Absorption refrigeration cycle (ARC) is a high-efficiency energy cycle for heat recovery from middle- and low- temperature heat sources in term of generating cold utility. ARC is utilised to the best advantage especially in heat exchanger networks (HENs) which have waste heat and refrigeration demand. In this work, a synthesis method is proposed to make the most effective heat management design of HEN with ARCs incorporated. A stage-wise superstructure is presented to integrate the generation and evaporation processes of ARCs within HEN where hot process streams provide heat to drive generators, and then are refrigerated to target temperatures by the evaporators of ARCs. Potential matches between ARCs and process streams are given in the superstructure to present the topological structure of coupling. Furthermore, the operating condition of ARC which refers to heat source temperature and evaporation temperature in this work is optimized simultaneously according to their cooperating influence on the coefficient of performance (COP). The optimal design purpose is realized via a mixed integer non-linear programming (MINLP) model formulated towards the objective of minimum total annualized cost (TAC). Finally, a case study is illustrated to demonstrate the application of the proposed method, the mutual relations among characteristics of process streams, COP, the structure of HEN with ARC incorporated and TAC are analysed, and the results show superiority in rational utilisation of energy and reduction of economic cost.