Multi-Objective Geometric Programming in Multiple-Response Stratified Sample Surveys with Quadratic Cost Function

Shafiullah

Multi-Objective Geometric Programming in Multiple-Response Stratified Sample Surveys with Quadratic Cost Function

Shafiullah * §

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§ Aligarh Muslim University, Aligarh

Multi-Objective Geometric Programming in Multiple-Response Stratified Sample Surveys with Quadratic Cost Function

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Abstract

In this paper, the problem of multiple-response in stratified sample surveys has been formulated as a multi-objective geometric programming problem (MOGPP). The fuzzy programming is described for solving the formulated MOGPP. The formulated MOGPP has been solved by Lingo software and the dual solution is obtained. Subsequently with the help of dual solution of formulated MOGPP and the primal-dual relationship theorem the optimum allocations of multiple-response are obtained. A numerical example is given to illustrate the procedure.

References

50 Cites in Article

Reference Format

1. J Ahmed,D Bonham Charles (1987). Application of Geometric Programming to Optimum Allocation Problems in Multivariate Double Sampling. Appl. Maths. and Comm, 21(2), 157-169.
2. M Ahsan,S Khan (1977). Optimum allocation in multivariate stratified random sampling using prior information. Journal of Indian Statistical Association, 15, 57-67.
3. Athar Ansari,Rahul Varshney,Najmussehar,Mohammad Ahsan (2011). An optimum multivariate-multiobjective stratified sampling design. METRON, 69(3), 227-250.
4. H Aoyama (1963). Stratified random sampling with optimum allocation for multivariate populations. Annals of the Institute of Statistical Mathematics, 14, 251-258.
5. Jillian Beardwood,J Halton,J Hammersley (1959). The shortest path through many points. Mathematical Proceedings of the Cambridge Philosophical Society, 55(4), 299-327.
6. J Bethel (1985). American Statistical Association Section on Survey Research Methods (ASA-SRMS). Proceedings of the Survey Research Methods section, 209-212.
7. J Bethel (1989). Sample allocation in multivariate surveys. Survey Methodology, 15, 47-57.
8. Miles Davis,Rudolph Schwartz (1987). Geometric programming for optimal allocation of integrated samples in quality control. Communications in Statistics - Theory and Methods, 16(11), 3235-3254.
9. J Díaz-García,L Cortez (2006). Optimum allocation in multivariate stratified sampling: multi-objective programming. Optimum allocation in multivariate stratified sampling: multi-objective programming
10. José Díaz-García,Rogelio Ramos-Quiroga (2008). Optimum Allocation in Multivariate Stratified Random Sampling: A Modified Prékopa’s Approach. Journal of Mathematical Modelling and Algorithms in Operations Research, 13(3), 315-330.
11. José Díaz-García,Rogelio Ramos-Quiroga (2008). Optimum Allocation in Multivariate Stratified Random Sampling: A Modified Prékopa’s Approach. Journal of Mathematical Modelling and Algorithms in Operations Research, 13(3), 315-330.
12. R Duffin,E Peterson,C Zener (1967). Geometric programming: Theory & applications. Geometric programming: Theory & applications
13. S Ghufran,S Khowaja,Najmussehar,M Ahsan (2011). A multiple response stratified sampling design with travel cost. The South Pacific Journal of Natural and Applied Sciences, 29, 31-39.
14. Neha Gupta,Irfan Ali,Abdul Bari (2013). An Optimal Chance Constraint Multivariate Stratified Sampling Design Using Auxiliary Information. Journal of Mathematical Modelling and Algorithms in Operations Research, 13(3), 341-352.
15. N Gupta,Shafiullah,S Iftekhar,A Bari (2012). Fuzzy Goal Programming Approach to solve Non-Linear Bi-Level Programming Problem in stratified double sampling design in presence of non-response. International Journal of Scientific & Engineering research, 3(10), 1-9.
16. S Iftekhar,S Haseen,Q Ali,A Bari (2013). A Compromise Solution in Multivariate Surveys with stochastic random cost function. International Journal of Engineering Science and Technology, 4(6), 2400-2406.
17. S Islam (2010). Multi-Objective Geometric Programming Problem and its Applications. Yugoslav Journal of Operations Research, 20(2), 213-227.
18. N Jahan,M Ahsan (1995). Optimum allocation using separable programming. Dhaka University Journal of Science, 43, 157-164.
19. N Jahan,M Khan,M Ahsan (1994). A generalized compromise allocation. Journal of the Indian Statistical Association, 32, 95-101.
20. N Jahan,M Khan,M Ahsan (2001). Optimum compromise allocation using dynamic programming. Dhaka University Journal of Science, 49, 197-202.
21. Z Kanaya (2010). An Interactive Method for Fuzzy Multi objective Nonlinear Programming Problems. JKAU Sci, 22(1), 103-112.
22. Mohammed Khan,Irfan Ali,Yashpal Raghav,Abdul Bari (2012). Allocation in Multivariate Stratified Surveys with Non-Linear Random Cost Function. American Journal of Operations Research, 02(01), 100-105.
23. M Khan,E Khan,M Ahsan (2003). An optimal multivariate stratified sampling design using dynamic programming. Australian & New Zealand J. Statist, 45, 107-113.
24. M Khan,E Khan,M Ahsan (2008). Optimum allocation in multivariate stratified sampling in presence of non-response. Journal of Indian Society of Agricultural Statistics, 62, 42-48.
25. M Khan,E Khan,M Ahsan (2010). Theory & Methods: An Optimal Multivariate Stratified Sampling Design Using Dynamic Programming. Australian & New Zealand Journal of Statistics, 45(1), 107-113.
26. M Khan,E Khan,M Ahsan (2010). Theory & Methods: An Optimal Multivariate Stratified Sampling Design Using Dynamic Programming. Australian & New Zealand Journal of Statistics, 45(1), 107-113.
27. B Kheirfam (2010). Sensitivity analysis for fuzzy linear Programming problems with Fuzzy variables. Advanced Model and Optimization, 12(2)
28. A Kokan,Sanaullah Khan (1967). Optimum Allocation in Multivariate Surveys : An Analytical Solution. Journal of the Royal Statistical Society Series B: Statistical Methodology, 29(1), 115-125.
29. M Kozak (2006). On sample allocation in multivariate surveys. Communication in Statistics-Simulation and Computation, 35, 901-910.
30. Clive Phillips (1415). Cattle: An Informal Social History L W Carlson (2001). Published by Ivan R Dee, 1332 North Halsted Street, Chicago, Illinois 60622-2694, USA. 321pp. Paperback (ISBN 1 56663 388 5). Price $16.95. Animal Welfare, 12(1), 136-139.
31. H Maleki (2002). Ranking functions and their applications to fuzzy linear programming. Appl. Math, 4, 283-301.
32. S Maqbool,A Mir,S Mir (2011). Geometric Programming Approach to Optimum Allocation in Multivariate Two-Stage Sampling Design. Electronic Journal of Applied Statistical Analysis, 4(1), 71-82.
33. S Mesbah,R Kerachian,A Torabian (2010). Trading Pollutant Discharge Permits in Rivers Using Fuzzy Nonlinear Cost Functions. Desalination, 250(1), 313-317.
34. S Nasseri (2008). FUZZY NONLINEAR OPTIMIZATION. Journal of Nonlinear Sciences and Applications, 01(04), 230-235.
35. Mohammad Nikoo,Reza Kerachian,Akbar Karimi,Ali Azadnia (2013). Optimal water and waste-load allocations in rivers using a fuzzy transformation technique: a case study. Environmental Monitoring and Assessment, 185(3), 2483-2502.
36. A Ojha,K Biswal (2010). Multi-objective geometric programming problem with ∊ -constraint method. Applied Mathematical Modelling, 38(2), 747-758.
37. Surapati Pramanik,Durga Banerjee (2012). Multi-Objective Chance Constrained Capacitated Transportation Problem based on Fuzzy Goal Programming. International Journal of Computer Applications, 44(20), 42-46.
38. Y Raghav,Irfan Ali,A Bari (2014). Allocation in Multivariate Stratified Sampling in Presence of Non-Response: A New Approach. Journal of Nonlinear Analysis and Optimization Theory & Applications
39. S Rehana,P Mujumdar (2009). An imprecise fuzzy risk approach for water quality management of a river system. Journal of Environmental Management, 90(11), 3653-3664.
40. M Sakawa,H Yano (1994). Fuzzy dual decomposition method for large-scale multi-objective non-linear programming problem. Fuzzy Sets and Systems, 67, 19-27.
41. Masatoshi Sakawa,Hitoshi Yano (1989). An interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy parameters. Fuzzy Sets and Systems, 30(3), 221-238.
42. Ali Shafiullah,I Bari,A (2013). Geometric Programming Approach in Three -Stage Sampling Design. International Journal of Scientific & Engineering Research, 4(6), 2229-5518.
43. Shafiullah,M Khan,I Ali (2014). Fuzzy geometric programming in multivariate stratified sample surveys in presence of non-response with quadratic cost function. American Journal of Operations Research, 4
44. R Shankar,N Ananda Rao,G Madhu Latha,J Sireesha,V (2010). Solving a Fuzzy Nonlinear Optimization Problem by Genetic Algorithm. Int. J. Contemp. Math. Sciences, 5(16), 791-803.
45. J Tang,D Wang (1997). A non-symmetric model for fuzzy nonlinear programming problems with penalty coefficients. Computers and Operations Research, 248, 717-725.
46. Jiafu Tang,Dingwei Wang,Richard Fung (1998). Model and method based on GA for nonlinear programming problems with fuzzy objective and resources. International Journal of Systems Science, 29(8), 907-913.
47. Jui-Fen C. Trappey,C Richard Liu,Tien-Chien Chang (1988). Fuzzy non-linear programming: Theory and application in manufacturing. International Journal of Production Research, 26(5), 975-985.
48. Rahul Varshney,Najmussehar,M Ahsan (2011). An optimum multivariate stratified double sampling design in presence of non-response. Optimization Letters, 6(5), 993-1008.
49. L Zadeh (1965). Fuzzy sets. Information and Control, 8(3), 338-353.
50. H Zimmermann (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1, 45-55.

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

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How to Cite This Article

Shafiullah. 2015. "Multi-Objective Geometric Programming in Multiple-Response Stratified Sample Surveys with Quadratic Cost Function". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 14 (GJSFR Volume 14 Issue F7).

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GJSFR Volume 14 Issue F7

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

fuzzy programming geometric programming multi-objective multiple-response primal-dual relationship

Classification

GJSFR-F Classification MSC 2010: 11D09

19L64

Submission ReceivedOctober 26, 2014
Peer Review Double Blind
Handling Editor
Accepted November 21, 2014
Published December 4, 2014

Version of record

v1.2

Issue date

January 8, 2015

Language

English

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Article Matrices

Total Score: 101

Country: India

Subject: Global Journal of Science Frontier Research - F: Mathematics & Decision

Authors: Shafiullah (PhD/Dr. count: 0)

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