In optimal assembly of tests from item banks, linear programming (LP) models have proved to be very useful. Assembly by hand has become nearly impossible, but these LP techniques are able to find the best solutions, given the demands and needs of the test to be assembled and the specifics of the item bank from which it is assembled. However, sometimes even LP techniques do not offer an acceptable solution to the test assembler. Infeasibility occurs when the demands are contradictory. These contradictions may be rather complex, especially when stated in terms of LP models. Techniques are described that can solve these infeasibility problems in different manners. The objectives are twofold. First, the assembler is given a helping hand to identify the bottlenecks in the specifications of the LP model. Second, a solution is forced, such that the test assembler is always presented a test as close as possible to the original specifications. These objectives should be realizable both automatically and interactively with the test assembler.