Energy Savings and Industrial Competitiveness Act This bill revises a variety of programs to encourage energy efficiency in buildings, industry, the federal government, and certain appliances, including by: requiring states and Indian tribes to measure their compliance with certain residential and commercial building energy codes; requiring the Department of Energy (DOE) to provide grants for establishing building training and assessment centers at institutions of higher education; requiring DOE to establish a process to recognize schools for implementing energy efficient and renewable energy projects; directing DOE to carry out an industry-government partnership program to research, develop, and demonstrate new sustainable manufacturing and industrial technologies and processes; establishing a Supply Star program within DOE to identify and promote practices, recognize companies, and recognize products that use highly efficient supply chains that conserve energy, water, and other resources; requiring DOE to establish rebate programs concerning energy efficient electric motors or transformers; revising requirements concerning the energy performance of federal buildings, certification under the Energy Star Program, certification of green buildings, and energy efficiency in federal real estate transactions and programs; and requiring the Department of Housing and Urban Development to establish a demonstration program for energy and water conservation improvements at multifamily residential units.