Hybrid heating system including: a heat pump water heating system; sensors, for measuring a system parameter; an input arrangement providing cost data pertaining to a first power cost for supplying power to the heat pump system, and to cost information pertaining to a second power cost for operating a conventional heating system; a processor storing criteria specifying when to operate the heat pump and conventional systems, the processor receiving and processing: cost data; cost information; system parameter data; flow information on a heat exchange system circulation arrangement, and heat pump system power consumption information and concurrently operating, upon demand, the heat pump system and a chiller system in opposite heating modes; wherein, when the chiller system operates in a cooling mode, the processor processes the cost data and information, system parameter data, and flow and power consumption information, and controls the systems based on the criteria.