Dependent chance goal programming model for multi-objective interval solid transportation problem in stochastic environment

Dependent chance goal programming model for multi-objective interval solid transportation problem in stochastic environment

  IJCOT-book-cover
 		 International Journal of Computer & Organization Trends  (IJCOT)          
 
© 2016 by IJCOT Journal
Volume - 6 Issue - 6
Year of Publication : 2016
Authors :   A.Nagarajan, M. Meenakshi, R.Satheeshkumar
DOI : 10.14445/22492593/IJCOT-V38P303

Citation

A.Nagarajan, M. Meenakshi, R.Satheeshkumar "Dependent chance goal programming model for multi-objective interval solid transportation problem in stochastic environment", International Journal of Computer & organization Trends (IJCOT), V6(6):40-49 Nov - Dec 2016, ISSN:2249-2593, www.ijcotjournal.org. Published by Seventh Sense Research Group.

Abstract In this paper Dependent Chance Goal Programming Model (DCGPM) is mainly focused on the classical Multi-Objective Solid Transportation Problem (MOSTP), where the multiple interval objective functions are minimized and the order relations that represent the decision makers’ preference between interval profits have been defined by the right limit, left limit, centre and half width of an interval. Finally, the equivalent transformed problem has been modeled in this paper, so that it could be solved by using a evolutionary technique.

References

[1] A.K.Bit, M.P.Biswal, S.S.Alam, Fuzzy programming approach to multi-objective solid transportation problem, Fuzzy Sets Systems. 57(1993) 183-194.
[2] R.E.Stuer, Algorithm for linear programming problems with interval objective function coefficient, Mathematics of Operations Research 6 (1981) 333-348.
[3] B.Liu, Theory and Practice of Uncertain Programming, Physica- Verlag, New York, 2002.
[4] B.Liu ,Depenedent chance programming with fuzzydecisions,IEEE Transactions on Fuzzy Systems, 7(3) (1999)354-360.
[5] U.Deshpande, A.Gupta, A.Basu, Task assignment with impreciseinformation for real time operation in a supply chain, Appl. Soft Computing 5 (2004) 101-117.
[6] H.Ishibuchi, H.Tanaka, multiobjective programming in optimization of the interval objective function, European Journal of Operations Research 48 (1990) 219-225.
[7] M.Papadrakakis, N.D.Lagaros, Soft computing methodologies for structural optimization, Appl. Soft Computing 3 (2003) 283-300.
[8] Lixing Yang and Linzhong Liu, Fuzzy fixed charge solid transportation problem and algorithm , Applied soft computing , 7(2007) 879-889.
[9] Lixing Yang, Yuan Feng, A bicriteria solid transportation problem with fixed charge under stochastic environment, Applied Mathematical Modeling 31 (2007) 2668-2683.
[10] S.R.Arora and Archana KHURANA, “Three dimensional fixed charge bi- criterion indefinite quadratic transportation problem”, Yugoslav Journal of Operations Research , 14(2004), Number 1, 83-97.
[11] G.Alefeld, J.Herzberger, Introduction to Interval computations, Academic Press, New York, 1983.
[12] R.E.Moore, Method and Applications of Interval Analysis, SLAM, Philadephia, PA, 1979.
[13] B.Liu, Theory and Practice of Uncertain Programming, Physica-Verlag, New York, 2002.
[14] B.Liu, K.Iwamura, Chance constrained programming with fuzzy parameters, Fuzzy Sets Syst. 94 (2) (1998) 227-237.
[15] A.Charnes, W.W.Cooper, Chance-constrained programming, Management Science 6 (1) (1959) 73-80.
[16] A.Charnes, W.W.Cooper, Chance-constrained and normal deviates. Journal of American Statistics Association 57, 134-118.
[17] A.Charnes, W.W.Cooper, Deterministics equivalents for optimizing and satisfying under chance constraints, Operations Research 11, 18-39.
[18] Stancu-Minasian, .M., 1984, Stochastic Programming with Multiple Objective Functions. D.Reidal Publishing Company, Dordrecht.
[19] Stancu-Minasian, .M., Giurgiutiu, V., 1985. Stochastic Programming with Multiple Objective Functions (Mathematics and its Applications), Kluwer Academic Publishers.
[20] Contini, B., 1968 . A stochastic approach to goal programming. Operations Research 16 (3), 576-586.
[21] A.Charnes, W.W.Cooper and R.Ferguson, 1955. Optimal estimation of executive compensation by linear programming. Management Sciences 1, 138-151.
[22] A.Charnes, W.W.Cooper, Management models and industrial applications of linear programming, 1961, volumes 1-2. Wiley New York.
[23] Lee, S.M., 1973, Goal programming for decision analysis of multiple objectives. Sloan Management Review 14, 11-24.
[24] Lee, S.M., Clayton, E.R., 1972. A goal programming model for academic resource allocation. Managemant Science 18 (8), B395-B408.
[25] B.Liu, “Dependent chance programming: A class of stochastic optimization”, Comput. Math. Applicat., vol.34, no.12, pp. 89-104, 1997.
[26] B.Liu and C.Ku, “Dependent chance goal programming and an application”, J.Syst.Eng. Electron., vol.4, no. 2, pp. 40-47, 1993.
[27] B.Liu , “Dependent chance goal programming and its genetic algorithm based approach”, Math.Comput. Modeling, vol.24, no. 7, pp. 43-52, 1996.
[28] B.Liu and K.Iwamura, “Modeling stochastic decision systems using dependent chance programming ”, European Journal Operations Research, vol. 101, no. 1, pp. 193-203, 199.
[29] S.K.Das, A.Goswami and S.S.Alam, Multi-objective transportation problem with intervsl cost, source and destination parameters, European Journal of Operations Research 117(1999)100-112.
[30] A.Nagarajan and K.Jeyaraman, Mathematical modeling of solid fixed cost bi-criterion indefinite quadratic transportation problem under stochastic environment, Emerging journal of engineering science and technology, Volume-02, Issue No-03, March 2009 – May 2009, pp.106 – 127.
[31] A.Nagarajan and K.Jeyaraman, Solution of expected value model for multi-objective interval solid transportation problem under stochastic environment using fuzzy programming approach, Emerging journal of engineering science and technology, Volume-04, Issue No-07, September 2009 – November 2009, pp. 53 – 70.
[32] A.Nagarajan and K.Jeyaraman, Chance constrained goal programming models for multi-objective interval solid transportation problem under stochastic environment, International journal of applied mathematics analysis and applications, Volume-05, Issue No-02, July-December 2010, pp. 229 – 255.
[33] A.Nagarajan and K.Jeyaraman, Solution of chance constrained programming problem for multi-objective interval solid transportation problem under stochastic environment using fuzzy approach, International journal computer applications, Volume-10- No .9, November 2010, pp. 19 – 29.
[34 ] A.Nagarajan and K.Jeyaraman, Theory and Methodology chance constrained programming model for multi-objective interval Solid transportation problem under stochastic environment using fuzzy approach, Proceedngs of International conference on emerging trends in mathematics And computer applications, December 16-18, 2010. Tamilnadu, India.

Keywords
Multi-objective solid transportation problem; Multi-objective interval solid transportation problem; Solid transportation problem; Stochastic programming; Goal programming; Dependent chance goal programming.