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In this paper, a combinatorial optimization model of mixture packaging of two types of items is treated, which arises in actual packing systems, so-called multi-head weighers. The primary objective is to minimize the total weight of chosen items for a package under the condition that the total weight must be no less than a specified target weight. For a package to be produced, the weight sum of chosen items of each type must be no less than a prescribed necessity minimum. In this paper, a heuristic algorithm is designed for the problem of minimizing the total weight, and for a given positive real e, the performance factor is shown to be (1+e).

Performance of a Heuristic Total Weight in Combinatorial Mixture Packaging of Two Types of Items