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

Bin packing and bin covering are important optimization problems in many industrial fields, such as packaging, recycling, food processing. The problem concerns a set of items, each with its own value, that to be sorted into bins way the total value bin, measured by sum item values, is not above (for packing) or below covering) given target value. minimizing, for packing, maximizing, covering, number bins. This combinatorial NP-hard problem, which true optimal solutions can only calculated specific cases, when restricted small items. To get around this suboptimal approaches exist. article describes formulations allow finding optimum, instance, counting hundreds items using general-purpose MILP-solvers. Also presented come within less than 10% optimum while taking significantly time calculate, even ten 100 times faster, depending on required accuracy.