Combinatorial Benders Decomposition for the Two-Dimensional Bin Packing Problem

The two-dimensional bin packing problem calls for a set of rectangular items into minimal larger bins. Items must be packed with their edges parallel to the borders bins, cannot rotated, and overlap among them. is interest because it models many real-world applications, including production, warehouse management, transportation. It is, unfortunately, very difficult, instances just 40 are unsolved proven optimality, despite attempts, since 1990s. In this paper, we solve combinatorial Benders decomposition that based on simple model in which bins represented by areas, infeasible packings imposed means exponentially no-good cuts. basic scheme quite naive, but enrich number preprocessing techniques, valid inequalities, lower bounding methods, enhanced algorithms produce strongest possible resulting algorithm behaved well benchmark sets instances, improving average previous from literature solving first time open instances. Summary Contribution: We address (2D-BPP), 2D-BPP difficult generalization standard one-dimensional problem, has been widely studied past enriched developed extensively tested most well-known literature, contains 500 well, upon algorithms, analyzed detail several configurations before obtaining best one discussed insights analysis manuscript.