Stackelberg solutions for fuzzy random two-level linear programming through level sets and fractile criterion optimization

This paper considers Stackelberg solutions for two-level linear programming problems under fuzzy random environments. To deal with the formulated fuzzy random two-level linear programming problem, an α -stochastic two-level linear programming problem is defined through the introduction of α -level s...

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Bibliographic Details
Published in:Central European journal of operations research Vol. 20; no. 1; pp. 101 - 117
Main Authors: Sakawa, Masatoshi, Katagiri, Hideki
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.03.2012
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Business and Management
Criteria
Decision making
Distribution costs
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Game theory
Linear programming
Mathematical models
Mathematical optimization
Mathematical programming
Operations research
Operations Research/Decision Theory
Optimization
Original Paper
Programming
Random variables
Simplex method
Studies
Supply chains
Japan
Two-level linear programming
Fractile criterion optimization
Fuzzy random variables
Level sets
Stackelberg solutions
ISSN:1435-246X, 1613-9178
Online Access:Get full text
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Summary:This paper considers Stackelberg solutions for two-level linear programming problems under fuzzy random environments. To deal with the formulated fuzzy random two-level linear programming problem, an α -stochastic two-level linear programming problem is defined through the introduction of α -level sets of fuzzy random variables. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the α -stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through fractile criterion optimization in stochastic programming, the transformed stochastic two-level programming problem can be reduced to a deterministic two-level programming problem. An extended concept of Stackelberg solution is introduced and a numerical example is provided to illustrate the proposed method.
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ISSN:1435-246X
1613-9178
DOI:10.1007/s10100-010-0156-5