A model and heuristic for solving very large item selection problems

Abstract

A model for solving very large item selection problems is presented. The model builds on previous work in binary programming applied to test construction. Expert test construction practices are applied to situations in which all specifications for item selection cannot necessarily be met. A heuristic for selecting items that satisfy the constraints in the model also is presented. The heuristic is particularly useful for situations in which the size of the test construction problem exceeds the limits of current implementations of linear programming algorithms. A variety of test construction problems involving real test specifications and item data from actual test assemblies were investigated using the model and the heuristic. Index terms: expert systems, heuristic algorithms, item response theory, linear programming, mathematical programming, test assembly, test construction, test design.