A mass exchange network (MEN), which consists of one or more mass exchangers, is a useful tool to realize pollution prevention in process industries. When a staged column is employed as a mass exchanger to synthesize a MEN, the number of trays must be rounded up to the next largest integer after obtaining an optimal design, which increases the capital cost. While designing a chemical process plant, when the capital cost increases, the operating cost should decrease. However, the operating cost was considered to be a fixed value in previous research even if the capital cost increased after rounding up the number of trays. Therefore, the total annual cost (TAC, including capital cost and operating cost) remained higher than the real optimal objective. To solve this problem, an integral function is added to the mathematical model to obtain the optimal MEN structure in this study. The application on two universal MEN synthesis mathematical models based on the Composition-Interval Diagram (CID) and stage-wise superstructure illustrate the practicability of the integral function. These modified models are applied to two examples of coke-oven gas sweetening and dephenolization of wastewater. The optimal results obtained in this study are found to be better in comparison to other works in the literature. This study demonstrates that the integral function can solve a series of MEN synthesis problems involving stage columns. Furthermore, a more accurate design scheme for MENS and a structure with lower TAC can be obtained by this function.