A New Computer Algorithm for Simultaneous Test Construction of Two-Stage and Multistage Testing

This paper discusses the simultaneous approach for test generation of two-stage and multistage tests from an item bank. However, most previous test generation problems involved binary programming models, and the efficiency of available solution algorithms is the major concern for these problems. Therefore, this study considers two important concepts on the solution process, i.e., alternative ways to formulate mathematical models and alternative solution algorithms. Based on these two concepts, this paper is two-fold. First, two binary programming models with a special network structure that would be explored computationally are presented for modeling these problems. The first model maximizes test information function at one specified ability point and the second model matches the target test information function at several specified ability points as closely as possible. Second, an efficient special-purpose network algorithm is then used to solve these two models. Hence, the test construction process tends to be improved in terms of both computational efforts and quality of tests. An empirical study shows the results in line with the above two criteria.