Item banks, large sets of test items, can be used for the construction of achievement tests. Mathematical programming models have been proposed for the selection of items from an item bank for a test. These models make automated test construction possible. However, to find an optimal or even an approximate optimal solution to a test construction model can be time consuming. This paper shows how test construction models, and in particular the Maximin Model, are solvable by the program MPSX/370 V2. This program offers the user several implementations of the branch-and-bound method, which can be used for solving test construction models. Several implementations are compared. The results show that test construction models are solvable in a practical amount of time if the user applies the options offered by the program in an intelligent way. An appendix describes the Extended Control Language (ECL) computer program. Five data tables and two figures are included. (Author/SLD)