A compromise solution method for the multiobjective minimum risk problem
- 15 Downloads
We develop an approach which enables the decision maker to search for a compromise solution to a multiobjective stochastic linear programming (MOSLP) problem where the objective functions depend on parameters which are continuous random variables with normal multivariate distributions. The minimum-risk criterion is used to transform the MOSLP problem into its corresponding deterministic equivalent which in turn is reduced to a Chebyshev problem. An algorithm based on the combined use of the bisection method and the probabilities of achieving goals is developed to obtain the optimal or epsilon optimal solution of this specific problem. An illustrated example is included in this paper to clarify the developed theory.
KeywordsMultiobjective programming Stochastic programming Nonlinear programming Minimum-risk criterion
We thank the anonymous referees for their useful comments that improved the content and presentation of the paper.
- Bazara M, Sherali H, Shetty C (1993) Theory and algorithms, 2nd edn. Wiley, New YorkGoogle Scholar
- Caballero R, Cerda E, Munoz MM, Rey L (2000) Relations among several efficiency concepts in stochastic multiple objective programming. In: Haimes YY, Steuer R (eds) Research and practice in multiple criteria decision making, vol 487. Lecture notes in economics and mathematical systems. Springer, Cham, pp 57–58CrossRefGoogle Scholar
- Fazlollahtabar H, Mahdavi I (2009) Applying Stochastic Programming for optimizing production time and cost in an automated manufacturing system. In: International conference on computers and industrial engineering, Troyes 6–9 July, pp 1226–1230Google Scholar
- Goicoechea A, Dukstein L, Bulfin RL (1976) Multiobjective stochastic programming, the PROTRADE-method. Operation Research Society of America, San FranciscoGoogle Scholar
- Miettinen KM (1999) Nonlinear multiobjective optimization. Kluwer’s international series. Kluwer, DordrechtGoogle Scholar
- Minc H, Marcus M (1964) A survey of matrix theory and matrix inequalities. Allyn and Bacon Inc., BostonGoogle Scholar
- Stancu-Minasian IM (1976) Asupra problemei de risk minim multiplu I: cazul a dou funcii obiectiv. II: cazul a r (r > 2) funciiobiectiv. Stud Cerc Mat 28(5):617–623Google Scholar
- Stancu-Minasian IM (1984) Stochastic programming with multiple objective functions. D. Reidel Publishing Company, DordrechtGoogle Scholar
- Teghem J (1990) Strange-Momix: an interactive method for mixed integer linear programming. In: Slowinski R, Teghem J (eds) Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty. Kluwer, Dordrecht, pp 101–115Google Scholar