Multiobjective two-level simple recourse programming problems with discrete random variables

In this paper, we focus on multiobjective two-level simple recourse programming problems, in which multiple objective functions are involved in each level, shortages and excesses arising from the violation of the constraints with discrete random variables are penalized, and the sum of the objective...

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Bibliographic Details
Published in:Optimization and engineering Vol. 22; no. 2; pp. 1181 - 1202
Main Authors: Yano, Hitoshi, Nishizaki, Ichiro
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2021
Springer Nature B.V
Subjects:
Algorithms
Control
Engineering
Environmental Management
Financial Engineering
Game theory
Integer programming
Mathematics
Mathematics and Statistics
Mixed integer
Operations Research/Decision Theory
Optimization
Random variables
Research Article
Stochastic programming
Systems Theory
Two-level programming
Pareto Stackelberg solutions
Simple recourse programming
Multiobjective programming
ISSN:1389-4420, 1573-2924
Online Access:Get full text
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Summary:In this paper, we focus on multiobjective two-level simple recourse programming problems, in which multiple objective functions are involved in each level, shortages and excesses arising from the violation of the constraints with discrete random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems, a concept of Pareto Stackelberg solutions based on the reference objective levels is introduced. Using the Kuhn–Tucker approach in two-level programming, we formulate as a mixed integer programming problem, and propose an interactive algorithm to obtain a satisfactory solution of the leader from among a Pareto Stackelberg solution set based on the reference objective levels. A numerical example illustrates the proposed algorithm for a multiobjective two-level stochastic programming problem with simple recourses under the hypothetical leader.
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ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-020-09532-9