Germany has become one of the leading players in the transformation of the electricity sector, now having up to 42% of electricity coming from renewable sources. However, the transformation of the heating sector is still in its infancy, and especially the provision of industrial process heating is highly dependent on unsustainable fuels. One of the most promising heating technologies for renewable energies is power-to-heat, especially heat pump technology, as it can use renewable electricity to generate heat efficiently. This research explores the economic and technical boundary conditions regarding the integration of heat pumps into existing industrial thermohydraulic heating and cooling networks. To calculate the optimum design and control of heat pumps, a mixed-integer linear programming model (MILP) is developed. The model seeks the most cost-efficient configuration of heat pumps and stratified thermal storage tanks. Additionally, it optimizes the operation of all energy converters and stratified thermal storage tanks to meet a specified heating and cooling demand over one year. The objective function is modeled after the net present value (NPV) method and considers capital expenditures (costs for heat pumps and stratified thermal storage tanks) and operational expenditures (electricity costs and costs for conventional heating and cooling). The comparison of the results via a simulation model reveals an accuracy of more than 90%.