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
Simplex algorithm
Linear programming
Algorithm
Parametric statistics
Simplex
Revised simplex method
Parametric programming
Computer science
Mathematical optimization
Linear-fractional programming
Mathematics
Combinatorics
Statistics
Subject Areas
Advanced Optimization Algorithms Research
·Numerical Analysis ·Physical Sciences
Optimization and Packing Problems
·Industrial and Manufacturing Engineering ·Physical Sciences