Mixed-Integer Programming Models For 1.5-Dimensional Cutting Problem With Technical Constraints

In solving cutting stock problems, generally, cutting patterns are generated first, and then it is determined which cutting plans will be used. On the other hand, the difficulty of generating all cutting patterns and often the large number of cutting patterns are the main problems encountered in this regard. In this study an integrated mathematical model that generates cutting patterns and finds the best patterns is developed for 1.5-dimensional cutting stock problems with order type and strip number constraints. This non-linear model has been linearized to eliminate solution difficulties. The performance of both models is compared with the performance of the model that uses the previously generated cutting patterns by using the randomly generated test problems. Obtained results show that the linear model, which also generates the cutting patterns itself, can be solved in a reasonable time up to a certain size. In particular, we believe that linearization of the nonlinear mathematical model for the problem will be an important contribution for the literature.