From the standpoint of an energetically and economically efficient waste elimination, the design and operation of optimized incineration power plants with the cogeneration of electricity and heat has become today an important issue. Decision models developed to minimize the total costs associated with such systems only partially respond to the problems associated with the choice of configuration (synthesis), component design, and the operation of the waste incineration / cogeneration unit. In fact, the time factor which greatly affects certain key parameters such as the amount of wastes and the electrical and heating demands placed on the system (to name just two) renders the problem of synthesis, design and operation very complex. A thermoeconomic methodology and the results of an application of it to a waste incineration system with cogeneration and a gas turbine topping cycle are presented here as Part I of a series of two articles. The second article (Part II; Olsommer et al., 1999) presents details of the approach used to incorporate reliability and availability considerations into the methodology.