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Bi-level and Multi-Level Programming Problems: Taxonomy of Literature Review and Research Issues

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Abstract

This paper presents taxonomy of detailed literature reviews on bi-level programming problems (BLPPs), multi-level programming problems (MLPPs) and associated research problems, while providing detail of solution techniques at the same time. In this taxonomy of review, we classified the multi-level programming problems into two types: (i) General multi-level programming problems (MLPPs) (ii) multi-level multi-objective programming problems (ML-MOPPs) which are further sub classified based on the algorithmic and optimality studies. Bi-level programming problems (BLPPs) are considered as special cases of multi-level programming problems with two level structures. The present literature review includes approximately all prior and latest references on BLPPs, and MLPPs, related solution methodologies. The general related concepts are briefly described while associated references are included for further investigations. The aim of this paper is to provide an easy and systematic road map of currently available literature studies on BLPPs and MLPPs for future researchers.

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Authors and Affiliations

  1. Department of Mathematics, Government Engineering College, Bikaner, Rajasthan, 334 004, India

    Kailash Lachhwani

  2. Department of Applied Science, National Institute of Technical Teachers Training and Research, Chandigarh, 160 019, India

    Kailash Lachhwani

  3. Department of Mathematics, Desh Bhagat University, Mandi Gobindgarh, Punjab, 147 301, India

    Abhishek Dwivedi

  4. Department of Applied Science, Himachal Institute of Engineering and Technology, Shahpur, Kangra, Himachal Pradesh, 176 233, India

    Abhishek Dwivedi

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  1. Kailash Lachhwani
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Lachhwani, K., Dwivedi, A. Bi-level and Multi-Level Programming Problems: Taxonomy of Literature Review and Research Issues. Arch Computat Methods Eng 25, 847–877 (2018). https://doi.org/10.1007/s11831-017-9216-5

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