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

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Abstract

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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  1. Numerical Optimizer, NTT DATA Mathematical Systems Inc., https://www.msi.co.jp/nuopt/.

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Authors and Affiliations

  1. Graduate School of Humanities and Social Sciences, Nagoya City University, 1, Yamanohata, Mizuho-cho, Mizuho-ku, Nagoya, 467-8501, Japan

    Hitoshi Yano

  2. Graduate School of Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, 739-8527, Japan

    Ichiro Nishizaki

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  1. Hitoshi Yano
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  2. Ichiro Nishizaki
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Correspondence to Hitoshi Yano.

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Yano, H., Nishizaki, I. Multiobjective two-level simple recourse programming problems with discrete random variables. Optim Eng 22, 1181–1202 (2021). https://doi.org/10.1007/s11081-020-09532-9

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