One-dimensional stock cutting: optimization of usable leftovers in consecutive orders

This paper deals with usable leftovers (UL) in one-dimensional stock cutting in consecutive orders. UL are leftovers longer than a certain threshold and are returned to stock in order to be used in future orders. Shorter leftovers are treated as trim-loss. If UL are being used at a slower pace, than they are being generated for a longer period of time, excessive growth of UL in stock can appear. This is not acceptable due to higher costs of manipulations and warehousing. However, a certain amount of UL in stock is desirable because it contributes to greater variety of stock lengths, which in general results in lower trim-loss. The method solves the problem of how to calculate the near optimal amount of UL in stock and how to control the stock. The proposed method is tested by using a computer simulation in which UL from previous orders are used in the next ones instead of being randomly generated. The computational results indicate that trim-loss in consecutive orders is reduced, and excessive growth of UL in stock is prevented.