The thermo-economic objective function of a heat transformer may include other objective functions such as the coefficient of performance and specific heat pumping load. It is defined as the heat-pumping load divided by the total cost per unit time and its expression is derived from the general cycle model of an irreversible heat-transformer. The general objective function is used to analyze the thermoeconomic and thermodynamic optimum performance of a heat transformer affected by multi-irreversibilities. The bounds of some important parameters are determined. The problem of how to choose optimally these parameters are discussed. The results obtained here can provide some new theoretical guidance for the optimal design and operation of heat transformers and heat engines. (c) 2004 Elsevier Ltd. All rights reserved.