A Genetic Algorithm for 1,5 Dimensional Assortment Problems with Multiple Objectives

In most studies on cutting stock problems, it is assumed that the sizes of stock materials are known and the problem is to find the best cutting pattern combinations. However, the solution efficiency of the problem depends strongly on the size of stock materials. In this study, a two-step approach is developed for a 1,5 dimensional assortment problem with multiple objectives. Cutting patterns are derived by implicit enumeration in the first step. The second step is used to determine the optimum sizes of stock materials by applying a genetic algorithm. The object is to find stock material sizes that minimize the total trim loss and also the variety of stock materials. Specialized crossover operator is developed to maintain the feasibility of the chromosomes. A real-life problem with 41 alternative stock materials, 289 order pieces and 1001 patterns is solved.