Linear programming models with 0-1 variables are useful for the construction of tests from an item bank. Most solution strategies for these models start with solving the relaxed 0-1 linear programming model, allowing the 0-1 variables to take on values between 0 and 1. Then, a 0-1 solution is found by just rounding, optimal rounding, or a heuristic. In most applications, the latter can be executed very rapidly. This paper uses the revised simplex method to solve the relaxed 0-1 linear programming method for test construction. The simplex method is modified such that the characteristics of test construction problems are taken into account. The modifications were implemented in the computer program LINPROG. Two item banks, each containing 450 items, were generated to determine if central processing unit (CPU) time was gained. Computational experiments showed a gain of CPU time for most modifications. Ten tables present the results for the modifications. (Author/SLD)