Different transformations for solving non-convex trim-loss problems by MINLP.

*(English)*Zbl 0955.90095Summary: In the present paper trim-loss problems, often named the cutting stock problem, connected to the paper industry are considered. The problem is to cut out a set of product paper rolls from raw paper rolls such that the cost function, including the trim-loss as well as the costs for the over production, is minimized. The problem is non-convex due to certain bilinear constraints. The problem can, however, be transformed into linear or convex form. The resulting transformed problems can, thereafter, be solved as mixed-integer linear programming problems or convex mixed-integer nonlinear programming problems. The linear and convex formulations are attractive from a formal point of view, since global optimal solutions to the originally non-convex problem can be obtained. However, as the examples considered will show, the numerical efficiency of the solutions from the different transformed formulations varies considerably. An example based on a trim optimization problem encountered daily at a Finnish paper converting mill is, finally, presented in order to demonstrate differences in the numerical solutions.

##### MSC:

90C11 | Mixed integer programming |

90C10 | Integer programming |

90C30 | Nonlinear programming |

90C05 | Linear programming |

##### Keywords:

optimization; mixed integer nonlinear programming; integer linear programming; trim-loss problems
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\textit{I. Harjunkoski} et al., Eur. J. Oper. Res. 105, No. 3, 594--603 (1998; Zbl 0955.90095)

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