An integer linear optimization model to the compartmentalized knapsack problem

Abstract

AbstractThe compartmentalized knapsack problem arose from two‐phased cutting stock problems, especially with steel roll cutting. In its original formulation, it refers to an integer nonlinear optimization model, which, up to now, has been solved through decomposition heuristics. The objective of this article is to show that the constrained compartmentalized knapsack problem has a linear optimization model. Therefore, we have considered the original nonlinear model and propose a linear model for the problem, demonstrating their equivalence. We also propose a new decomposition heuristic and perform numerical tests to verify the limits of the proposed model and the quality of the heuristic solutions.