Some general procedures for optimizing energy systems have previously been presented. However, it is practically difficult to obtain an optimal design of thermodynamic systems that have several system parameters. The optimization is considered at three levels: synthesis (configuration), design (component characteristics), and operation. In this paper, the syntheses of two absorption heat pump systems are evaluated and their design/operation optimization is performed efficiently based on an energy-utilization diagram (EUD) for performance improvement. Cycle models of an absorption heat pump system, including an absorber heat exchanger (AHX) and a solution heat exchanger (SHX), are constructed. These models consider exergy destruction caused by heat transfer and pressure loss. The exergy analysis is performed to evaluate the system performance, and an EUD is drawn to evaluate the margins for improvement. The design parameters and operating points are improved for reducing the exergy destruction in the components where dominant exergy destruction occurs, based on an EUD. Before improvements, COP and exergy efficiency are higher in the SHX cycle, while the margin for improvement is larger in the AHX cycle. In the absorber, exergy destruction is reduced by adjusting the operating point to make the temperature slopes at the hot and cold sides coincide. In other components, exergy destruction is reduced by adjusting the design parameters to improve the heat transfer performances. The results show that exergy efficiency is improved by the distribution of exergy destruction of each component. After these improvements, COP is higher in the SHX cycle, while exergy efficiency is higher in the AHX cycle. It is concluded that we can efficiently realize the design/operation optimization of a thermodynamic system using an EUD. This is because an EUD presents both exergy destruction and margin for improvement at the components comprehensively, as well as the operating point of the system.