Gomoryskärplan

Gomoryskärplan refers to a mathematical concept in the field of operations research and integer programming. It is a type of cutting plane method, a technique used to solve integer linear programming problems. Integer programming problems are optimization problems where some or all of the decision variables must take on integer values. Standard linear programming solvers, which assume continuous variables, do not directly address this integer requirement. Cutting plane methods, like Gomoryskärplan, introduce additional constraints (cutting planes) to the problem formulation that eliminate fractional solutions without cutting off any feasible integer solutions.

The Gomoryskärplan method, named after its developers Ralph Gomory and others who contributed to the theory of cutting planes, generates these constraints from the simplex tableau of a relaxed linear programming problem (where integer constraints are initially ignored). Specifically, it focuses on rows of the simplex tableau that correspond to fractional basic variables. From these rows, Gomoryskärplan constructs an inequality that, when added to the problem, forces the fractional solution to become infeasible while ensuring that all valid integer solutions remain feasible. This process is repeated iteratively, with new cutting planes being added until an optimal integer solution is found. While conceptually important and foundational for integer programming theory, pure Gomoryskärplan methods can sometimes be computationally inefficient in practice compared to more advanced techniques like branch and bound or other cutting plane algorithms. However, its principles are fundamental to understanding how integer programming problems can be solved.