## 4 Results  
We employed IBM ILOG CPLEX 22.1 [11] to solve the ILP models and used Coluna 0.4.2 (JuMP 1.1.0 and Julia 1.8) [12] to run the CG technique. Coluna implements a default CG procedure and provides dual and primal bounds for each iteration of the method. We set CPLEX as underlying ILP solver to handle master and subproblem. For the search tree, we considered a maximum number \(M=1,000,000\) of cutting patterns. The hill climbing algorithm was implemented in Java language and, after preliminary tests, the values of the parameters of the G&S method were chosen: \(\tau_{G\&R}=600\) s, \(\tau_{solver}=10\) s, \(\rho=10\%\), and \(\alpha=2\). The computational experiments were performed on Intel Core i7 7500U CPU 2.70 GHz 8 GB RAM machines. Benchmark instances from the literature [3], divided into 5 classes, were used to carry out a comparative analysis of the performance of the different methods. We set an execution timeout of 600 s for all methods. The comparative results are presented in Tables 1-5. Along with the characterisation of the instances, we present the computational results for the different methods. Since G&S is stochastic, we provide the best and average values over 10 (ten) executions of this method, besides the average time to best (_ttb_), i.e., the elapsed time until finding the best solution of an execution. For the CG algorithm, we provide the dual lower bound (_db_) and the primal upper bound (_pb_). Note that, when the CG algorithm stops before convergence due to the time limit of 600 s, the dual bound may not represent the object value of the linear relaxation of the original ILP formulation. For each instance, we mark the proven optimal solutions with the symbol \({}^{*}\) and highlight in boldface the best solutions found among those obtained by the competitive approaches. Particularly, in Table 1, we present as well computational results for the ILP formulations proposed by [PERSON] [5,6] (GG-ILP) and [PERSON] [18] (REFLECT-ILP), in an attempt to investigate the scalability of the exact approach. In this table, \(lb\) and \(ub\) define, respectively, a primal lower bound and a primal upper bound for the ILP models. The computational results for the set of instances of class \(U\) are presented in Table 1. The characteristics of these instances are as follows: the number of types of items ranges from 15 to 1005; the length of each item is between 31.66% and 35.01% of the length of the object; and the demand multiplicity (i.e., the average demand per item type), calculated as the average value among all instances of the class, is unitary. CPLEX was able to obtain feasible solutions to the GG-ILP formulation only for the instances with up to 495 item types. For the small sized instances, GG-ILP obtained proven optimal solutions very fast. The REFLECT-ILP, in turn, obtained feasible solutions for the instances with up to 675 item types. Despite the fact that REFLECT-ILP proved to be more time consuming for small sized instances compared to GG-ILP, CPLEX scaled better with this formulation. CG and G&S methods were able to find feasible solutions for all instances of this class. CG proved to be the most effective and time efficient for small sized instances (with up to 405 item types). It is important to remark that, for medium sized instances, CG outperforms the G&S approach. G&S obtained optimal solutions for instances with up to 285 item types. In addition, for large sized instances, G&S provided the best feasible solutions, and, therefore, the strategy of artificially limiting the number of cutting patterns proved to be very effective. The set of instances of class _hard28_, presented in Table 2, has between 136 to 189 types of items. In these instances, the length of each item is between 0.1% and 80.0% of the length of the object and the demand multiplicity is of 1.1221. The demands vary from 1 (one) to 3 (three). The wide variety of the length of the items in relation to the length of the object stands out. CG method obtained the proven optimal solution for 15 out of 28 instances.