An efficient mathematical model for solving one-dimensional cutting stock problem using sustainable trim

Abstract

The cutting process is an important stage of the industries which are dealing with cutting of small pieces from large items in such a way so that the wastage should be minimum. In this study, we present an effective model for solving one-dimensional cutting stock problem (1D-CSP) using sustainable trim based on Cesàro means of order $\lambda$ ($\lambda$ is real $>-1$), with the provision of cutting at most two order lengths at a time, which is acceptable in many practical cases. Additionally, we present the comparison of the model with Residual Greedy Rounding (RGR) and CUT. It is shown that increased sustainable trim decreases the total trim loss by providing greater variety of stock lengths, which can be effectively used in future orders.