Title: Proposal of a numerical approximation theory to solve the robust convex problem of production planning

Authors: Marcelo Carneiro Gonçalves; Rafael Rodrigues Guimarães Wollmann; Raimundo José Borges De Sampaio

Addresses: Department of Industrial Engineering, Pontifical Catholic University of Paraná, 1155 Imaculada Conceição, Building 9, Curitiba, PR, 80215-901, Brazil ' Department of Industrial Engineering, Pontifical Catholic University of Paraná, 1155 Imaculada Conceição, Building 9, Curitiba, PR, 80215-901, Brazil ' Department of Industrial Engineering, Pontifical Catholic University of Paraná, 1155 Imaculada Conceição, Building 9, Curitiba, PR, 80215-901, Brazil

Abstract: This research seeks to solve the production planning problem modelled as a queuing system to propose to managers a production planning model that uses efficient, simple and robust methods. First, a robust mathematical model of nonlinear programming was proposed considering the concepts of queuing systems to estimate production capacity. Next, this model was approximated by a family of affine functions using the strategy of approximating a convex set by a polyhedral set. Finally, a theorem was proposed to demonstrate that a robust nonlinear programming model can be approximated by a robust linear programming model. From a numerical experiment with data from an electronic equipment company, it was possible to observe the effectiveness of the approximation method.

Keywords: robust optimisation; linear programming; convex programming; queuing systems.

DOI: 10.1504/IJOR.2025.144318

International Journal of Operational Research, 2025 Vol.52 No.2, pp.171 - 191

Received: 06 Sep 2021
Accepted: 28 Jun 2022
Published online: 07 Feb 2025 *

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