Research Article
PDF Zotero Mendeley EndNote BibTex Cite

Year 2019, Volume 48, Issue 6, 1824 - 1837, 08.12.2019
https://doi.org/10.15672/HJMS.2019.659

Abstract

References

  • [1] Z. Babic and I. Pavic Multicriterial production planning by de novo programming approach, Int. J. Prod. Econ. 43 (1), 59–66, 1996.
  • [2] C. Carlsson and P. Korhonen, A parametric approach to fuzzy linear programming, Fuzzy sets and systems, 20 (1), 17–30, 1986.
  • [3] S. Chackraborty and D. Bhattacharya, A new approach for solution of multi-stage and multi-objective decision-making problem using de novo programming, Eur. J. Sci. Res. 79 (3), 393–417, 2012.
  • [4] S. Chackraborty and D. Bhattacharya, Optimal system design under multi-objective decision making using de-novo concept: A new approach, Int. J. Comput. Appl. 63 (12), 20–27, 2013.
  • [5] A. Charnes and W.W. Cooper Management models and industrial applications of linear programming, Management Science, 4 (1), 38–91, 1957.
  • [6] J.K.C. Chen and G.-H. Tzeng, Perspective strategic alliances and resource allocation in supply chain systems through the de novo programming approach, Int. J. Sustain. Strat. Manag. 1 (3), 320–339, 2009.
  • [7] Y.-W. Chen and H.-E. Hsieh Fuzzy multi-stage de-novo programming problem, Appl. Math. Comput. 181 (2), 1139–1147, 2006.
  • [8] R.B. Flavell, A new goal programming formulation, Omega, 4 (6), 731–733, 1976.
  • [9] J.J. Huang, G.-H. Tzeng and C.-S. Ong, Choosing best alliance partners and allocating optimal alliance resources using the fuzzy multi-objective dummy programming model, J. Oper. Res. Soc. 57 (10), 1216–1223, 2006.
  • [10] J.P. Ignizio, Linear programming in single and multiple objective systems, Prentice- Hall. Inc., Englewood Cliffs, New Jersey, 1982.
  • [11] Y. Ijiri. Management goals and accounting for control, North Holland Publication, 3, 1965.
  • [12] D.F. Jones and M. Tamiz, Goal programming in the period 1990 - 2000. In Multiple Criteria Optimization: State of the art annotated bibliographic surveys, 129–170, 2003.
  • [13] S.M. Lee, Goal programming for decision analysis, Auerbach Publishers, Philadelphia, 1972.
  • [14] R.J. Li and E.S. Lee, Fuzzy approaches to multicriteria de novo programs, J. Math. Anal. Appl. 153 (1), 97–111, 1990.
  • [15] R.J. Li and E.S. Lee, Multi-criteria de novo programming with fuzzy parameters, Comput. Math. Appl. 19 (5), 13–20, 1990.
  • [16] M.K. Luhandjula, Compensatory operators in fuzzy linear programming with multiple objectives, Fuzzy sets and systems, 8 (3), 245–252, 1982.
  • [17] D.Y. Miao, W.W. Huang, Y.P. Li and Z.F. Yang, Planning water resources systems under uncertainty using an interval-fuzzy de novo programming method, J. Environ. Inform. 24 (1), 11–23, 2014.
  • [18] C. Romero, Handbook of critical issues in goal programming, Elsevier, 2014.
  • [19] S. Saeedi, M. Mohammadi and S. Torabi A de novo programming approach for a robust closed-loop supply chain network design under uncertainty: An m/m/1 queueing model, Int. J. Ind. Eng. Comput. 6 (2), 211–228, 2015
  • [20] Y. Shi Studies on optimum-path ratios in multicriteria de novo programming problems, Comput. Math. Appl. 29 (5), 43–50, 1995.
  • [21] Y. Shi Optimal system design with multiple decision makers and possible debt: a multicriteria de novo programming approach, Oper. Res. 44 (5), 723–729, 1999.
  • [22] N. Umarusman, Min-max goal programming approach for solving multi-objective de novo programming problems, Int. J. Oper. Res. 10, 92–99, 2013.
  • [23] J.L. Verdegay, A dual approach to solve the fuzzy linear programming problem, Fuzzy sets and systems, 14 (2), 131–141, 1984.
  • [24] L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 100, 9–34, 1999.
  • [25] M. Zeleny, Multi-objective design of high-productivity systems, Joint Automatic Control Conference-Paper APPL9-4, ASME, Newyork, 13, 297–300, 1976.
  • [26] M. Zeleny (Ed), Mathematical programming with multiple objectives(special issue), Comput. Oper. Res. 7, 101–107, 1980.
  • [27] M. Zeleny, A case study in multi-objective design: De novo programming, Multiple Criteria Analysis: Operational Methods, (Edited by P. Nijkamp and J. Spronk), Gower publishing Co., Hampshire, 37–52, 1981.
  • [28] M. Zeleny, On the squandering of resources and profits via linear programming, Interfaces, 11 (5), 101–107, 1981.
  • [29] M. Zeleny, Optimal system design with multiple criteria: De novo programming approach, Eng. Cost. Prod. Econ. 10 (2), 89–94, 1986.
  • [30] M. Zeleny, Optimizing given systems vs. designing optimal systems: The de novo programming approach, Int. J. Gen. Syst. 17 (4), 295–307, 1990.
  • [31] Y.M. Zhang, G.H. Huang and X.D. Zhang. Inexact de novo programming for water resources systems planning, European J. Oper. Res. 199 (2), 531–541, 2009.
  • [32] H.J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems, 1 (1), 45–55, 1978.

One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters

Year 2019, Volume 48, Issue 6, 1824 - 1837, 08.12.2019
https://doi.org/10.15672/HJMS.2019.659

Abstract

Multi-objective De Novo Programming is a user-friendly device for optimal system design. There exist no method for solving general multi-objective De Novo Programs. Only some special cases have been discussed. This paper proposes a one-step method for solving a general De Novo Programming Problem using a Min-max Goal Programming technique where the parameters involved are all fuzzy numbers. The solution obtained is an efficient solution of the problem considered. The present approach is much more realistic than the standard De Novo Programming with crisp parameters. Two numerical examples are given to illustrate the solution procedure.

References

  • [1] Z. Babic and I. Pavic Multicriterial production planning by de novo programming approach, Int. J. Prod. Econ. 43 (1), 59–66, 1996.
  • [2] C. Carlsson and P. Korhonen, A parametric approach to fuzzy linear programming, Fuzzy sets and systems, 20 (1), 17–30, 1986.
  • [3] S. Chackraborty and D. Bhattacharya, A new approach for solution of multi-stage and multi-objective decision-making problem using de novo programming, Eur. J. Sci. Res. 79 (3), 393–417, 2012.
  • [4] S. Chackraborty and D. Bhattacharya, Optimal system design under multi-objective decision making using de-novo concept: A new approach, Int. J. Comput. Appl. 63 (12), 20–27, 2013.
  • [5] A. Charnes and W.W. Cooper Management models and industrial applications of linear programming, Management Science, 4 (1), 38–91, 1957.
  • [6] J.K.C. Chen and G.-H. Tzeng, Perspective strategic alliances and resource allocation in supply chain systems through the de novo programming approach, Int. J. Sustain. Strat. Manag. 1 (3), 320–339, 2009.
  • [7] Y.-W. Chen and H.-E. Hsieh Fuzzy multi-stage de-novo programming problem, Appl. Math. Comput. 181 (2), 1139–1147, 2006.
  • [8] R.B. Flavell, A new goal programming formulation, Omega, 4 (6), 731–733, 1976.
  • [9] J.J. Huang, G.-H. Tzeng and C.-S. Ong, Choosing best alliance partners and allocating optimal alliance resources using the fuzzy multi-objective dummy programming model, J. Oper. Res. Soc. 57 (10), 1216–1223, 2006.
  • [10] J.P. Ignizio, Linear programming in single and multiple objective systems, Prentice- Hall. Inc., Englewood Cliffs, New Jersey, 1982.
  • [11] Y. Ijiri. Management goals and accounting for control, North Holland Publication, 3, 1965.
  • [12] D.F. Jones and M. Tamiz, Goal programming in the period 1990 - 2000. In Multiple Criteria Optimization: State of the art annotated bibliographic surveys, 129–170, 2003.
  • [13] S.M. Lee, Goal programming for decision analysis, Auerbach Publishers, Philadelphia, 1972.
  • [14] R.J. Li and E.S. Lee, Fuzzy approaches to multicriteria de novo programs, J. Math. Anal. Appl. 153 (1), 97–111, 1990.
  • [15] R.J. Li and E.S. Lee, Multi-criteria de novo programming with fuzzy parameters, Comput. Math. Appl. 19 (5), 13–20, 1990.
  • [16] M.K. Luhandjula, Compensatory operators in fuzzy linear programming with multiple objectives, Fuzzy sets and systems, 8 (3), 245–252, 1982.
  • [17] D.Y. Miao, W.W. Huang, Y.P. Li and Z.F. Yang, Planning water resources systems under uncertainty using an interval-fuzzy de novo programming method, J. Environ. Inform. 24 (1), 11–23, 2014.
  • [18] C. Romero, Handbook of critical issues in goal programming, Elsevier, 2014.
  • [19] S. Saeedi, M. Mohammadi and S. Torabi A de novo programming approach for a robust closed-loop supply chain network design under uncertainty: An m/m/1 queueing model, Int. J. Ind. Eng. Comput. 6 (2), 211–228, 2015
  • [20] Y. Shi Studies on optimum-path ratios in multicriteria de novo programming problems, Comput. Math. Appl. 29 (5), 43–50, 1995.
  • [21] Y. Shi Optimal system design with multiple decision makers and possible debt: a multicriteria de novo programming approach, Oper. Res. 44 (5), 723–729, 1999.
  • [22] N. Umarusman, Min-max goal programming approach for solving multi-objective de novo programming problems, Int. J. Oper. Res. 10, 92–99, 2013.
  • [23] J.L. Verdegay, A dual approach to solve the fuzzy linear programming problem, Fuzzy sets and systems, 14 (2), 131–141, 1984.
  • [24] L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 100, 9–34, 1999.
  • [25] M. Zeleny, Multi-objective design of high-productivity systems, Joint Automatic Control Conference-Paper APPL9-4, ASME, Newyork, 13, 297–300, 1976.
  • [26] M. Zeleny (Ed), Mathematical programming with multiple objectives(special issue), Comput. Oper. Res. 7, 101–107, 1980.
  • [27] M. Zeleny, A case study in multi-objective design: De novo programming, Multiple Criteria Analysis: Operational Methods, (Edited by P. Nijkamp and J. Spronk), Gower publishing Co., Hampshire, 37–52, 1981.
  • [28] M. Zeleny, On the squandering of resources and profits via linear programming, Interfaces, 11 (5), 101–107, 1981.
  • [29] M. Zeleny, Optimal system design with multiple criteria: De novo programming approach, Eng. Cost. Prod. Econ. 10 (2), 89–94, 1986.
  • [30] M. Zeleny, Optimizing given systems vs. designing optimal systems: The de novo programming approach, Int. J. Gen. Syst. 17 (4), 295–307, 1990.
  • [31] Y.M. Zhang, G.H. Huang and X.D. Zhang. Inexact de novo programming for water resources systems planning, European J. Oper. Res. 199 (2), 531–541, 2009.
  • [32] H.J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems, 1 (1), 45–55, 1978.

Details

Primary Language English
Subjects Mathematics
Journal Section Mathematics
Authors

Susanta BANİK This is me
National Institute of Technology
0000-0002-2914-3238
India


Debasish BHATTACHARYA This is me (Primary Author)
National Institute of Technology
0000-0002-9264-9813
India

Publication Date December 8, 2019
Published in Issue Year 2019, Volume 48, Issue 6

Cite

Bibtex @research article { hujms515726, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, pages = {1824 - 1837}, doi = {10.15672/HJMS.2019.659}, title = {One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters}, key = {cite}, author = {Banik, Susanta and Bhattacharya, Debasish} }
APA Banik, S. & Bhattacharya, D. (2019). One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters . Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1824-1837 . DOI: 10.15672/HJMS.2019.659
MLA Banik, S. , Bhattacharya, D. "One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1824-1837 <https://dergipark.org.tr/en/pub/hujms/article/515726>
Chicago Banik, S. , Bhattacharya, D. "One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1824-1837
RIS TY - JOUR T1 - One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters AU - Susanta Banik , Debasish Bhattacharya Y1 - 2019 PY - 2019 N1 - doi: 10.15672/HJMS.2019.659 DO - 10.15672/HJMS.2019.659 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1824 EP - 1837 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2019.659 UR - https://doi.org/10.15672/HJMS.2019.659 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters %A Susanta Banik , Debasish Bhattacharya %T One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/HJMS.2019.659 %U 10.15672/HJMS.2019.659
ISNAD Banik, Susanta , Bhattacharya, Debasish . "One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1824-1837 . https://doi.org/10.15672/HJMS.2019.659
AMA Banik S. , Bhattacharya D. One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1824-1837.
Vancouver Banik S. , Bhattacharya D. One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1824-1837.
IEEE S. Banik and D. Bhattacharya , "One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters", Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, pp. 1824-1837, Dec. 2019, doi:10.15672/HJMS.2019.659