Three related methods are presented for determining the least-cost generating capacity investments required to meet given future demands for electricity. The models are based on application of large-scale mathematical programming decomposition techniques. In the first method, decomposition techniques are applied to linear programming models such as those presented by Anderson (Bell Journal of Economics, Spring 1972). An important result is that the subproblems, representing optimal operation of a set of plants of given capacity in each year, can be solved essentially by inspection. In the second method, decomposition is applied to an equivalent non-linear programming model, with the same result that the subproblems are very simple to solve. The third method extends the second to include the probabilistic simulation technique of Baleriaux and Booth (IEEE Transactions on Power Apparatus and Systems, Jan.-Feb., 1972), which determines the optimal operating costs when plants can fail randomly. Though the model is non-linear, the subproblems involving the probabilistic simulation can be solved without using non-linear programming.Research supported by the Energy Research and Development Administration through Contract 421072-S with Brookhaven National Laboratory and by the U.S. Army Research Office (Durham) under Contract DAAG29-76-C-0064.