Vapor recompression heat pump-assisted distillation columns (VRC) have gained attention as a sustainable alternative for distillation process design. A variety of different VRC configurations have been proposed and analyzed by different researchers primarily based on their experience. The existing approach does not provide any insights into the economic viability of using VRC as an alternative to conventional distillation, nor does it identify the optimal configuration. This work proposes a novel systematic design methodology to determine the minimum achievable utility cost for a VRC process prior to design. The optimal VRC configuration for work and heat integration is obtained by effectively leveraging the existing Pinch Technology method for heat exchanger network design. Application of the proposed method for the separation of Propane/Propylene and Benzene/Toluene mixtures shows that VRC configurations with significantly lower utility costs can be obtained as compared to the existing configurations in the literature.