Cut order planning is the problem of planning the fabric cut for a set of apparel orders. A specified set of garments is ordered by the customer to be produced by a given date. Affiliated with this order is a set of garment sizes, and patterns for cutting each size. The fabric for cutting the order must be arranged on the cutting table in such a way as to minimize the cost of cutting the order. This plan must incorporate a partition of the pattern pieces to be arranged on top of the fabric layout. A mathematical model of the problem is developed and analyzed. On the basis of this analysis, solution approaches are developed that have been implemented on a desktop PC-based computer. Validated on representative industry problems, the approach is shown to be effective and versatile.