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 w i and priorities γ i , the problem asks to find a subset I (⊆ I) so that the total weight i∈I w i 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 i∈I γ i 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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