Arc-flow modelforthetwo-dimensionalguillotinecuttingstockproblem

We describeanexactmodelforthetwo-dimensionalcuttingstockproblemwithtwostagesandthe guillotine constraint.Itisanintegerlinearprogramming(ILP)arc-flowmodel,formulatedasaminimum flow problem,whichisanextensionofamodelproposedbyValériodeCarvalhofortheonedimensional case. Inthispaper,weexplorethebehaviorofthismodelwhenitissolvedwithacommercialsoftware, explicitly consideringallitsvariablesandconstraints.Wealsoderiveanewfamilyofcuttingplanesand a newlowerbound,andconsidersomevariantsoftheoriginalproblem.Themodelwastestedonasetof real instancesfromthewoodindustry,withverygoodresults.Furthermorethelowerboundsprovided by thelinearprogrammingrelaxationofthemodelcomparefavorablywiththelowerboundsprovided by modelsbasedonassignmentvariables.