In this paper, we treat a lexicographic bi-criteria combinatorial optimization model of mixture packaging of two types of items, which arises in actual food packing systems, so-called multi-head weighers.The primary objective is to minimize the total weight of chosen items for a package, and the second objective is to maximize the total priority of them.The constraints are that the total weight mpu63zm/a must be no less than a given target weight, and that the weight sum of chosen items of each type must also be no less than a given necessity minimum.The weight of an item of each type is bounded by the necessity minimum from the above.
We show that a greedy heuristic solution with the total weight at most g5210t-p90 twice the minimum attains the total priority at least the conditionally maximum, which is an improved performance guarantee of greedy heuristic solutions for the lexicographic bi-criteria mixture packaging problem of two types of items.