Solving a production optimization problem in a paper-converting mill with MILP

Abstract

The present paper deals with a production optimization problem connected with the paper-converting industry. The problem considered is to produce a set of product paper reels from larger raw paper reels such that a cost function is minimized. The problem is generally non-convex due to a bilinear objective function and some bilinear constraints, both of which give rise to certain problems. The problem can, however, be solved as a two-step optimization procedure, in which the latter step is a mixed integer linear programming problem. A numerical example is introduced to illustrate the proposed procedure. The example is taken from a real-life daily production optimization problem encountered at a Finnish paper-converting mill, Wisapak Oy, having an annual production of just over 100,000 tons of printed paper.