The minimum total annualized cost problem for a series of nonisentropic compressors and coolers that brings a gas with constant compressibility factor from a specified initial pressure and temperature to a specified final pressure and the same temperature is studied in this work. It is established analytically that at the global optimum, the cooler outlet temperatures are equal to the minimum allowable temperature. For constant heat capacity, constant compressibility factor gases, additional properties of the globally optimal compressor sequence are analytically established for the minimum operating cost case. The aforementioned properties permit development of a solution strategy that identifies the globally minimum operating cost. Several case studies are presented to illustrate the developed theorems and solution strategies. (c) 2014 American Institute of Chemical Engineers AIChE J 60: 4134-4149, 2014