This work compares two optimization approaches for combined cooling, heating and power (CCHP or Tri-generation) energy systems scheduling. Both approaches are developed through dedicated software codes and are based on simulation models capable of evaluating of the best operating strategy (both economically and energy-wise) to run a given trigeneration plant while dealing with time-variable loads and tariffs. The simultaneous use of different prime movers operating in parallel is taken into consideration as well as their part load performance, the influence of ambient temperature and the usage of a heat storage system. Cooling may be generated through absorption chillers or electrically driven compression cycles. One of the models is heuristic and adopts an optimization strategy based on a multi-step approach: it simulates several cases according to a pre-defined number of paths, exploring the most reasonable operational modes and comparing them systematically. The other relies on a mathematical approach, based on a Mixed Integer Linear Programming (MILP) optimization model which has been developed in order to deal with more complex systems without the need of predefining a too large variety of operation paths. Results of the two models are compared against a test case based on real plant specifications, discussing their performance by the point of view of simulation capabilities, quality and accuracy of the optimization results (in terms of differences in energy and economic performance) and computational resources.