An Approximation Scheme for a Packing Problem in Automatic Combination Weighers

Abstract

A combinatorial optimization problem of food packing in actual equipments, so-called automatic combination weighers, is treated. The primary objective of the food packing problem aims at the total weight of chosen items for a package as close to a specified target weight as possible. The food packing problem is NP-hard, while for a given real ε > 0, an O(n² /ε) time algorithm delivers the heuristic total weight at most (1 + ε) times the optimal total weight. Numerical issues of the O(n² /ε) time heuristic algorithm are discussed.