Methods for Solving the Linear Cutting-stock Problem on Several Slitting Machines with Minimizing the Number of Waste and Knife Rearrangements

This article presents the methods for solving the linear cutting problem. The linear cutting problem is, in general, an optimization problem that involves arranging the given types of material (orders) in such a way as to minimize waste and/or maximize the use of raw materials, taking into account the restrictions on the number of knives, the width of the master roll and the required orders. A special case of the problem includes an additional condition of minimizing knife rearrangements. There are also multiple slitting machines with different widths of the master roll. It makes the problem more complex and requires proper algorithms. The following approaches to its solution are considered: the full enumeration method, and a genetic search based on genetic and evolutionary algorithms. Pseudocode is presented for various methods of solving the problem. An example is provided for the genetic search method. A comparison is made between both algorithms in terms of algorithmic complexity, controllability of execution time and accuracy.