A restriction and feasible direction algorithm for a capacity expansion problem

This paper examines the problem of optimally expanding existing capacity in order to meet an expected load in the context of an electric utility. A pre-optimization (Phase I) analysis is presented in order to easily determine (a) the capacities of existing equipments which will be used at an optimal solution; (b) the optimal (nonnegative) capacities of a subset of the new equipments to be purchased, and (c) a good quality starting solution. Having thus restricted a part of the solution to its optimal value, the problem is transformed into one of minimizing a convex, differentiable function, subject to a single generalized upper bounding constraint along with nonnegativity restrictions. An efficient specialization of a feasible directions algorithm (Phase II) is presented to solve this problem. The algorithm is versatile in that it provides a preview of whether or not all existing equipment capacity will be used in the light of available equipments, and which new equipments may be used in the optimal expansion plan. The algorithm can also solve the problem which enforces the use of all existing equipment capacity. Furhtermore, Phase I, which is the principal part of this algorithm, provides the user with insightful information. A numerical problem is analyzed to illustrate the effectiveness of the procedure.