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Fuzzy Chance Constrained Linear Programming Model for Optimizing the Scrap Charge in Steel Production

Aiying Rong, Risto Lahdelma, Fuzzy Chance Constrained Linear Programming Model for Optimizing the Scrap Charge in Steel Production. European Journal of Operational Research 186(3), 953–964, 2008.

Abstract:

Optimizing the charge in secondary steel production is challenging because the chemical composition of the scrap is highly
uncertain. The uncertainty can cause a considerable risk of the scrap mix failing to satisfy the composition requirements for
the final product. In this paper, we represent the uncertainty based on fuzzy set theory and constrain the failure risk based on a
possibility measure. Consequently, the scrap charge optimization problem is modeled as a fuzzy chance constrained linear
programming problem. Since the constraints of the model mainly address the specification of the product, the crisp equivalent
of the fuzzy constraints should be less relaxed than that purely based on the concept of soft constraints. Based on the appli-
cation context we adopt a strengthened version of soft constraints to interpret fuzzy constraints and form a crisp model with
consistent and compact constraints for solution. Simulation results based on realistic data show that the failure risk can be
managed by proper combination of aspiration levels and confidence factors for defining fuzzy numbers. There is a tradeoff
between failure risk and material cost. The presented approach applies also for other scrap-based production processes.

BibTeX entry:

@ARTICLE{jRoLa08a,
  title = {Fuzzy Chance Constrained Linear Programming Model for Optimizing the Scrap Charge in Steel Production},
  author = {Rong, Aiying and Lahdelma, Risto},
  journal = {European Journal of Operational Research},
  volume = {186},
  number = {3},
  pages = {953–964},
  year = {2008},
  keywords = {Fuzzy sets; Linear programming; Chance constraint; Scrap charge optimization; Steel production},
}

Belongs to TUCS Research Unit(s): Algorithmics and Computational Intelligence Group (ACI)

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