Combinatorial optimization (CO) has proven to be a very helpful approach for addressing test assembly issues and for providing solutions. Furthermore, CO has been applied for several test designs, including: (1) for the development of linear test forms; (2) for computerized adaptive testing and; (3) for multistage testing. In his seminal work, van der Linden (2006) laid out the basis for using linear models for simultaneously assembling exams and item pools in a variety of conditions: (1) for single tests and multiple tests; (2) with item sets, etc. However, for some testing programs, the number and complexity of test specifications can grow rapidly. Consequently, the mathematical representation of the test assembly problem goes beyond most approaches reported either in van der Linden’s book or in the majority of other publications related to test assembly. In this presentation, we extend van der Linden’s framework by including the concept of blocks for test specifications. We modify the usual mathematical notation of a test assembly problem by including this concept and we show how it can be applied to various test designs. Finally, we will demonstrate an implementation of this approach in a stand-alone software, called the ATASolver.

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