Operations - Producing and selling existing products using existing technologies at profit to the organization.
Innovation: Development of new products, features and processes
Industrial Engineering: Cost reduction of existing products and existing processes. Industrial engineering also examines new products and processes for cost reduction possibilities. But its role is long term - cost reduction over the life cycle of the product using learning curve effect, cost reduction technologies developed by outside agencies and focused periodic attempts to evaluate the products and processes for cost reduction opportunities.
George A. Taylor in his book "Managerial and Engineering Economy" expressed similar view when he said every executive has basically two roles. First role is maintaining standards and second role is improving standards. Improvement is reflected in innovation and industrial engineering. Maintaining standards is operations.