Generalization of the Method Based on Parameterization Developed for Solving Integer Linear Programming Problems

Creative Commons License

Şimşek Alan K.

12th INTERNATIONAL CONFERENCE ON APPLIED ANALYSIS AND MATHEMATICAL MODELING, İstanbul, Türkiye, 19 Temmuz - 23 Ekim 2024, ss.183

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.183
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

This study presents the generalization of methods based on parameterization proposed for solving integer programming problems with linear objectives and linear constraints. Initially, the method based on parameterization, proposed for solving 2, 3, and 4-variable integer linear programming problems, is generalized to n-variable integer linear programming problems. The proposed method relies on the parameterization obtained from Diophantine equations. Using this parameterization, the original problem is reformulated as another integer linear programming problem that can be solved more efficiently using simple mathematical programming. The method can be used regardless of the number of constraints of the problem and also provides all alternative solutions to the decision maker. It is demonstrated with some examples that this method provides an efficient algorithm.

This work was supported by Yildiz Technical University Scientific Research Projects Coordination Unit. Project Number: FBA-2021-4032.