Optimal assembly of tests with item sets

Six methods for assembling tests from a pool with an item-set structure are presented. All methods are computational and based on the technique of mixed integer programming. The methods are evaluated using such criteria as the feasibility of their linear programming problems and their expected solution times. The methods are illustrated for two item pools with a set structure from the Law School Admission Test (LSAT). The methods are:(1) simultaneous selection of items and sets;(2) simultaneous selection with pivot items;(3) all items per set selected;(4) decision variables for subsets (power set approach);(5) two-stage selection; and (6) two-stage selection (alternative version).