A Stochastic Cutting Stock Procedure: Cutting Rolls of Insulating Tape

This paper develops a one-dimensional cutting stock procedure which will minimize material wastage when a batch of small pieces are cut from several long pieces. The problem differs from the classical one-dimensional cutting stock problem in that the dimensions of the material to be cut are random variables due to fringe defects caused by the production process. Examples of such processes include the production of flat glass, laminated board, corrugated board, adhesive tape, carpeting, and insulating tape. The cutting procedure inevitably generates some material wastage and process delays caused by the need to set cutting knives in required positions. The approach followed in this paper is to minimize material wastage when cutting a batch of identical rolls of insulating tape from several long rolls with stationary cutting knives. An exact solution is presented for the case in which the variability of defects at both ends is independently distributed and the two distributions differ by a location parameter only. An approximate solution is also presented when the two end defect distributions differ by both scale and location parameters. The wastage resulting from the use of these procedures is then compared with the wastage generated when the positioning of the knives is altered every time an original piece is cut. This comparison enables management to decide when the positioning of the cutting knives should be fixed.