In this work, a novel hybrid method is proposed for the global solution of an infinite collection of instances of the minimum total annualized cost (TAC) problem for a series of gas compressors and coolers that brings a gas from a given pressure and temperature to a specified final pressure and the same temperature. The gas is considered to possess a constant compressibility factor, and a constant, ideal gas, constant pressure, heat capacity. The collection of TAC problem instances considered is parametrized by the overall compression ratio. The proposed method combines the TAC problems first and second order necessary conditions of optimality with interval analysis, to determine converging upper and lower bounds to the globally optimal solution and associated optimal solution vector components, for all considered instances of the TAC problem. Two case studies are presented to illustrate the novel solution method and the impact of economies of scale on the global optimum.