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This paper presents an exact scalarization method to solve bi-objective integer linear optimization problems. This method uses diverse reference points in the iterations, and it is free from any kind of a priori chosen weighting factors. In addition, two new adapted scalarization methods from literature and the modified Tchebycheff method are studied. Each one of them results in different ways to obtain the Pareto frontier. Computational experiments were performed with random real size instances of two special problems related to the manufacturing industry, which involve lot sizing and cutting stock problems. Extensive tests confirmed the very good performance of the new scalarization method with respect to the computational effort, the number of achieved solutions, the ability to achieve different solutions, and the spreading and spacing of solutions at the Pareto frontier. [ABSTRACT FROM AUTHOR]

This article addresses the bi-objective integer cutting stock problem in one dimension. This problem has great importance and use in various industries, including steel mills. The biobjective model considered aims to minimize the frequency of cutting patterns to meet the minimum demand for each item requested and the number of different cutting patterns to be used, being these conflicting objectives. In this study, we apply three classic methods of scalarization: weighted sum, Chebyshev metric and ɛ-Constraint. This last method is developed to obtain all of the efficient solutions. Also, we propose and test a fourth method, modifying the Chebyshev metric, without the insertion of additional variables in the formulation of the subproblems. The computational experiments with randomly generated real size instances illustrate and attest the suitability of the bi-objective model for this problem, as well as the applicability of all the proposed exact algorithms, thus showing that they are useful tools for decision makers in this area. Moreover, the modified metric method improved with respect to the performance of the classical version in the tests. [ABSTRACT FROM AUTHOR]