On the Use of Equivalence Classes for Optimal and Sub-Optimal Bin Covering

Bin covering is an important optimization problem 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 collected into bins in such a way that the total value of each bin, as measured by the sum of its item values, is not lower than a target value. The optimization problem concerns maximizing the 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 a formulation of the bin covering that allows to find the true optimum for a rather large number of items, over 1000. Also presented is a suboptimal solution, which is compared to the true optimum and found to come within less than 10% of the optimum.