Incomplete identification models for group‐testable items

A set of items is called group‐testable if for any subset of these items it is possible to carry out a simultaneous test with two possible outcomes: “success,” indicating that all items in the subset are good, and “failure,” indicating a contaminated subset. In this article we compare two alternatives of purchasing group‐testable items in order to meet a demand of d good items. These two alternatives are (i) purchasing d good items from a 100% quality population with a relatively high cost per item, and (ii) purchasing N items, N>d, from a 100q% (0<q<1) quality population with a relatively low cost per item, group‐testing groups of fixed size m, and recording good groups until d good items are accumulated, where both N and m are decision variables. We present three models (of which two are probabilistic and one is deterministic) which are related to purchasing items by alternative (ii) and are costwise competitive with alternative (i).