A Requirement for the Number of Items in a Package Produced by Multi-headWeighers

摘要

A subset selection problem from a finite set of items is considered, which arises in automated packaging systems, so-called multi-head weighers. Given a finite set of items with their integral weights, the problem asks to find a subset of the items so that the total weight of chosen items is no less than an integral target weight, and it is also made as close to the target weight as possible. When discrete items (e.g., green peppers) are given, the packaging quality may depend on the cardinality of a selected subset, i.e., the number of chosen items in a package, as well as the total weight of them. A cardinality constraint is imposed on the subset selection problem to be discussed in this paper, where the cardinality of a selected subset is allowed to be either a prescribed positive integer or it plus one at most. In this paper, a pseudo-polynomial time algorithm is designed to solve the problem under an assumption on the range of item weights. Numerical experiments are also conducted to demonstrate the performance of the proposed algorithm on the cardinality of a selected subset, and the results are reported.