An algorithm for the two-dimensional assortment problem

In this paper we consider the two-dimensional assortment problem. This is the problem of choosing from a set of stock rectangles a subset which can be used for cutting into a number of smaller rectangular pieces. Constraints are imposed upon the number of such pieces which result from the cutting.A heuristic algorithm for the guillotine cutting version of the problem is developed based on a greedy procedure for generating two-dimensional cutting patterns, a linear program for choosing the cutting patterns to use and an interchange procedure to decide the best subset of stock rectangles to cut.Computational results are presented for a number of test problems which indicate that the algorithm developed produces good quality results both for assortment problems and for two-dimensional cutting problems.