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2020 | 141 | 91-102
Article title

Adjustable Robust Counterpart Optimization Model for Maximum Flow Problems with Box Uncertainty

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Abstracts
EN
The maximum flow problem is an optimization problem that aims to find the maximum flow value on a network. This problem can be solved by using Linear Programming. The obstacle that is often faced in determining the maximum flow is the magnitude of the capacity of each side of the network can often be changed due to certain factors. Therefore, we need one of the optimization fields that can calculate the uncertainty factor. The field of optimization carried out to overcome these uncertainties is Robust Optimization. This paper discusses the Optimization model for the maximum flow problem by calculating the uncertainties on parameters and adjustable variables using the Adjustable Robust Counterpart (ARC) Optimization model. In this ARC Optimization model it is assumed that there are indeterminate parameters in the form of side capacity in a network and an uncertain decision variable that is the amount of flow from the destination point (sink) to the source point (source). Calculation results from numerical simulations show that the ARC Optimization model provides the maximum number of flows in a network with a set of box uncertainty. Numerical simulations were obtained with Maple software.
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Year
Volume
141
Pages
91-102
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Contributors
  • Department of Mathematics, Faculty of Mathematics and Natural Science, University of Padjadjaran, Jalan Raya Bandung-Sumedang Km. 21 Jatinangor Sumedang 45363, Indonesia
author
  • Department of Mathematics, Faculty of Mathematics and Natural Science, University of Padjadjaran, Jalan Raya Bandung-Sumedang Km. 21 Jatinangor Sumedang 45363, Indonesia
author
  • Department of Mathematics, Faculty of Mathematics and Natural Science, University of Padjadjaran, Jalan Raya Bandung-Sumedang Km. 21 Jatinangor Sumedang 45363, Indonesia
References
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  • [2] Ben-Tal, A., & Nemirovski, A. 2002. Robust optimization-Methodology and applications. Math. Programming, 92(3), 453-480.
  • [3] Ben-Tal, A., Ghaoui, L., Nemirovski, A. 2009. Robust Optimization. Princeton, New Jersey, United Kingdom: Priceton University Press.
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  • [6] Ford, L.R., Fulkerson, D.R. 1956. Maximal flow through a network. Canadian Journal of Mathematics, 8, 399–404.
  • [7] Gorissen, B. L., Yanikoglu, I., Hertog, D. D. 2015. A Practical Guide to Robust Optimization. Omega: The International Journal of Management Science, 53, 124-137.
  • [8] Sözüer S., Thiele A.C. (2016). The State of Robust Optimization. In: Doumpos M., Zopounidis C., Grigoroudis E. (eds) Robustness Analysis in Decision Aiding, Optimization, and Analytics. International Series in Operations Research & Management Science, Vol. 241. Springer, Cham. https://doi.org/10.1007/978-3-319-33121-8_5
  • [9] Soyster, A.L. 1973. Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research 21(5), 1154–1157
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article
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bwmeta1.element.psjd-d3bda928-14de-4915-9abf-b14cfee42610
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