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

Authors

  • Gizem Temelcan Ergenecosar Department of Software Engineering, Beykoz University, Beykoz, Turkiye
  • Hale Gonce Kocken Department of Mathematical Engineering, Yildiz Technical University, Esenler, Turkiye
  • Inci Albayrak Department of Mathematical Engineering, Yildiz Technical University, Esenler, Turkiye
  • Mustafa Sivri Department of Mathematical Engineering, Yildiz Technical University, Esenler, Turkiye

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.

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Published

2026-01-23

Issue

Vol. 17 No. 1 (2026): CRORR

Section

CRORR Journal Regular Issue

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