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Empirical Performance of Lexicographic Bi-criteria Solutions during an Operating Run of Repetitive Packaging by a Combinatorial Weigher

Last modified: 2017-02-21

#### Abstract

In this paper, a lexicographic bi-criteria combinatorial optimization problem arising in actual food packaging equipments and its solutions are considered. In each packaging operation, a set I = {i | i = 1, 2, . . . , n} of current n items (for example, n green peppers) with their weights wi and priorities pi , and a target weight t of a package are given. Then the problem asks to find a subset I ′ ⊆ I so that the total weight ∑ i∈I ′ wi is minimized as the primary objective, meeting the target weight constraint ∑ i∈I ′ wi ≥ t, and the total priority ∑ i∈I ′ pi is maximized as the second objective. Such a problem is repeatedly solved during an operating run of the food packing system, in which a large number of packages are produced one by one. The priority of an item is defined to be the duration of the item in the food packing system, and it is expected to avoid the frequent occurrence of items with longer durations. In this paper, all input data are assumed to be integral, and the effectiveness of the lexicographic bi-criteria solutions in an operating run is empirically observed by means of an O(nt) time exact algorithm for the food packing problem.

#### Keywords

Mechanical; Information

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