Abstract
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 Σi∈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 Σi∈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.
