IRT test assembly using network-flow programming

Ronald D. Armstrong, Douglas H. Jones, Charles S. Kunce

Research output: Contribution to journalArticle

22 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)237-247
Number of pages11
JournalApplied Psychological Measurement
Issue number3
StatePublished - Sep 1998

All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Psychology (miscellaneous)


  • Automated test assembly
  • Automated test assembly using passages
  • Certification testing
  • Item response theory
  • Network-flow programming
  • Optimal test assembly
  • Test construction

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