American Institute of Mathematical Sciences

Advanced
July  2015, 11(3): 747-762. doi: 10.3934/jimo.2015.11.747

Optimizing multi-objective decision making having qualitative evaluation

Hamed Fazlollahtabar 1, and  Mohammad Saidi-Mehrabad 2,

1. 

PhD. Student of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
2. 

Faculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

Received  November 2012 Revised  July 2014 Published  October 2014

We develop a ranking process for multi-objective decision making. For optimizing the multi-objective problem having both quantitative and qualitative objectives, weight assessment is important to convert the problem into the corresponding single objective problem. Therefore, a ranking process is proposed to simultaneously obtain the objective weights and the evaluation of alternatives with multiple objectives. Several new concepts are developed to handle the dynamism in distance computation and ranking of decisions in a multi-objective model having qualitative evaluations. The proposed process is illustrated in a numerical example.
Keywords: Multi-objective decision making, ranking process, qualitative evaluations..
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Hamed Fazlollahtabar, Mohammad Saidi-Mehrabad. Optimizing multi-objective decision making having qualitative evaluation. Journal of Industrial and Management Optimization, 2015, 11 (3) : 747-762. doi: 10.3934/jimo.2015.11.747
References:
[1]

M. A. Badri, A. K. Mortagy and C. A. Alsyed, A multiobjective model for locating fire stations, European Journal of Operational Research, 110 (1998), 243-260.

[2]

C. Briggs and P. Little, Impacts of organizational culture and personality traits on decision-making in technical organizations, Systems Engineering, 11 (2008), 15-26.

[3]

V. Chankong and Y. Y. Haimes, Multiobjective Decision Making: Theory and Methodology, Dover, New York, USA, 2008.

[4]

J. Daniels, P. W. Werner and T. Bahill, Quantitative methods for tradeoff analysis, Systems Engineering, 4 (2001), 190-212.

[5]

M. H. DeGroot, Optimal Statistical Decisions, McGraw-Hill, New York, USA, 1970.

[6]

R. Y. Dicdican and Y. Y. Haimes, Relating multiobjective decision trees to the multiobjective risk impact analysis method, Systems Engineering, 8 (2005), 95-108.

[7]

M. Ehrgott and X. Gandibleaux, (Editors), Multiple criteria optimization: State of the Art Annotated Bibliographic Surveys, Springer, New York, 2002.

[8]

A. O. Esogbue and R. E. Bellman, Fuzzy dynamic programming and its extensions, TIMS/Studies Management Sci., 20 (1984), 147-167.

[9]

H. I. Frohwein, J. H. Lambert, Y. Y. Haimes and L. A. Schiff, Multicriteria framework to aid comparison of roadway improvement projects, J Transportation Engineering, 125 (1999), 224-230.

[10]

K. Golabi, Selecting a group of dissimilar projects for funding, IEEE Transaction in Engineering Management, 34 (1987), 138-145.

[11]

S. D. Guikema and M. W. Milke, Sensitivity analysis for multi-attribute project selection problems, Civil Engineering Environmental Systems, 20 (2003), 143-162.

[12]

M. J. Hodgson, K. E. Rosing and A. L. G. Storrier, Testing a bicriterion location-allocation model with real world network traffic: The case of Edmonton, Canada, Multicriteria Analysis, Climaco, J. (Editor), Springer, Berlin, (1997),484-495.

[13]

M. L. Hussein and M. A. Abo-Sinna, Decomposition of multi-objective programming problems by hybrid fuzzy dynamic programming, Fuzzy Sets Systems, 60 (1993), 25-32. doi: 10.1016/0165-0114(93)90286-Q.

[14]

M. L. Hussein and M. A. Abo-Sinna, A fuzzy dynamic approach to the multicriteria resource allocation problem, Fuzzy Sets Systems, 69 (1995), 115-124. doi: 10.1016/0165-0114(94)00231-U.

[15]

J. Kacprzyk, Multistage Fuzzy Control, Wiley, Chichester, USA, 1997.

[16]

J. Kacprzyk and A. O. Esogbue, Fuzzy dynamic programming: Main developments and applications, Fuzzy Sets Systems, 81 (1996), 31-45. doi: 10.1016/0165-0114(95)00239-1.

[17]

J. Kacprzyk and L. Sugianto, Multistage fuzzy control involving objective and subjective aspects, in L.C. Jain, R.K. Jain (Eds.), Proceedings of the Second International Conference on Knowledge Based Intelligent Electronic Systems, Adelaide, Australia, (1998), 564-573.

[18]

S. Kullback, Information Theory and Statistics, John Wiley and Sons, NY, 1959.

[19]

S. Kullback and R. A. Leibler, On Information and Sufficiency, Annals of Mathematical Statistics, 22 (1951), 79-86. doi: 10.1214/aoms/1177729694.

[20]

J. H. Lambert, J. A. Baker and K. D. Peterson, Decision aid for allocation of transport funds to guardrails, Accident Anal Prevention, 35 (2003), 47-57.

[21]

J. H. Lambert, Y. Y. Haimes, D. Li, R. M. Schoof and V. Tulsiani, Identification, ranking and management of risks in a major systems acquisition, Reliability Engineering and Systems Safety, 72 (2001), 315-325.

[22]

J. H. Lambert, N. N. Joshi, K. D. Peterson and S. M. Wadie, Coordination and diversification of investments in multimodal transportation, Public Works Management Policy, 11 (2007), 250-265.

[23]

J. H. Lambert, K. A. Peterson and N. N. Joshi, Synthesis of quantitative and qualitative evidence for risk-based analysis of highway projects, Accident Anal Prevention, 38 (2006), 925-935.

[24]

J. H. Lambert, K. D. Peterson, S. M. Wadie and M. W. Farrington, Development of a methodology to coordinate and prioritize multimodal investment networks, Virginia Transportation Research Council Publication, Charlottesville, VA, Vol. 5, 2005.

[25]

D. B. Lee, Methods for evaluation of transportation projects in the USA, Transportation Policy, 7 (2000), 41-50.

[26]

L. M. Meade and A. Presley, R and D project selection using the analytic process, IEEE Transaction in Engineering Management, 49 (2002), 59-66.

[27]

D. A. Niemeier, Z. B. Zabinsky, Z. Zeng and G. S. Rutherford, Optimization models for transportation project programming process, Journal of Transportation Engineering, 121 (1995), 14-26.

[28]

G. S. Parnell, R. E. Metzger, J. Merrick and R. Eiler, Multiobjective decision analysis of theater missile defense architectures, Systems Engineering, 4 (2001), 24-34.

[29]

M. Sanchez, N. Agell and G. Ormazabal, Multiple-criteria evaluation for value management in civil engineering, Journal of Management Engineering, 21 (2005), 131-137.

[30]

J. S. Shang, Y. Tjader and Y. Ding, A unified framework for multicriteria evaluation of transportation, IEEE Transaction in Engineering Management, 51 (2004), 300-313.

[31]

P. J. Smith, M. Shafi and H. Gao, Quick simulation: A review of importance sampling techniques in communication systems, IEEE J.Select.Areas Commun., 15 (1997), 597-613.

[32]

R. Srinivasan, Importance Sampling - Applications in Communications and Detection, Springer-Verlag, Berlin, 2002. doi: 10.1007/978-3-662-05052-1.

[33]

J. L. Tsang, J. H. Lambert and R. C. Patev, Multiple-criteria decision making in the design of innovative lock walls for barge impact: Phase 2, implementation methodologies, ERDC/ITL TR-02-5, ERDC Vicksburg Publications, Innovations for Navigation Projects Research Program, US Army Engineer Research and Development Center, Vicksburg, MS, 2002.

[34]

C. R. Weisbin, G. Rodriguez, A. Elfes and J. H. Smith, Toward a systematic approach for selection of NASA technology portfolios, 7 (2004), 285-302.

[35]

S. Y. Chen and G. T. Fu, Combining fuzzy iteration model with dynamic programming to solve multiobjective multistage decision making problems, Fuzzy Sets and Systems, 152 (2005), 499-312. doi: 10.1016/j.fss.2004.10.006.

[36]

J. Q. Wang and J. J. Li, Multi-criteria fuzzy decision-making method based on cross entropy and score functions, Expert Systems with Applications, 38 (2011), 1032-1038.

[37]

A. R. Jafarian-Moghaddam and K. Ghoseiri, Fuzzy dynamic multi-objective Data Envelopment Analysis model, Expert Systems with Applications, 38 (2011), 850-855.

show all references

References:
[1]

M. A. Badri, A. K. Mortagy and C. A. Alsyed, A multiobjective model for locating fire stations, European Journal of Operational Research, 110 (1998), 243-260.

[2]

C. Briggs and P. Little, Impacts of organizational culture and personality traits on decision-making in technical organizations, Systems Engineering, 11 (2008), 15-26.

[3]

V. Chankong and Y. Y. Haimes, Multiobjective Decision Making: Theory and Methodology, Dover, New York, USA, 2008.

[4]

J. Daniels, P. W. Werner and T. Bahill, Quantitative methods for tradeoff analysis, Systems Engineering, 4 (2001), 190-212.

[5]

M. H. DeGroot, Optimal Statistical Decisions, McGraw-Hill, New York, USA, 1970.

[6]

R. Y. Dicdican and Y. Y. Haimes, Relating multiobjective decision trees to the multiobjective risk impact analysis method, Systems Engineering, 8 (2005), 95-108.

[7]

M. Ehrgott and X. Gandibleaux, (Editors), Multiple criteria optimization: State of the Art Annotated Bibliographic Surveys, Springer, New York, 2002.

[8]

A. O. Esogbue and R. E. Bellman, Fuzzy dynamic programming and its extensions, TIMS/Studies Management Sci., 20 (1984), 147-167.

[9]

H. I. Frohwein, J. H. Lambert, Y. Y. Haimes and L. A. Schiff, Multicriteria framework to aid comparison of roadway improvement projects, J Transportation Engineering, 125 (1999), 224-230.

[10]

K. Golabi, Selecting a group of dissimilar projects for funding, IEEE Transaction in Engineering Management, 34 (1987), 138-145.

[11]

S. D. Guikema and M. W. Milke, Sensitivity analysis for multi-attribute project selection problems, Civil Engineering Environmental Systems, 20 (2003), 143-162.

[12]

M. J. Hodgson, K. E. Rosing and A. L. G. Storrier, Testing a bicriterion location-allocation model with real world network traffic: The case of Edmonton, Canada, Multicriteria Analysis, Climaco, J. (Editor), Springer, Berlin, (1997),484-495.

[13]

M. L. Hussein and M. A. Abo-Sinna, Decomposition of multi-objective programming problems by hybrid fuzzy dynamic programming, Fuzzy Sets Systems, 60 (1993), 25-32. doi: 10.1016/0165-0114(93)90286-Q.

[14]

M. L. Hussein and M. A. Abo-Sinna, A fuzzy dynamic approach to the multicriteria resource allocation problem, Fuzzy Sets Systems, 69 (1995), 115-124. doi: 10.1016/0165-0114(94)00231-U.

[15]

J. Kacprzyk, Multistage Fuzzy Control, Wiley, Chichester, USA, 1997.

[16]

J. Kacprzyk and A. O. Esogbue, Fuzzy dynamic programming: Main developments and applications, Fuzzy Sets Systems, 81 (1996), 31-45. doi: 10.1016/0165-0114(95)00239-1.

[17]

J. Kacprzyk and L. Sugianto, Multistage fuzzy control involving objective and subjective aspects, in L.C. Jain, R.K. Jain (Eds.), Proceedings of the Second International Conference on Knowledge Based Intelligent Electronic Systems, Adelaide, Australia, (1998), 564-573.

[18]

S. Kullback, Information Theory and Statistics, John Wiley and Sons, NY, 1959.

[19]

S. Kullback and R. A. Leibler, On Information and Sufficiency, Annals of Mathematical Statistics, 22 (1951), 79-86. doi: 10.1214/aoms/1177729694.

[20]

J. H. Lambert, J. A. Baker and K. D. Peterson, Decision aid for allocation of transport funds to guardrails, Accident Anal Prevention, 35 (2003), 47-57.

[21]

J. H. Lambert, Y. Y. Haimes, D. Li, R. M. Schoof and V. Tulsiani, Identification, ranking and management of risks in a major systems acquisition, Reliability Engineering and Systems Safety, 72 (2001), 315-325.

[22]

J. H. Lambert, N. N. Joshi, K. D. Peterson and S. M. Wadie, Coordination and diversification of investments in multimodal transportation, Public Works Management Policy, 11 (2007), 250-265.

[23]

J. H. Lambert, K. A. Peterson and N. N. Joshi, Synthesis of quantitative and qualitative evidence for risk-based analysis of highway projects, Accident Anal Prevention, 38 (2006), 925-935.

[24]

J. H. Lambert, K. D. Peterson, S. M. Wadie and M. W. Farrington, Development of a methodology to coordinate and prioritize multimodal investment networks, Virginia Transportation Research Council Publication, Charlottesville, VA, Vol. 5, 2005.

[25]

D. B. Lee, Methods for evaluation of transportation projects in the USA, Transportation Policy, 7 (2000), 41-50.

[26]

L. M. Meade and A. Presley, R and D project selection using the analytic process, IEEE Transaction in Engineering Management, 49 (2002), 59-66.

[27]

D. A. Niemeier, Z. B. Zabinsky, Z. Zeng and G. S. Rutherford, Optimization models for transportation project programming process, Journal of Transportation Engineering, 121 (1995), 14-26.

[28]

G. S. Parnell, R. E. Metzger, J. Merrick and R. Eiler, Multiobjective decision analysis of theater missile defense architectures, Systems Engineering, 4 (2001), 24-34.

[29]

M. Sanchez, N. Agell and G. Ormazabal, Multiple-criteria evaluation for value management in civil engineering, Journal of Management Engineering, 21 (2005), 131-137.

[30]

J. S. Shang, Y. Tjader and Y. Ding, A unified framework for multicriteria evaluation of transportation, IEEE Transaction in Engineering Management, 51 (2004), 300-313.

[31]

P. J. Smith, M. Shafi and H. Gao, Quick simulation: A review of importance sampling techniques in communication systems, IEEE J.Select.Areas Commun., 15 (1997), 597-613.

[32]

R. Srinivasan, Importance Sampling - Applications in Communications and Detection, Springer-Verlag, Berlin, 2002. doi: 10.1007/978-3-662-05052-1.

[33]

J. L. Tsang, J. H. Lambert and R. C. Patev, Multiple-criteria decision making in the design of innovative lock walls for barge impact: Phase 2, implementation methodologies, ERDC/ITL TR-02-5, ERDC Vicksburg Publications, Innovations for Navigation Projects Research Program, US Army Engineer Research and Development Center, Vicksburg, MS, 2002.

[34]

C. R. Weisbin, G. Rodriguez, A. Elfes and J. H. Smith, Toward a systematic approach for selection of NASA technology portfolios, 7 (2004), 285-302.

[35]

S. Y. Chen and G. T. Fu, Combining fuzzy iteration model with dynamic programming to solve multiobjective multistage decision making problems, Fuzzy Sets and Systems, 152 (2005), 499-312. doi: 10.1016/j.fss.2004.10.006.

[36]

J. Q. Wang and J. J. Li, Multi-criteria fuzzy decision-making method based on cross entropy and score functions, Expert Systems with Applications, 38 (2011), 1032-1038.

[37]

A. R. Jafarian-Moghaddam and K. Ghoseiri, Fuzzy dynamic multi-objective Data Envelopment Analysis model, Expert Systems with Applications, 38 (2011), 850-855.

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