A Method for Determining the Maximum Number of Nonoverlapping Linear Test Forms That Can Be Assembled From an Item Pool (CT-03-04)
by Ronald Armstrong, Rutgers Business School, Newark/New Brunswick, Rutgers University and Dmitry Belov, Law School Admission Council.

Executive Summary

The last two decades have seen an increased use of automated test assembly methods at testing agencies. These methods save hundreds of hours of personnel time. A test form assembled by a computer can be assured to satisfy all test specifications. While the review of the form by specialists may still be desirable, the review generally entails a small number of alterations to account for constraints not coded in the database.
The problem of assembling a linear test can be stated as a mixed integer programming problem. Several test assembly methods exist to obtain the (approximate) solution to the problem. The most straightforward approach is to state the mathematical model formally, and then solve the resulting problem with a commercial software package designed for this general class of problems. This approach is taken here.

The assembly of a single linear test form has become a basic task with most item pools and assembly approaches. However, the assembly of the maximum number of nonoverlapping test forms from an item pool has not been (to our knowledge) successfully solved. Knowing the maximum number of linear test forms supported by an item pool assists with monitoring the pool and guides the development of new items. The focus of this paper will be the use of a mixed integer programming code to solve a sequence of problems that will, under stated conditions, provide the maximum number of nonoverlapping linear test forms from an item pool. When it cannot be proven that the maximum number of nonoverlapping forms have been assembled, methods to obtain an upper bound and a lower bound for the maximum will be discussed.
 

A Method for Determining the Maximum Number of Nonoverlapping Linear Test Forms That Can Be Assembled From an Item Pool (CT-03-04)

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