Duplex and quasi-duplex operations in automated food packing systems

In this paper, we deal with duplex and quasi-duplex operations in automated food packing systems known as so-called automatic combination weighers. A typical food packing system possesses n weighing hoppers. Some amount of foods is thrown into each hopper, and it is called an item. In a duplex operation, two disjoint subsets I\´ and I" are simultaneously chosen from the set I of current n items to produce two packages of foods, while in a quasi-duplex operation, I\´ is first chosen from I and then I" from I - I\´. The duplex food packing problem has been formulated as a lexicographic bi-criteria combinatorial optimization problem, and shown in theory to be solved in O(nT²) time, where T is an integer denoting the target weight for each package. In this paper, we implement a naive and an improved versions of the O(nT²) time algorithm, and examine their execution times by conducting numerical experiments.We also report the empirical performance of the quasi-duplex operation comparing with the duplex operation.