Numerical and environmental considerations on a complex industrial mixed integer non-linear programming (MINLP) problem

Iiro Harjunkoski*, Tapio Westerlund, Ray Pörn

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

34 Citations (Scopus)


In the present paper an essential problem in the process industry, the trim-loss problem, is considered. The problem can be identified in many different industries (for instance in the paper and metal industry) but here, the main focus is on the paper industry or more precisely, the paper-converting industry. In the trim-loss problem at a paper-converting mill, an optimal strategy is sought for cutting a wide raw-paper reel into narrower, customer-specified product reels in such a way that the appearance of waste, the trim loss, is minimized. Besides being a numerically challenging non-convex mixed integer non-linear programming problem, the choice of objective is of great importance and a non-trivial task in order to alter sustainable and environmentally benign solutions. Therefore, in the following some transformation techniques for overcoming bilinearity and solving the original problem into its global optimality are presented. The transformations are followed by an analysis and comparison of different ways to formulate the objective function. Finally, a set of example problems are solved in order to project the theoretical considerations to more practical level.

Original languageEnglish
Pages (from-to)1545-1561
Number of pages17
JournalComputers and Chemical Engineering
Issue number10
Publication statusPublished - 1 Dec 1999
MoE publication typeA1 Journal article-refereed


  • Mixed integer non-linear programming
  • Optimization
  • Trim-loss problems
  • Waste minimization


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