Issue: 2026/Vol.36/No.1, Pages 24-52
A GLOBAL PRICING EXTENSION OF THE SIMPLEX METHOD
Biressaw Chali Wolde
, Torbjörn Larsson 
Cite as: B. C. Wolde, T. Larsson. A global pricing extension of the simplex method. Operations Research and Decisions 2026: 36(1), 24-52. DOI 10.37190/ord/211420
Abstract
We introduce the use of a global, nonlinear price function in linear programming and the simplex method. The usual, linear price function of this method captures the objective's behaviour over the cone of directions defined by the nonbasic columns, whereas the global price function adds information about the topology of the whole feasible set. This is achieved by using an exterior penalty function. Further, degeneracy is effectively handled through explicit degeneracy-breaking constraints. The use of the global price function leads to a pricing problem that yields an improving, non-edge feasible direction, which is converted to an auxiliary variable to be used in the simplex method. Preliminary computational results with nondegenerate and highly degenerate linear programs show that the introduction of a global price function in the simplex method, and degeneracy-breaking constraints if needed, may significantly enhance its performance.
Keywords: linear programming; simplex method; pricing; feasible direction; external pivoting
Received: 15 March 2025 Accepted: 4 October 2025
Published online: 4 October 2025