Genetic Algorithm for Linear Cutting Problem

The article deals with the problem of calculating the volume calendar plan of a paper mill. To find the optimal schedule, a combination of the following criteria is used: minimal trim loss, minimal changes to the knives setup and smooth transitions by product grades. Solution algorithms are presented that use a combination of the simplex method, the column generation, the branch and bound methods, the greedy algorithm. The specifics of paper production and sales are taken into account — customer orders are measured not in the whole number of units of finished products, but by weight, which is specified with "tolerances". A variant of the genetic type algorithm for the paper production planning problem is proposed. The algorithm uses special crossover and mutation operators based on the multiple solution of quadratic or linear programming problems. The result of a computational experiment based on real production data of a paper mill in European part of Russia shows that the algorithm can be effectively used to plan the work of one paper machine for several shifts or as an auxiliary tool when devising cutting plans for a group of paper machines. The proposed algorithm provides an optimal solution with no more than 400 cutting plans, which corresponds to approximately 8 orders for rolls of the same diameter and density produced on one paper machine. That is, it can be used when planning production for no more than two days. To build planning systems for longer periods of time (week, month), it is necessary to develop special algorithms.