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

Author

Listed:
  • Marcelo Carneiro Gonçalves
  • Rafael Rodrigues Guimarães Wollmann
  • Raimundo José Borges De Sampaio

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.

Suggested Citation

  • Marcelo Carneiro Gonçalves & Rafael Rodrigues Guimarães Wollmann & Raimundo José Borges De Sampaio, 2025. "Proposal of a numerical approximation theory to solve the robust convex problem of production planning," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 52(2), pages 171-191.
    • Handle: RePEc:ids:ijores:v:52:y:2025:i:2:p:171-191
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