An operational planning problem for a cogeneration system is discussed under a complex utility rate structure which imposes demand charges due to total utility consumption over a specified period as well as demand and energy charges due to hourly utility consumption. Operational strategy of constituent equipment and contract demands for total utility consumption are assessed so as to minimize the operational cost over the period subject to energy demand requirement. This problem is formulated as a large-scale mixed-integer linear programming (MILP) one, and it is solved efficiently by a revised decomposition method for MILP problems with block angular structure. Through a numerical study on a gas engine-driven cogeneration system installed in a hotel or an office building, the effect of rate structure on operational strategy is clarified.