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We advance the state of the art in Mixed-Integer Linear Programming (MILP)formulations for Guillotine 2D Cutting Problems by (i) adapting a previouslyknown reduction to our preprocessing phase and by (ii) enhancing a previousformulation by cutting down its size and symmetries. Our focus is theGuillotine 2D Knapsack Problem with orthogonal and unrestricted cuts,constrained demand, unlimited stages, and no rotation -- however, theformulation may be adapted to many related problems. The code is available.Concerning the set of 59 instances used to benchmark the original formulation,and summing the statistics for all models generated, the enhanced formulationhas only a small fraction of the variables and constraints of the originalmodel (respectively, 3.07% and 8.35%). The enhanced formulation also takesabout 4 hours to solve all instances while the original formulation takes 12hours to solve 53 of them (the other six runs hit a three-hour time limiteach). We integrate, to both formulations, a pricing framework proposed for theoriginal formulation; the enhanced formulation keeps a significant advantage inthis situation. Finally, in a recently proposed set of 80 harder instances, theenhanced formulation (with and without the pricing framework) found: 22 optimalsolutions for the unrestricted problem (5 already known, 17 new); 22 optimalsolutions for the restricted problem (all are new and they are not the same 22of the optimal unrestricted solutions); better lower bounds for 25 instances;better upper bounds for 58 instances.

Enhanced Formulation for Guillotine 2D Cutting Problems