.740.430.590.720.140.250.61
240.410.810.810.950.730.460.770.660.50.680.470.630.690.230.310.3
250.270.440.630.550.940.690.720.180.280.740.610.710.580.210.000.59
260.280.370.530.550.850.470.680.330.750.780.460.650.670.180.350.7
270.640.790.630.70.890.450.570.150.690.770.660.710.650.250.550.52
280.310.890.990.620.670.60.790.250.380.720.510.80.540.390.110.55
290.60.020.760.730.640.70.50.670.530.640.420.790.620.450.990.36
300.420.230.760.90.810.660.790.960.690.780.560.510.760.20.510.36
310.80.480.80.510.830.430.660.840.30.780.480.580.690.480.120.31
320.580.050.660.60.730.610.730.230.870.740.490.670.770.320.030.68
330.570.210.860.710.640.540.780.450.550.740.680.770.560.310.990.41
340.760.630.650.930.660.440.680.990.750.720.520.80.50.20.50.38
350.280.040.710.670.720.430.570.440.720.710.450.50.750.410.290.47
360.450.750.870.70.620.410.570.920.630.730.620.780.670.340.360.35
370.730.10.750.980.730.550.560.340.750.690.620.520.730.230.610.57
380.750.20.750.720.950.510.670.720.460.720.660.660.750.490.910.58
390.80.980.520.860.860.680.50.310.690.650.630.640.760.170.270.43
410.330.440.840.840.680.70.580.980.370.60.50.780.540.520.270.7
420.660.970.590.70.780.590.770.720.440.680.670.710.660.160.340.54
430.320.720.750.580.730.580.560.260.210.620.510.660.780.280.620.62
440.520.170.560.990.760.650.770.590.460.730.670.670.50.410.870.56
450.590.530.80.780.930.460.710.070.780.660.520.590.680.160.710.36
460.460.010.770.770.990.50.710.760.90.780.590.60.790.480.460.54
470.790.070.820.680.810.590.740.30.640.750.650.620.720.120.410.6
480.410.180.640.590.790.460.730.890.760.640.620.540.580.530.220.41
490.450.090.530.860.650.640.740.270.280.770.620.580.710.460.840.4
500.40.490.910.620.880.580.750.390.350.710.650.780.640.130.390.44
510.660.470.710.610.670.570.660.020.310.60.610.750.760.510.690.35
520.620.420.810.540.930.540.520.110.220.690.680.790.620.350.550.69
530.70.930.660.520.90.450.570.650.310.640.560.580.80.230.250.43
540.250.910.820.990.630.650.580.880.360.760.460.780.640.520.170.62
550.280.370.520.550.690.60.650.630.280.630.70.720.620.150.880.67
560.640.421.001.000.910.690.710.110.890.770.510.620.560.420.210.63
570.490.630.910.820.840.540.80.010.530.790.620.560.520.480.190.49
580.490.970.560.70.60.660.580.260.820.80.420.610.770.460.590.56
590.710.090.620.50.790.520.670.590.210.660.440.510.730.290.60.4
600.270.060.970.680.980.590.580.250.20.690.40.750.680.540.720.49
No.In1In2In3In4In5In6In7In8In9In10In11In12In13In14In15In16
10.540.820.50.620.750.450.620.640.710.60.50.570.520.350.230.6
20.50.040.630.630.950.460.60.760.40.770.50.60.80.530.380.47
30.270.660.720.970.930.480.780.120.370.780.680.630.80.350.120.33
40.430.340.710.750.920.560.720.440.530.680.640.680.720.370.320.3
50.720.130.540.730.680.50.520.650.710.790.620.610.540.550.190.35
60.710.450.810.520.90.520.550.020.310.720.70.650.70.340.10.34
70.50.430.890.940.850.410.580.50.580.610.630.530.760.520.760.34
80.340.770.740.550.740.420.70.060.80.760.40.630.790.440.240.49
90.520.290.860.570.730.620.590.310.710.710.650.650.770.460.740.69
100.390.580.650.760.670.660.620.40.210.610.420.60.520.560.940.36
110.40.530.970.810.960.470.760.170.690.770.420.740.670.240.240.51
120.580.070.750.540.650.60.530.10.860.720.630.740.70.30.060.55
130.40.120.620.870.620.70.730.040.620.790.60.80.790.210.590.64
140.340.810.870.860.630.670.520.940.20.730.490.520.770.50.220.32
150.80.730.890.50.80.590.580.940.260.740.650.620.570.10.440.52
160.620.270.570.891.000.440.70.670.20.620.440.560.590.410.860.65
170.260.010.860.710.910.510.540.610.370.80.420.640.650.290.370.66
180.330.630.960.930.610.650.730.230.440.710.70.640.540.520.170.63
190.50.540.910.860.860.530.740.610.650.710.570.610.740.550.940.48
210.330.890.680.620.810.590.510.380.510.750.510.770.790.410.860.35
220.610.40.560.540.830.70.530.370.630.70.560.640.580.330.970.67
230.680.840.980.90.880.440.690.030.60.740.430.590.720.140.250.61
240.410.810.810.950.730.460.770.660.50.680.470.630.690.230.310.3
250.270.440.630.550.940.690.720.180.280.740.610.710.580.210.000.59
260.280.370.530.550.850.470.680.330.750.780.460.650.670.180.350.7
270.640.790.630.70.890.450.570.150.690.770.660.710.650.250.550.52
280.310.890.990.620.670.60.790.250.380.720.510.80.540.390.110.55
290.60.020.760.730.640.70.50.670.530.640.420.790.620.450.990.36
300.420.230.760.90.810.660.790.960.690.780.560.510.760.20.510.36
310.80.480.80.510.830.430.660.840.30.780.480.580.690.480.120.31
320.580.050.660.60.730.610.730.230.870.740.490.670.770.320.030.68
330.570.210.860.710.640.540.780.450.550.740.680.770.560.310.990.41
340.760.630.650.930.660.440.680.990.750.720.520.80.50.20.50.38
350.280.040.710.670.720.430.570.440.720.710.450.50.750.410.290.47
360.450.750.870.70.620.410.570.920.630.730.620.780.670.340.360.35
370.730.10.750.980.730.550.560.340.750.690.620.520.730.230.610.57
380.750.20.750.720.950.510.670.720.460.720.660.660.750.490.910.58
390.80.980.520.860.860.680.50.310.690.650.630.640.760.170.270.43
410.330.440.840.840.680.70.580.980.370.60.50.780.540.520.270.7
420.660.970.590.70.780.590.770.720.440.680.670.710.660.160.340.54
430.320.720.750.580.730.580.560.260.210.620.510.660.780.280.620.62
440.520.170.560.990.760.650.770.590.460.730.670.670.50.410.870.56
450.590.530.80.780.930.460.710.070.780.660.520.590.680.160.710.36
460.460.010.770.770.990.50.710.760.90.780.590.60.790.480.460.54
470.790.070.820.680.810.590.740.30.640.750.650.620.720.120.410.6
480.410.180.640.590.790.460.730.890.760.640.620.540.580.530.220.41
490.450.090.530.860.650.640.740.270.280.770.620.580.710.460.840.4
500.40.490.910.620.880.580.750.390.350.710.650.780.640.130.390.44
510.660.470.710.610.670.570.660.020.310.60.610.750.760.510.690.35
520.620.420.810.540.930.540.520.110.220.690.680.790.620.350.550.69
530.70.930.660.520.90.450.570.650.310.640.560.580.80.230.250.43
540.250.910.820.990.630.650.580.880.360.760.460.780.640.520.170.62
550.280.370.520.550.690.60.650.630.280.630.70.720.620.150.880.67
560.640.421.001.000.910.690.710.110.890.770.510.620.560.420.210.63
570.490.630.910.820.840.540.80.010.530.790.620.560.520.480.190.49
580.490.970.560.70.60.660.580.260.820.80.420.610.770.460.590.56
590.710.090.620.50.790.520.670.590.210.660.440.510.730.290.60.4
600.270.060.970.680.980.590.580.250.20.690.40.750.680.540.720.49
[1]

Tien-Fu Liang, Hung-Wen Cheng. Multi-objective aggregate production planning decisions using two-phase fuzzy goal programming method. Journal of Industrial & Management Optimization, 2011, 7 (2) : 365-383. doi: 10.3934/jimo.2011.7.365

[2]

Xia Zhao, Jianping Dou. Bi-objective integrated supply chain design with transportation choices: A multi-objective particle swarm optimization. Journal of Industrial & Management Optimization, 2018, 13 (5) : 1-26. doi: 10.3934/jimo.2018095

[3]

Hui Zhang, Jian-Feng Cai, Lizhi Cheng, Jubo Zhu. Strongly convex programming for exact matrix completion and robust principal component analysis. Inverse Problems & Imaging, 2012, 6 (2) : 357-372. doi: 10.3934/ipi.2012.6.357

[4]

Masoud Mohammadzadeh, Alireza Arshadi Khamseh, Mohammad Mohammadi. A multi-objective integrated model for closed-loop supply chain configuration and supplier selection considering uncertain demand and different performance levels. Journal of Industrial & Management Optimization, 2017, 13 (2) : 1041-1064. doi: 10.3934/jimo.2016061

[5]

Qingshan You, Qun Wan, Yipeng Liu. A short note on strongly convex programming for exact matrix completion and robust principal component analysis. Inverse Problems & Imaging, 2013, 7 (1) : 305-306. doi: 10.3934/ipi.2013.7.305

[6]

Zhiqing Meng, Qiying Hu, Chuangyin Dang. A penalty function algorithm with objective parameters for nonlinear mathematical programming. Journal of Industrial & Management Optimization, 2009, 5 (3) : 585-601. doi: 10.3934/jimo.2009.5.585

[7]

Behrouz Kheirfam, Kamal mirnia. Multi-parametric sensitivity analysis in piecewise linear fractional programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 343-351. doi: 10.3934/jimo.2008.4.343

[8]

Jian Xiong, Zhongbao Zhou, Ke Tian, Tianjun Liao, Jianmai Shi. A multi-objective approach for weapon selection and planning problems in dynamic environments. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1189-1211. doi: 10.3934/jimo.2016068

[9]

Dušan M. Stipanović, Claire J. Tomlin, George Leitmann. A note on monotone approximations of minimum and maximum functions and multi-objective problems. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 487-493. doi: 10.3934/naco.2011.1.487

[10]

Hamed Fazlollahtabar, Mohammad Saidi-Mehrabad. Optimizing multi-objective decision making having qualitative evaluation. Journal of Industrial & Management Optimization, 2015, 11 (3) : 747-762. doi: 10.3934/jimo.2015.11.747

[11]

Lisha Wang, Huaming Song, Ding Zhang, Hui Yang. Pricing decisions for complementary products in a fuzzy dual-channel supply chain. Journal of Industrial & Management Optimization, 2018, 13 (5) : 1-22. doi: 10.3934/jimo.2018046

[12]

Yanqin Bai, Chuanhao Guo. Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems. Journal of Industrial & Management Optimization, 2014, 10 (2) : 543-556. doi: 10.3934/jimo.2014.10.543

[13]

Bao Qing Hu, Song Wang. A novel approach in uncertain programming part II: a class of constrained nonlinear programming problems with interval objective functions. Journal of Industrial & Management Optimization, 2006, 2 (4) : 373-385. doi: 10.3934/jimo.2006.2.373

[14]

Behrouz Kheirfam. Multi-parametric sensitivity analysis of the constraint matrix in piecewise linear fractional programming. Journal of Industrial & Management Optimization, 2010, 6 (2) : 347-361. doi: 10.3934/jimo.2010.6.347

[15]

Xiao-Bing Li, Qi-Lin Wang, Zhi Lin. Optimality conditions and duality for minimax fractional programming problems with data uncertainty. Journal of Industrial & Management Optimization, 2018, 13 (5) : 1-19. doi: 10.3934/jimo.2018089

[16]

Adriel Cheng, Cheng-Chew Lim. Optimizing system-on-chip verifications with multi-objective genetic evolutionary algorithms. Journal of Industrial & Management Optimization, 2014, 10 (2) : 383-396. doi: 10.3934/jimo.2014.10.383

[17]

Zongmin Li, Jiuping Xu, Wenjing Shen, Benjamin Lev, Xiao Lei. Bilevel multi-objective construction site security planning with twofold random phenomenon. Journal of Industrial & Management Optimization, 2015, 11 (2) : 595-617. doi: 10.3934/jimo.2015.11.595

[18]

Liwei Zhang, Jihong Zhang, Yule Zhang. Second-order optimality conditions for cone constrained multi-objective optimization. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1041-1054. doi: 10.3934/jimo.2017089

[19]

Danthai Thongphiew, Vira Chankong, Fang-Fang Yin, Q. Jackie Wu. An on-line adaptive radiation therapy system for intensity modulated radiation therapy: An application of multi-objective optimization. Journal of Industrial & Management Optimization, 2008, 4 (3) : 453-475. doi: 10.3934/jimo.2008.4.453

[20]

Min Zhang, Gang Li. Multi-objective optimization algorithm based on improved particle swarm in cloud computing environment. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1413-1426. doi: 10.3934/dcdss.2019097

2017 Impact Factor: 0.994

Article outline

Figures and Tables

[Back to Top]