A new approach to the integrated cutting stock problem and pattern sequencing.

We propose a new approach to the Integrated One-Dimensional Cutting Stock Problem (CSP) and the Minimization of Open Stacks Problem (MOSP), in which material waste and the number of open piles are minimized simultaneously. We refer to this CSP extension as the Cutting Stock Problem with Open Stacks (CSP-OS). To solve CSP-OS, we propose three approaches based on the ε-constraint and weighted sum methods. We have developed an exact approach to solve the One-Dimensional Cutting Stock Problem with a Limited Number of Open Stacks (CS-LOSP) by dividing it into sub-problems solved via an Integer Linear Programming solver and propose a formulation that requires no prior knowledge of feasible cutting patterns. We performed computational tests to verify the quality of the proposed approaches and compare their performance with the current state-of-the-art formulation in the literature.