Original scientific paper
https://doi.org/10.17535/crorr.2026.0003
Solution to the single parametric linear programming problems via simplex-based algorithms: handling the uncertainties in costs, left or right-hand sides
Gizem Temelcan Ergenecosar
orcid.org/0000-0002-1885-0674
; Department of Software Engineering, Beykoz University, Kavacik, Beykoz İstanbul, Turkiye
*
Hale Gonce Kocken
; Department of Mathematical Engineering, Yildiz Technical University, Esenler İstanbul, Turkiye
Inci Albayrak
orcid.org/0000-0001-6906-9880
; Department of Mathematical Engineering, Yildiz Technical University, Esenler İstanbul, Turkiye
Mustafa Sivri
; Department of Mathematical Engineering, Yildiz Technical University, Esenler İstanbul, Turkiye
* Corresponding author.
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.
Keywords
dual-simplex method; generalized-simplex method; parametric linear programming problem; primal-simplex method
Hrčak ID:
331619
URI
Publication date:
3.6.2025.
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