An integrated optimization model for the 2-stage two-dimensional cutting stock problem with tardiness penalties

This research addresses the Two-Dimensional Stock Cutting and Scheduling Problem (2D-CSSP), which is the combination of the Two-Dimensional Stock Cutting Problem (2D-CSP) and the scheduling problem. This problem, frequently encountered in industrial environments, aims to minimize the sum of terms related to raw material consumption and the maximum and total amount of late periods in fulfilling orders formed by one or more types of items. An integer linear programming model is proposed for the integrated problem, extending a pseudo-polynomial model from the literature developed for the 2D-CSP. An enumeration procedure is presented to obtain 2-stage non-exact guillotine cutting patterns. Computational tests were performed to validate the model using a commercial solver on benchmark instances adapted for the problem.