Cutting Stock Problems

Abstract

Column generation has been proposed by Gilmore and Gomory to solve cutting stock problem, independently of Dantzig-Wolfe decomposition. We survey the basic models proposed for cutting stock and the corre- sponding solution approaches. Extended Dantzig-Wolfe decomposition is surveyed and applied to these models in order to show the links to Gilmore-Gomory model. Branching schemes discussion is based on the subproblem formulation corresponding to each model. Integer solutions are obtained by combining heuristics and branch-and-price schemes. Linear relaxations are solved by column generation. Stabilization tech- niques such as dual-optimal inequalities and stabilized column gener- ation algorithms that have been proposed to improve the efficiency of this process are briefly discussed.