A mixed integer programming model for multiple stage adaptive testing

The last decade has seen paper-and-pencil (P&P) tests being replaced by computerized adaptive tests (CATS) within many testing programs. A CAT may yield several advantages relative to a conventional P&P test. A CAT can determine the questions or test items to administer, allowing each test form to be tailored to a test taker's skill level. Subsequent items can be chosen to match the capability of the test taker. By adapting to a test taker's ability, a CAT can acquire more information about a test taker while administering fewer items. A Multiple Stage Adaptive test (MST) provides a means to implement a CAT that allows review before the administration. The MST format is a hybrid between the conventional P&P and CAT formats. This paper presents mixed integer programming models for MST assembly problems. Computational results with commercial optimization software will be given and advantages of the models evaluated. Published by Elsevier B.V.