An algorithm for the determination of optimal cutting patterns

This paper presents a new mathematical programming formulation for the problem of determining the optimal manner in which several product rolls of given sizes are to be cut out of raw rolls of one or more standard types. The objective is to perform this task so as to maximize the profit taking account of the revenue from the sales, the costs of the original rolls, the costs of changing the cutting pattern and the costs of disposal of the trim. A mixed integer linear programming (MILP) model is proposed which is solved to global optimality using standard techniques. A number of example problems, including an industrial case study, are presented to illustrate the efficiency and applicability of the proposed model.