IRT test assembly using network-flow programming

The use of mathematical programming techniques to generate parallel test forms with passages and item characteristics based on item response theory was investigated, using the Fundamentals of Engineering Examination. The problem of creating one test form is modeled as a network-flow problem with additional constraints. This formulation is then used in a heuristic assembly of several parallel forms. The network-flow problem is solved with a special-purpose combinatorial polynomial algorithm. The non-network constraints are handled using Lagrangian relaxation and heuristic search techniques. From an item bank with almost 1,100 items, four parallel test forms with 157 items each were generated in 3 minutes. The results of the mathematical programming approach were compared with human-generated forms. It was concluded that the mathematical programming approach can produce test forms of the same quality as those produced entirely by human effort.