Arc-flow formulations for the one-dimensional cutting stock problem with multiple manufacturing modes

In this paper, an integration of the one-dimensional cutting stock problem with an operational problem that arises in the manufacture of concrete poles is studied. Seeing that poles have a steel structure, different thicknesses of steel bars can be used in their manufacture. This variety in combining the materials to produce the structure of the poles is known as alternative production modes or multiple manufacturing modes. The problem considered here has the objective of minimizing the total cost to meet the demand for poles using the different available configurations. This problem has already been introduced in the literature and it has been formulated as an integer programming problem. To solve it, the column generation procedure was used. The contribution of this paper is to reformulate the cutting stock problem with multiple manufacturing modes using arc-flow formulations. Arc-flow formulations are promising tools to model and solve complex combinatorial problems. Computational tests are performed comparing the formulations using instances from the literature, which were generated based on the data from a civil construction plant. The arc-flow formulations increased the number of instances solved to proven optimality and also reduced solution time. Lower and upper bounds are also improved when compared with the solution proposed in the literature