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

Year 2019, , 1824 - 1837, 08.12.2019

Susanta Banik Debasish Bhattacharya

https://doi.org/10.15672/HJMS.2019.659

Cited By: 2

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.

Keywords

De Novo Programming, Fuzzy Numbers, Min-max Goal Programming, Multi-Objective Programming, Degree of Possibility

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.