Solution to the single parametric linear programming problems via simplex-based algorithms: handling the uncertainties in costs, left or right-hand sides

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Ergenecosar G. T., KÖÇKEN H., ALBAYRAK F. İ., Sivri M.

Croatian Operational Research Review, vol.17, no.1, pp.29-40, 2026 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.17535/crorr.2026.0003
  • Journal Name: Croatian Operational Research Review
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, ABI/INFORM, EconLit, MathSciNet, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.29-40
  • Keywords: dual-simplex method, generalized-simplex method, parametric linear programming problem, primal-simplex method
  • Yıldız Technical University Affiliated: Yes

Abstract

Parametric programming is one of the notable approaches to expressing the uncertainties encountered in real life. Many studies express the parameters of the objective function and right-hand side parametrically, but only a few include the parametric coefficient matrix of the constraints. This paper examines the feasibility and optimality conditions of the simplex table and proposes a simplex-based algorithm (dual-simplex, generalized-simplex, or primal-simplex). In the solution process, each case is considered independently through the mathematical analysis of simplex multipliers. Distinct numerical examples illustrate each case to demonstrate the algorithm’s implementation.