A controller for equipment obtains utility rate data indicating a price of one or more resources consumed by the equipment to serve energy loads. The controller generates an objective function that expresses a total monetary cost of operating the equipment over an optimization period as a function of the utility rate data and an amount of the one or more resources consumed by the equipment at each of a plurality of time steps. The controller optimizes the objective function to determine a distribution of predicted energy loads across the equipment at each of the plurality of time steps. Load equality constraints on the objective function ensure that the distribution satisfies the predicted energy loads at each of the plurality of time steps. The controller operates the equipment to achieve the distribution of the predicted energy loads at each of the plurality of time steps.