Distributional Efficiency in Multiobjective Stochastic Linear Programming

Several concepts of distributional efficiency are proposed for the Multiobjective Stochastic Linear Programming (MSLP) problem, in contexts where the probability distribution of random parameters is known and the decision maker (DM) has an unknown multi-attribute utility function belonging to a given glass U. We present a general efficient set, the U-admissible solutions, and two subsets, the U-unanimous and U-advocated solutions, the latter being particularly relevant to the case of a single DM. We show how advocated solutions can be generated and/or tested when U is the class of non-decreasing additive concave functions.

[1]  Ron S. Dembo,et al.  Scenario optimization , 1991, Ann. Oper. Res..

[2]  Bezalel Peleg,et al.  Efficiency Analysis for Multivariate Distributions , 1975 .

[3]  R L Keeney,et al.  A multiattribute utility analysis of alternative sites for the disposal of nuclear waste. , 1987, Risk analysis : an official publication of the Society for Risk Analysis.

[4]  R. Tyrrell Rockafellar,et al.  Scenarios and Policy Aggregation in Optimization Under Uncertainty , 1991, Math. Oper. Res..

[5]  J. Stiglitz.  Behavior Towards Risk with Many Commodities , 1969 .

[6]  K. Marti,et al.  Computation of Efficient Solutions of Stochastic Optimization Problems with Applications to Regression and Scenario Analysis , 1990 .

[7]  Pascal Lang,et al.  Pointwise Efficiency in Multiobjective Stochastic Linear Programming , 1994 .

[8]  Marco Scarsini,et al.  Stochastic dominance with pair-wise risk aversion , 1985 .

[9]  David Connolly,et al.  Handbooks in Operations Research and Management Science, Volume 1 — Optimization , 1990 .

[10]  D. E. Bell,et al.  Conflicting Objectives in Decisions , 1978 .

[11]  Tae Kun Seo,et al.  Ordering Uncertain Prospects: The Multivariate Utility Functions Case , 1978 .

[12]  Marco Scarsini,et al.  Dominance Conditions for Multivariate Utility Functions , 1988 .

[13]  T. Gal.  A general method for determining the set of all efficient solutions to a linear vectormaximum problem , 1977 .

[14]  J. Ecker,et al.  Generating all maximal efficient faces for multiple objective linear programs , 1980 .

[15]  Martin Weber.  Decision Making with Incomplete Information , 1987 .

[16]  Haim Levy,et al.  Multi-Period Stochastic Dominance , 1974 .

[17]  Simon French,et al.  Multi-Objective Decision Analysis with Engineering and Business Applications , 1983 .

[18]  T. Farmer.  TESTING THE ROBUSTNESS OF MULTIATTRIBUTE UTILITY THEORY IN AN APPLIED SETTING , 1987 .

[19]  R. Słowiński,et al.  Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty , 1990, Theory and Decision Library.

[20]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  Raymond Nadeau,et al.  Multiobjective Stochastic Linear Programming with Incomplete Information: A General Methodology , 1990 .

[22]  Peter Kall,et al.  Stochastic Linear Programming , 1975 .

[23]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[24]  E. Lehmann.  Ordered Families of Distributions , 1955 .

[25]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[26]  T. Gal.  On Efficient Sets in Vector Maximum Problems — A Brief Survey , 1986 .

[27]  Karl Mosler,et al.  Stochastic Dominance Decision Rules when the Attributes are Utility Independent , 1984 .

[28]  S. Richard.  Multivariate Risk Aversion, Utility Independence and Separable Utility Functions , 1975 .

[29]  H. Wolf,et al.  Die Ermittlung effizienter Lösungen zur stochastischen linearen Optimierungsaufgabe , 1985 .

[30]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

[31]  R. Wets,et al.  Stochastic programming , 1989 .

[32]  J. Teghem,et al.  STRANGE: an interactive method for multi-objective linear programming under uncertainty , 1986 .

[33]  Leonard J. Mirman,et al.  Risk aversion with many commodities , 1974 .

[34]  Ambrose Goicoechea,et al.  Multiple objectives under uncertainty: An illustrative application of protrade , 1979 .