Among the options for industrial waste heat recovery and reuse which are currently discussed, heat pumping receives far less attention than other technologies (e.g. organic rankine cycles). This, in particular, can be linked to a lack of comprehensive methods for optimal design of industrial heat pump and refrigeration systems, which must take into account technical insights, mathematical principles and state-of-the-art features. Such methods could serve in a twofold manner: (1) in providing a foundation for analysis of heat pump economic and energetic saving potentials in different industries, and further (2) in giving directions for experimentalists and equipment manufacturers to adapt and develop heat pump equipment to better fit the process needs. This work presents a novel heat pump synthesis method embedded in a computational framework to provide a basis for such analysis. The superstructure-based approach is solved in a decomposition solution strategy based on mathematical programming. Heat pump features are incorporated in a comprehensive way while considering technical limitations and providing a set of solutions to allow expert-based decision making at the final stage. Benchmarking is completed by applying the method on a set of literature cases which yields improved-cost solutions between 5% and 30% compared to those reported previously. An extended version of one case is presented considering fluid selection, heat exchanger network (HEN) cost estimations, and technical constraints. The extended case highlights a trade-off between energy efficiency and system complexity expressed in number of compression stages, gas- and sub-cooling. This is especially evident when comparing the solutions with 3 and 5 compression stages causing an increase of the COP from 2.9 to 3.1 at 3% increase in total annualized costs (TAC).