**5. Mathematical Formulation**

The synthesis of the overall network is performed with a mathematical model in MINLP. The mass balances, heat balances, feasibility constraints, and formulas for device related and cost related calculations are all given to describe the characteristics contained in the superstructure. The model is decomposed into three parts for understanding: model for HEN synthesis, constraints for the utility system, and the objective function. Implementation of the model is also introduced.

As mentioned in problem statement, the given parameters in the model contain:


The notation for these parameters is listed in the Nomenclature section. The rest of the notations in the model indicate the variables that should be determined within model implementation. The binary variables (*zi*,*j*,*k*, *zcui*, *zhuj*,*k*,*n*, *zhusj*,*k*,*n*) indicate the existences of heat exchangers, determining the structure of the network, and the continuous variables (including inlet and outlet temperatures, stream flowrate, heat load, heat exchange area of each exchanger, quantity of generated steam and power, and cost results) refer to the operation and assessment aspects of the obtained network.
