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.