A greedy algorithm for decomposing large clothing orders into lays

Abstract

Garments are often produced by cutting stacks of layers of fabric into pieces, thus yielding copies of each piece. Given a requested number of garments for each size, we are interested in determining the number of layers of each stack, as well as which pieces are to be cut from each stack, in such a way that (1) the requested number of garments of each size is produced, and (2) both the fabric and the labor costs are minimized. In [3], we described a Prolog program for decomposing clothing orders into stacks of layers using a branch-and-bound method. Because the order-decomposition problem is inherently complex, such a branch-and-bound method proved to be practical only for "small" orders, with up to seven sizes. In the current paper we extend the previous method to larger orders by preceding the branch-and-bound method by a greedy method that repetitively tries to place as many garments as possible in each stack. Once the order to be decomposed is small enough, we switch to the branch-and-bound method.