The lexicographic bi-criteria combinatorial food packing problem to be discussed in this paper is described as follows. Given a set
I = {
i |
i = 1, 2, . . . ,
n} of current
n items (for example,
n green peppers) with their weights
wi and priorities
γi, the problem asks to find a subset
I' (⊆
I) so that the total weight Σ
i∈I' wi is no less than a specified target weight
T for each package, and it is minimized as the primary objective, and further the total priority Σ
i∈I' γi is maximized as the second objective. The problem has been known to be NP-hard, while it can be solved exactly in
O(
nT) time if all the input data are assumed to be integral. In this paper, we design a heuristic algorithm for the problem by applying a data rounding technique to an
O(
nT) time dynamic programming procedure. We also conduct numerical experiments to examine the empirical performance such as execution time and solution quality.
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