In this paper, we deal with a f0od packing problem in an automated food packing system. The packing system has
n hoppers, where an item is thrown into each hopper. An integer weight
ui, and a priority γ
i are associated with each item
i, where any
wi is assumed to be bounded by an integer
wmax. Given a set
I of n items in the hoppers, the packing system chooses a subset
I' (⊂e;
I) of items, and puts them into a package with a specified target weight
B. After that, the packing system updates the set
I by taking the union of the remaining items in
I-
I' and new items thrown into empty hoppers. Repeating these operations, it makes a large number of packages one by one. In the packing system, an item may be left in a hopper for a long time until it is chosen. The priority γ
i is introduced to avoid such a situation, if possible. The packing problem is formulated as a lexicographic bi-criteria discrete optimization problem, where the first objective is to minimize Σ
i∈
Iu'
i such that Σ
i∈I'
wi≥
B must be satisfied, and the second is to maximize Σ
i∈
Iγ
i.In this paper, we propose an O (
n2wmax) time algorithm based on dynamic programming to the packing problem. We also examine the performance of the proposed approach by means of numerical experiments, and report the results.
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