Procedures for solving single-pass strip layout problems

Strip layout is an important step in the planning of operations using blanking dies. Typically the strip layout problem has been resolved using methods which provide approximate solutions, since it is viewed as a class of general 2-D nesting problem which is NP-Hard. This implies that we need to investigate special cases of the strip layout problem that will permit polynomial running time algorithms, while having some practical application in processes of cutting shapes from sheet stock. In this paper we present an exact procedure with polynomial running time for the single-pass single-row layout problem. This problem tries to layout identical shapes on a strip that will go thorough a single row die only once, such as to maximize the number of parts to be yielded by the strip. The paper investigates this problem for two cases: the case for which the width of the strip is larger than any possible orientation of the part, and the case for which the width of the strip is restricted so that not every orientation is feasible. We also consider the problem of cutting a sheet of metal into strips so as to maximize the sum of the parts yielded by each sheet.