On the Use of Equivalence Classes for Optimal and Suboptimal Bin Packing and Bin Covering

Sabino Roselli, Fredrik Hagebring, Sarmad Riazi, Martin Fabian, Knut Akesson
2020 IEEE Transactions on Automation Science and Engineering  
Bin packing and bin covering are important optimization problems in many industrial fields, such as packaging, recycling, and food processing. The problem concerns a set of items, each with its own value, that are to be sorted into bins in such a way that the total value of each bin, as measured by the sum of its item values, is not above (for packing) or below (for covering) a given target value. The optimization problem concerns minimizing, for bin packing, or maximizing, for bin covering,
more » ... number of bins. This is a combinatorial NP-hard problem, for which true optimal solutions can only be calculated in specific cases, such as when restricted to a small number of items. To get around this problem, many suboptimal approaches exist. This paper describes formulations of the bin packing and covering problems that allows to find the true optimum for instances counting hundreds of items using general purpose MILP-solvers. Also presented are sub-optimal solutions that come within less than 10% of the optimum, while taking significantly less time to calculate, even ten to 100 times faster, depending on the required accuracy.
doi:10.1109/tase.2020.3022986 fatcat:oeevrcolazamfcttncn6qg6xqi