Data banks with items calibrated under an item response model can be used for the construction of tests. Mathematical programming models like the Maximin Model are formulated for computerized item selection from a bank. In this paper, mathematical programming models based on the Maximin Model are proposed for the construction of weakly parallel tests. Numerical experiments were conducted to obtain an impression of the practicality of the approach using an item bank of 600 items from college placement mathematics examinations (520 items were from 13 previously administered American College Testing Assessment Program tests, and 80 were from the Collegiate Mathematics Placement Program). Six tests were constructed, and their test information functions were computed. The results demonstrate that tests constructed with the proposed models were near-optimal with respect to the Maximin criteria and were approximately weakly parallel. Five tables present information about the constructed tests. Four graphs illustrate the information functions. (Author/SLD)