A detailed optimization model is presented for planning the short-term operation of combined cooling, heat and power (CCHP) energy systems. The purpose is, given the design of a cogeneration system, to determine an operating schedule that minimizes the total operating and maintenance costs minus the revenue due to the electricity sold to the grid, while taking into account time-varying loads, tariffs and ambient conditions. The model considers the simultaneous use of different prime movers (generating electricity and heat), boilers, compression heat pumps and chillers, and absorption chillers to satisfy given electricity, heat and cooling demands. Heat and cooling load can be stored in storage tanks. Units can have one or two operative variables, highly nonlinear performance curves describing their off-design behavior, and limitations or penalizations affecting their start-up/shut-down operations. To exploit the effectiveness of state-of-the-art Mixed Integer Linear Program (MILP) solvers, the resulting Mixed Integer Nonlinear Programming (MINLP) model is converted into a MILP by appropriate piecewise linear approximation of the nonlinear performance curves. The model, written in the AMPL modeling language, has been tested on several plant test cases. The computational results are discussed in terms of the quality of the solutions, the linearization accuracy and the computational time.