Computation of some stochastic linear programming problems with Cauchy and extreme value distributions

References

• Dantzig , G. B. 1955 . Linear programming under uncertainty . Management Science , 1 : 3 – 4 .
   Web of Science ®Google Scholar
• Charnes , A. and Cooper , W. W. 1959 . Chance constrained programming . Management Science , 6 : 227 – 43 .
   Web of Science ®Google Scholar
• Charnes , A. and Cooper , W. W. 1963 . Deterministic equivalents for optimizing under chance constraints . Operations Research , 11 : 18 – 39 .
   Web of Science ®Google Scholar
• Goicoechea , A. , Hansen , D. R. and Duckstein , L. 1982 . Multi-objective Decision Analysis with Engineering and Business Applications , New York : John Wiley .
   Google Scholar
• Infanger , G. 1994 . Planning Under Uncertainty: Solving Large-Scale Stochastic Linear Programs , San Francisco, CA : Boyd & Fraser .
   Google Scholar
• Biswal , M. P. , Biswal , N. P. and Li , D. 1998 . Probabilistic linear programming problems with exponential random variables: a technical note . European Journal of Operational Research , 111 : 589 – 97 .
   Web of Science ®Google Scholar
• Stancu-Minasian , I. M. 1984 . Stochastic Programming with Multiple Objective Functions , Dordrecht : Reidel .
   Google Scholar
• Leclercq , J. P. 1982 . Stochastic programming: an interactive multicriteria approach . European Journal of Operational Research , 10 : 33 – 41 .
   Web of Science ®Google Scholar
• Pre’kopa , A. 1995 . Stochastic Programming , Dordrecht : Kluwer Academic .
   Google Scholar
• Kall , P. and Wallace , S. W. 1994 . Stochastic Programming , New York : John Wiley .
   Google Scholar
• Kibzun , A. I. and Kan , I. S. 1996 . Stochastic Programming Problems with Probability and Quantile Function , New York : John Wiley .
   Google Scholar
• Mohan , C. and Nguyen , H. T. 1997 . A fuzzifying approach to stochastic programming . OPSEARCH , 34 : 73 – 96 .
   Google Scholar
• Sakawa , M. , Kato , K. and Nishizaki , I. 2003 . An interactive fuzzy satisficing method for multi-objective stochastic linear programming problems through an expectation model . European Journal of Operational Research , 145 : 665 – 72 .
   Web of Science ®Google Scholar
• Ignizio , J. P. 1982 . Linear Programming in Single and Multiple Objective Systems , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Ignizio , J. P. and Cavalier , T. M. 1994 . Linear Programming , Englewood Cliffs, NJ : Prentice Hall .
   Google Scholar
• Aouni , B. and Kettani , O. 2001 . Goal programming model: a glorious history and a promising future . European Journal of Operational Research , 133 : 225 – 31 .
   Web of Science ®Google Scholar
• Romero , C. 2004 . A general structure of achievement function for a goal programming model . European Journal of Operational Research , 153 : 675 – 86 .
   Web of Science ®Google Scholar
• Ballestero , E. 2001 . Stochastic goal programming: a mean-variance approach . European Journal of Operational Research , 131 : 476 – 81 .
   Web of Science ®Google Scholar
• Aouni , B. , Abdelaziz , F. B. and Martel , J. M. 2004 . Decision-makers’ preferences modeling in the stochastic goal programming . European Journal of Operational Research , in press.
   Google Scholar
• Bellman , R. E. and Zadeh , L. A. 1970 . Decision making in a fuzzy environment . Management Science , 17 : 141 – 64 .
   Web of Science ®Google Scholar
• Zimmermann , H. J. 1978 . Fuzzy programming and linear programming with several objective functions . Fuzzy Sets and Systems , 1 : 45 – 55 .
   Google Scholar
• Sakawa , M. 1993 . Fuzzy Sets and Interactive Multi-objective Optimization , New York : Plenum Press .
   Google Scholar
• Mohamed , R. H. 1997 . The relationship between goal programming and fuzzy programming . Fuzzy Sets and Systems , 89 : 215 – 22 .
   Web of Science ®Google Scholar
• Chankong , V. and Haimes , Y. Y. 1983 . Multiobjective Decision Making Theory and Methodology , Amsterdam : North-Holland .
   Google Scholar
• Stewart , T. J. 1992 . A critical survey on the status of the multiple criteria decision making theoy and practice . OMEGA International Journal of Management Science , 20 : 569 – 86 .
   Web of Science ®Google Scholar
• Everitt , B. S. 2002 . The Cambridge Dictionary of Statistics , Cambridge : Cambridge University Press .
   Google Scholar