Recent advances in micro-computer technology have made possible the practical application of convex programming algorithms such as used in the simplex methods, the out-of-kilter method, Beale's method, the supporting plane methods, the ellipsoidal methods, Gomory's method, and the branch and bound methods to the optimization of construction scheduling problems as defined by the critical path method. These algorithms have been adapted and coded with the IBM BASIC computer language for the solution of problems involving the minimization of schedule overall costs, total man count, and direct supervision costs to demonstrate the feasibility and practicality of the methods.