Several techniques exist to automatically put together a test meeting a number of specifications. In an item bank, the items are stored with their characteristics. A test is constructed by selecting a set of items that fulfills the specifications set by the test assembler. Test assembly problems are often formulated in terms of a model consisting of restrictions and an objective to be maximized or minimized. A problem arises when it is impossible to construct a test from the item pool that meets all specifications, that is, when the model is not feasible. Several methods exist to handle these infeasibility problems. In this article, test assembly models resulting from two practical testing programs were reconstructed to be infeasible. These models were analyzed using methods that forced a solution (Goal Programming, Multiple-Goal Programming, Greedy Heuristic), that analyzed the causes (Relaxed and Ordered Deletion Algorithm (RODA), Integer Randomized Deletion Algorithm (IRDA), Set Covering (SC), and Item Sampling), or that analyzed the causes and used this information to force a solution (Irreducible Infeasible Set-Solver). Specialized methods such as the IRDA and the Irreducible Infeasible Set-Solver performed best. Recommendations about the use of different methods are given.
Huitzing, H. A., Veldkamp, B. P., Verschoor, A. J., & Verschoor, A. J. (2005). Infeasibility in automatic test assembly models: a comparison study of different methods. Journal of educational measurement, 42(3), 223-244. https://doi.org/10.1111/j.1745-3984.2005.00012.x