A review and analysis of “graph theoretical-matrix permanent” approach to decision making with example applications

Artificial Intelligence Review

Volumn 42, Issue 4, 2014, Pages 573-605

  Baykasoglu, Adil ^a  

^a DOKUZ EYLUL UNIVERSITY   (Turkey)

Author keywords

Combinatorics; Fuzzy variables; Graph theory; Matrix permanents; Multiple attribute decision making

Indexed keywords

DECISION MAKING; DECISION THEORY; HIERARCHICAL SYSTEMS; MATRIX ALGEBRA; TREES (MATHEMATICS);

COMBINATORICS; COMPLEX DECISION; FUZZY VARIABLE; HIERARCHICAL MODEL; INDUSTRY SECTORS; MATRIX PERMANENT; MULTIPLE ATTRIBUTE DECISION MAKING; SUPERMARKET LOCATIONS;

GRAPH THEORY;

EID: 84911360070     PISSN: 02692821     EISSN: 15737462     Source Type: Journal    
DOI: 10.1007/s10462-012-9354-y     Document Type: Article

References (105)

1. Anand A, Wani MF (2010) Product life-cycle modeling and evaluation at the conceptual design stage a digraph and matrix approach. J Mech Des 132(9): 091010-1–091010-9
2. Baykasoglu A (2009a) Quantifying machine flexibility. Int J Prod Res 47(15): 4109–4123
3. Baykasoglu A (2009b) A practical fuzzy digraph model for modeling manufacturing flexibility. Cybern Syst 40(6): 475–489
4. Baykasoglu A, Dereli T, Tanis S, Sevim T (2003) Supermarket yer secimi problemiicin AHP yaklasimi III. Ulusal Uretim Arastirmalari Sempozyumu Bildiriler Kitabi, Kultur University, Istanbul, pp 491–497, 19–20 Apr 2003 (in Turkish)
5. Babu BJC, Prabhakaran DRT, Agrawal VP (2008) Quality evaluation of resin transfer molded products. J Reinf Plast Compos 27(6): 559–581
6. Baykasoglu A, Ozbay E, Gogus MT, Oztas A (2009) Contractor selection with multi criteria decision support tools. Int J Ind Syst Eng 4(2): 174–197
7. Benjamin AT, Cameron NT (2005) Counting on determinants. Am Math Mon 112(6): 481–492
8. Bereketli I, Genevois ME, Albayrak YE, Ozyol M (2011) WEEE treatment strategies’ evaluation using fuzzy LINMAP method. Expert Syst Appl 38(1): 71–79
9. Bhosle SP, Basu SK (2008) Quantitative decision making in assessing the life cycle cost and reliability growth of a productive asset. IE(I) J PR 88: 3–10
10. Büyüközkan G, Feyzioğlu O, Nebol E (2008) Selection of the strategic alliance partner in logistics value chain. Int J Prod Econ 113(1): 148–158
11. Chakladar ND, Das R, Chakraborty S (2009) A digraph-based expert system for non- traditional machining process selection. Int J Adv Manuf Technol 43: 226–237
12. Chen S-J, Hwang CL (1992) Fuzzy multiple attribute decision making: methods and applications. Springer-Verlag, Berlin and New York. ISBN 3540549986
13. Chen LY, Wang T-C (2009) Optimizing partners’ choice in IS/IT outsourcing projects: the strategic decision of fuzzy VIKOR. Int J Prod Econ 120(1): 233–242
14. Darvish M, Yasaei M, Saeedi A (2009) Application of the graph theory and matrix methods to contractor ranking. Int J Proj Manag 27: 610–619
15. Dereli T, Durmuşoğlu A, Seçkiner SU, Avlanmaz N (2010) A fuzzy approach for personnel selection process. Turkish J Fuzzy Syst 1(2): 126–140
16. Dereli T, Baykasoglu A, Altun K, Durmusoglu A, Turksen IB (2011) Industrial applications of type-2 fuzzy sets and systems: a concise review. Comput Ind 62(2): 125–137
17. Faisal MN, Banwet DK, Shankar R (2007a) Supply chain agility: analysing the enablers. Int J Agile Syst Manag 2(1): 76–91
18. Faisal MN, Banwet DK, Shankar R (2007b) Information risks management in supply chains: an assessment and mitigation framework. J Enterp Inf Manag 20(6): 677–699
19. Faisal MN, Banwet DK, Shankar R (2007c) An approach to measure supply chain agility. Int J Ind Syst Eng 2(1): 79–98
20. Faisal MN, Banwet DK, Shankar R (2007d) Quantification of risk mitigation environment of supply chains using graph theory and matrix methods. Eur J Ind Eng 1(1): 22–39
21. Gadakh VS, Shinde VB (2011) Selection of cutting parameters in side milling operation using graph theory and matrix approach. Int J Adv Manuf Technol 56: 857–863
22. Gandhi OP, Agrawal VP (1992) FMEA-a digraph and matrix approach. Reliab Eng Syst Saf 35: 147–158
23. Gandhi OP, Agrawal VP (1994) A digraph approach to system wear evaluation and analysis. Trans ASME J Tribol 116: 268–274
24. Gandhi OP, Agrawal VP (1996) Failure cause analysis—a structural approach. Trans ASME J Press Vessel Technol 118: 434–440
25. Gandhi OP, Agrawal VP, Shishodia KS (1991) Reliability analysis and evaluation of systems. Reliab Eng Syst Saf 32: 283–305
26. Garg RK, Agrawal VP, Gupta VK (2006) Selection of power plants by evaluation and comparison using graph theoretical methodology. Electr Power Energy Syst 28: 429–435
27. Garg RK, Gupta VK, Agrawal VP (2007a) Quality evaluation of a thermal power plant by graph-theoretical methodology. Int J Power Energy Syst 27(1): 42–48
28. Garg RK, Gupta VK, Agrawal VP (2007b) Reliability modelling and analysis of a tribo-mechanical system. Int J Model Simul 27(3): 288–294
29. Glynn DG (2010) The permanent of a square matrix. Eur J Combin 31: 1887–1891
30. Grover S, Agrawal VP, Khan IA (2004) A digraph approach to TQM evaluation of an industry. Int J Prod Res 42(19): 4031–4053
31. Grover S, Agrawal VP, Khan IA (2005) Human resource performance index in TQM environment. Int J Manag Pract 1(2): 131–151
32. Grover S, Agrawal VP, Khan IA (2006) Role of human factors in TQM—a graph theoretic approach. Benchmarking Int J 13(4): 447–468
33. Grover S, Singh V (2007) A graph theoretic approach to the use of quality tools and techniques. Int J Oper Quantum Manag 13(3): 199–209
34. Hatush Z, Skitmore M (1998) Contractor selection using multicriteria utility theory. Build Environ 33(2–3): 105–115
35. Hokkanen J, Salminen P, Rossi E, Ettala M (1995) The choice of a solid waste management system using the Electre II decision-aid method. Waste Manag Res 13(2): 175–193
36. Ionica A, Edelhauser E (2006) A digraph model for evaluating the c-s relationship in the QMS context. Ann Univ Petroşani Mech Eng 8: 51–56
37. Jaya J, Thanushkodi K (2009) Structural modeling and analysis of computer aided diagnosis (CAD) system: a graph theoretic approach. Int J Comput Sci Appl 2(1): 5–8
38. Jangra K, Grover S, Aggarwal A (2011a) Digraph and matrix method for the performance evaluation of carbide compacting die manufactured by wire EDM. Int J Adv Manuf Technol 54: 79–591
39. Jangra K, Grover S, Chan FTS, Aggarwal A (2011b) Digraph and matrix method to evaluate the machinability of tungsten carbide composite with wire EDM. Int J Adv Manuf Technol 56: 959–974
40. Kahraman C, Cebeci U, Ruan D (2004) Multi-attribute comparison of catering service companies using fuzzy AHP: the case of Turkey. Int J Prod Econ 87(2): 171–184
41. Kaur A, Kanda A, Deshmukh SG (2006) A graph theoretic approach for supply chain coordination. Int J Logist Syst Manag 2(4): 321–341
42. Kayakutlu G, Buyukozkan G (2011) Assessing performance factors for a 3PL in a value chain. Int J Prod Econ 131(2): 441–452
43. Kiran CP, Clement S, Agrawal VP (2011) Design for X-abilities of a mechatronic system-a concurrent engineering and graph theory based approach. Concurr Eng Res Appl 19(1): 55–70
44. Kulkarni S (2005) Graph theory and matrix approach for performance evaluation of TQM in Indian industries. TQM Mag 17(6): 509–526
45. Kumar A, Agrawal VP (2008) Structural modelling and analysis of electroplating system: a graph theoretic system approach. Int J Surf Sci Eng 2(6): 520–540
46. Kumar A, Clement S, Agrawal VP (2010) Structural modeling and analysis of an effluent treatment process for electroplating—a graph theoretic approach. J Hazard Mater 179: 748–761
47. Kumar A, Clement S, Agrawal VP (2011) Concurrent design of electroplating system for X-abilities: a graph theoretic approach. Int J Ind Syst Eng 9(3): 350–371
48. Minc H (1978) Permanents. Addison-Wesley, Reading
49. Mohan M, Gandhi OP, Agrawal VP (2003) Systems modelling of a coal-based steam power plant. In: Proceedings of the institution of mechanical engineers—Part A. Journal of Power and Energy 217: 259–277
50. Mohan M, Gandhi OP, Agrawal VP (2004) Maintenance strategy for a coal-based steam power plant equipment—a graph theoretic approach. In: Proceedings of the institution of mechanical engineers—Part A. Journal of Power and Energy 218: 619–636
51. Mohan M, Gandhi OP, Agrawal VP (2006) Real time efficiency index of a steam power plant: a systems approach. In: Proceedings of the institution of mechanical engineers—Part A. Journal of Power and Energy 220: 103–131
52. Mohan M, Gandhi OP, Agrawal VP (2007) Real-time commercial availability index of a steam power plant—graph theory and matrix method. In: Proceedings of the institution of mechanical engineers—Part A. Journal of Power and Energy, 221: 885–898
53. Mohan M, Gandhi OP, Agrawal VP (2008) Real-time reliability index of a steam power plant: a systems approach. In: Proceedings of the institution of mechanical engineers—Part A. Journal of Power and Energy 222: 355–369
54. Nijenhuis A, Wilf HS (1975) Combinatorial algorithms. Academic Press, New York
55. Nourani Y, Andersen B (1999) Exploration of NP-hard enumeration problems by simulated annealing—the spectrum values of permanents. Theor Comput Sci 215: 51–68
56. Paramasivam A, Senthil V (2009) Analysis and evaluation of product design through design aspects using digraph and matrix approach. Int J Interact Des Manuf 3: 13–23
57. Paramasivam A, Senthil V, Ramasamy NR (2010, in press) Decision making in equipment selection: an integrated approach with digraph and matrix approach, AHP and ANP. Int J Adv Manuf Technol. doi:10.1007/s00170-010-2997-4
58. Paramasivam V, Padmanaban KP, Senthil V (2010) Optimum design selection of jigs/fixtures using digraph and matrix methods. Int J Manuf Technol Manag 20(1–4): 358–371
59. Parkan C, Wu M-L (2000) Comparison of three modern multicriteria decision-making tools. Int J Syst Sci 31(4): 497–517
60. Prabhakaran RTD, Durai Babu BJC, Agrawal VP (2006a) Design for ‘X’-abilities of RTM products—a graph theoretic approach. Concurr Eng Res Appl 14(2): 151–161
61. Prabhakaran RTD, Babu BJC, Agrawal VP (2006b) Quality modeling and analysis of polymer composite products. Polym Compos 27: 329–340
62. Prabhakaran RTD, Babu BJC, Agrawal VP (2006c) Structural modeling and analysis of FRP composite product subsystems-a systems approach. Polym Compos 27: 681–699
63. Prabhakaran RTD, Babu BJC, Agrawal VP (2006d) Structural modeling and analysis of composite product system-a graph theoretic approach. J Compos Mater 40: 1987–2007
64. Prince AA, Agrawal VP (2009) Structural modeling and integrative analysis of microelectromechanical systems product using graph theoretic approach. Microsyst Technol 15: 1083–1096
65. Qureshi MN, Kumar P, Kumar D (2009) Selection of 3PL service providers: a combined approach of AHP and graph theory. Int J Serv Technol Manag 12(1): 35–60
66. Qureshi MN, Kumar P, Kumar D (2009) Selection of logistics services provider (LSP) under fuzzy environment: a graph-theoretic and matrix approach. Int J Logist Syst Manag 5(5): 551–573
67. Raj T, Attri R (2010) Quantifying barriers to implementing total quality management (TQM). Eur J Ind Eng 4(3): 308–335
68. Raj T, Shankar R, Suhaib M, Khan RA (2010) A graph-theoretic approach to evaluate the intensity of barriers in the implementation of FMSs. Int J Serv Oper Manag 7(1): 24–52
69. Rao RV (2000) Graph theory and matrix approach for the performance evaluation of technical institutions. Indian J Tech Educ 23(2): 27–33
70. Rao RV (2006a) A decision-making framework model for evaluating flexible manufacturing systems using digraph and matrix methods. Int J Adv Manuf Technol 30: 1101–1110
71. Rao RV (2006b) A material selection model using graph theory and matrix approach. Mater Sci Eng A 431: 248–255
72. Rao RV (2006c) Plant location selection using fuzzy digraph and matrix methods. Int J Ind Eng 13(2): 166–176
73. Rao RV (2006d) Machine group selection in a flexible manufacturing cell using digraph and matrix methods. Int J Ind Syst Eng 1(4): 502–518
74. Rao RV (2008) Environmental impact assessment of manufacturing processes using a combinatorial mathematics based decision making method. Int J Sustain Manuf 1(1): 42–50
75. Rao RV, Gandhi OP (2001) Digraph and matrix method for the selection, identification and comparison of metal-cutting fluids. In: Proceedings of the institution of mechanical engineers—Part J. Journal of Engineering Tribology 215: 25–33
76. Rao RV, Gandhi OP (2002) Digraph and matrix methods for the machinability evaluation of work materials. Int J Mach Tools Manuf 42: 321–330
77. Rao RV, Gandhi OP (2002) Failure cause analysis of machine tools using digraph and matrix methods. Int J Mach Tools Manuf 42: 521–528
78. Rao RV (2004) Digraph and matrix methods for evaluating environmentally conscious manufacturing programs. Int J Environ Conscious Des Manuf 12(2): 23–33
79. Rao RV, Padmanabhan KK (2006) Selection, identification and comparison of industrial robots using digraph and matrix methods. Robot Comput Integr Manuf 22: 373–383
80. Rao RV, Padmanabhan KK (2007) Rapid prototyping process selection using graph theory and matrix approach. J Mater Process Technol 194: 81–88
81. Rao RV, Parnichkun M (2009) Flexible manufacturing system selection using a combinatorial mathematics-based decision-making method. Int J Prod Res 47(24): 6981–6998
82. Rao RV, Padmanabhan KK (2010) Selection of best product end-of-life scenario using digraph and matrix methods. J Eng Des 21(4): 455–472
83. Rao RV (2007) Decision making in the manufacturing environment: using graph theory and fuzzy multiple attribute decision making methods. Springer series in advanced manufacturing. Springer, London
84. Sehgal R, Gandhi OP, Angra S (2000) Reliability evaluation and selection of rolling element bearings. Reliab Eng Syst Saf 68: 39–52
85. Shriver B, Eberlein PJ, Dixon RD (1969) Algorithm 361: permanent function of a square matrix I and II. Commun ACM 12(11): 634
86. Singh R, Sekhon GS (1996) A computerized diagraph and matrix approach for evaluation of metal stamping layouts. J Mater Process Technol 59: 285–293
87. Singh R, Agrawal VP (2008) Structural modelling and integrative analysis of manufacturing systems using graph theoretic approach. J Manuf Technol Manag 19(7): 844–870
88. Tapkan P, Ozbakir L, Baykasoglu A, Kulluk S, Kayhan B (2007) Analitik hiyerarsi yonteminin endustri muhendisligi mezunlarinin sektor secimi problemine uygulanmasi: ornek olay, 13. Ulusal Ergonomi Kongresi, Erciyes University, Kayseri, Turkey, 6–8 December 2007 (in conference CD, in Turkish)
89. Thakkar J, Kanda A, Deshmukh SK (2008) Evaluation of buyer-supplier relationships using an integrated mathematical approach of structural modeling. J Manuf Technol Manag 19(1): 92–124
90. Upadhyay N, Agrawal VP (2007) Structural modeling and analysis of intelligent mobile learning environment a graph theoretic system approach. J Appl Quant Methods 2(2): 226–248
91. Upadhyay N (2008) Structural modelling and analysis of object oriented systems. Int J Control Commun 1(2): 240–255
92. Upadhyay N, Deshpande BM, Agrawal VP (2010) Developning maintainability index of a software component: a digraph and matrix approach. ACM SIGSOFT Softw Eng Notes 35(5): 1–11
93. Upadhyay N, Deshpande BM, Agrawal VP (2009) MACBSS: modeling and analysis of component based software system. 2009 world congress on computer science and information engineering, IEEE Computer Society, pp 595–601. doi:10.1109/CSIE.2009.964
94. Vardi I (1991) Computational recreations in mathematica. Addison-Wesley, Reading, pp 108 and 110–112
95. Venkatasamy R, Agrawal VP (1995) System and structural-analysis of an automobile vehicle—a graph-theoretic approach. J Veh Des 16: 477–505
96. Venkatasamy R, Agrawal VP (1996) Selection of automobile vehicle by evaluation graph theoretical methodology. Int J Veh Des 17(4): 449–470
97. Venkatasamy R, Agrawal VP (1997) A digraph approach to quality evaluation of an automotive vehicle. Qual Eng 9(3): 405–417
98. Weisstein Eric W (2010) Permanent. From MathWorld-a wolfram web resource (last access 30 Nov 2010). http://mathworld.wolfram.com/Permanent.html
99. Wagner SM, Neshat N (2010) Assessing the vulnerability of supply chains using graph theory. Int J Prod Econ 126(1): 121–129
100. Wani MF, Gandhi OP (2002) Maintainability design and evaluation of mechanical systems based on tribology. Reliab Eng Syst Saf 77: 181–188
101. Wani MF, Gandhi OP (1999) Development of maintainability index for mecha nical systems. Reliab Eng Syst Saf 65: 259–270
102. Xu G, Tian W, Qian L, Zhang X (2007) A novel conflict reassignment method based on grey relational analysis (GRA). Pattern Recognit Lett 28(15): 2080–2087
103. Yadav N, Khan IA, Grover S (2010) Operational-economics based evaluation and selection of a power plant using graph theoretic approach. Int J Energy Power Eng 3(4): 249–259
104. Yoo D-I, Ohta H (1995) Optimal pricing and product-planning for new multiattribute products based on conjoint analysis. Int J Prod Econ 38(2-3): 245–253
105. Zhong LJ, Yu AB, Yu SY, Du HY (2006) Machinability evalua tion of engineering ceramics with digraph method. Key Eng Mater 304: 256–260