In the cutting stock problem (CSP) a given order for smaller pieces has to be cut from larger stock material with some objectives under some constraints. This note discusses the relationships between the models for one-dimensional cutting stock problem (1CSP) under two different constraints and two different objectives. The two constraints are equality and inequality constraints; and the two objectives are to minimize the number and the trim loss of stock material needed to produce the ordered pieces. Under equality constraint, we have proved that the models with both objectives are equivalent, and their corresponding continuous relaxation problems are also equivalent. Under inequality constraint, we have given an example to show that the models with these two objectives are not equivalent, and their corresponding continuous relaxation problems are also not equivalent
Xie, Jinxing and Dong, Jiefang, "A Note on One-Dimensional Cutting Stock Problem" (2001). ICEB 2001 Proceedings. 146.