The construction of parallel tests from item response theory (IRT) based item banks is discussed. Tests are considered parallel whenever their information functions are identical. After the methods for constructing parallel tests are considered, the computational complexity of 0-1 linear programming and the heuristic procedure applied are discussed. Two methods for selecting parallel tests in succession (sequential test construction) are formulated. The first uses a non-partitioned item bank (Method 1), and the second uses a partitioned item bank (Method 2). Two methods are also reviewed for simultaneous test construction, one for non-partitioned item banks (Method 3) and one for partitioned item banks (Method 4). A heuristic procedure is used for solving these 0-1 linear programming problems. A simulation study compared these methods using two item banks, each consisting of 100 items. Satisfactory results were obtained, both in terms of the amount of central processing unit time needed and the differences between the information functions of the parallel tests selected. It was concluded that when the Rasch model fits the items, sequential test construction methods are preferable. For the three-parameter model, the use of Method 1 is inappropriate. Three tables give the results by different methods. (SLD)