A generalized stochastic goal programming model

Applied Mathematics and Computation

Volumn 215, Issue 12, 2010, Pages 4347-4357

  Aouni, Belaid ^a   La Torre, Davide ^b  

^a LAURENTIAN UNIVERSITY   (Canada)

^b UNIVERSITY OF MILAN   (Italy)

Author keywords

Deterministic equivalent problems; Stochastic goal programming; Stochastic Pareto optimal solutions

Indexed keywords

CENTRAL LIMIT THEOREM; COMPUTATIONAL TIME; DETERMINISTIC EQUIVALENTS; DETERMINISTIC PROBLEMS; DEVELOPED MODEL; FEASIBLE SET; GOAL PROGRAMMING MODEL; GOAL PROGRAMMING TECHNIQUE; MULTI-OBJECTIVE PROBLEM; NUMERICAL EXAMPLE; OPTIMIZATION PROGRAMS; PARETO OPTIMAL SOLUTIONS; RANDOM SET; SAMPLE SIZES; STATISTICAL MOMENTS; STOCHASTIC GOAL PROGRAMMING; STOCHASTIC PROBLEMS; STOCHASTIC SOLUTION;

OPTIMAL SYSTEMS; OPTIMIZATION; RANDOM PROCESSES; RANDOM VARIABLES; SET THEORY; STOCHASTIC SYSTEMS;

STOCHASTIC MODELS;

EID: 76849088369     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.12.065     Document Type: Article

References (32)

1. Abdelaziz F.B., Aouni B., and El Fayedh R. Multi-objective stochastic programming for portfolio selection. Eur. J. Oper. Res. 177 (2007) 1811-1823
2. Abdelaziz F.B., Lang P., and Nadeau R. Dominance and efficiency in multicriteria decision under uncertainty. Theory Decisions 47 3 (1999) 191-211
3. F.B. Abdelaziz, P. Lang, R. Nadeau, Distributional unanimity multiobjective stochastic linear programming, in: J. Climaco (Ed.), Multicriteria Analysis: Proceedings of the XIth International Conference on MCDM, Springer-Verlag, Berlin, 1997, pp. 225-236.
4. Aouni B. Linéarisation des expressions quadratiques en programmation mathématique: des bornes plus efficaces, Administrative Sciences Association of Canada. Manage. Sci. 17 (1996) 38-46
5. Aouni B., and Kettani O. Goal programming model: a glorious history and a promising future. Eur. J. Oper. Res. 133 2 (2001) 1-7
6. Aouni B., Kettani O., and Martel J.-M. Estimation through imprecise goal programming model. Advances in Multi-Objective and Goal Programming. Lecture Notes in Economics and Mathematical Systems vol. 455 (1997), Springer 120-130
7. Aouni B., Abdelaziz F.B., and Martel J.-M. Decision-maker's preferences modeling in the stochastic goal programming. Eur. J. Oper. Res. 162 (2005) 610-618
8. Aumann R.J. Integrals of set-valued functions. J. Math. Anal. Appl. 12 (1965) 112
9. Brans J.P., Vincke Ph., and Marechal B. How to select and how to rank projects: the Promethee method. Eur. J. Oper. Res. 24 (1986) 228-238
10. Caballero R., Cerda E., Munoz M.M., Rey L., and Stancu-Minasian I.M. Efficient solution concepts and their relations in stochastic multiobjective programming. J. Opt. Theor. Appl. 110 1 (2001) 53-74
11. Caballero R., Cerda E., Munoz M.M., and Rey L. Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems. Eur. J. Oper. Res. 158 (2004) 633-648
12. Charnes A., and Cooper W.W. Chance constraints and normal deviates. J. Am. Stat. Assoc. 57 (1952) 134-148
13. Charnes A., and Cooper W.W. Chance-constrained programming. Manage. Sci. 6 (1959) 73-80
14. Charnes A., and Cooper W.W. Management Models and Industrial Applications of Linear Programming (1961), Wiley
15. Charnes A., and Cooper W.W. Deterministic equivalents for optimising and satisfying under chance constraints. Oper. Res. 11 (1968) 11-39
16. Charnes A., Cooper W.W., and Ferguson R. Optimal estimation of executive compensation by linear programming. Manage. Sci. 1 (1955) 138-351
17. Contini B. A stochastic approach to goal programming. Oper. Res. 16 3 (1968) 576-586
18. Fernandeza I.C., and Molchanovb I. A stochastic order for random vectors and random sets based on the Aumann expectation. Stat. Prob. Lett. 63 (2003) 295-305
19. Goicoechea A., Hansen D.R., and Duckstein L. Multiobjective Decision Analysis with Engineering and Business Applications (1982), Wiley, New York
20. Kharrat A., Chabchoub H., Aouni B., and Smaoui S. Serial correlation estimation through the imprecise goal programming model. Eur. J. Oper. Res. 177 (2007) 1839-1851
21. Lee S.M. Goal programming for decision analysis of multiple objectives. Sloan Manage. Rev. 14 (1973) 11-24
22. Lee S.M., and Clayton S.R. A goal programming model for academic resource allocation. Manage. Sci. 18 8 (1972) B395-B408
23. Lee S.M., and Olson D.L. Gradiend algorithm for chance-constrained nonlinear goal programming. Eur. J. Oper. Res. 22 3 (1985) 359-369
24. Lindo/PC Release 6.0, Lindo Systems, Inc. Chicago, IL 60622, US, 1996.
25. Lingo/PC Release 3.0, Lindo Systems, Inc. Chicago, IL 60622, US, 1996.
26. Martel J.-M., and Aouni B. Diverse imprecise goal programming model formulations. J. Global Opt. 12 (1998) 127-138
27. Romero C. Handbook of Critical Issues in Goal Programming (1991), Pergamon Press
28. Sawaragi Y., Nakayama H., and Tanino T. Theory of Multiobjective Optimization (1985), Academic Press, New York
29. Stancu-Minasian I.M. Stochastic Programming with Multiple Objective Functions (1984), D. Reidel Publishing Company, Dordrecht
30. I.M. Stancu-Minasian, S. Tigan, 1984. The vectorial minimum risk problem, in: Proceedings of the Colloquium on Approximation and Optimization, Cluj-Napoca, pp. 321-328.
31. Vitale R.V. An alternate formulation of mean value for random geometric figures. J. Microsc. 151 3 (1988) 197204
32. White D.J. Optimality and Efficiency (1982), Wiley, Chichester