ROI is equivalent to ROCE in a company. In a company context the ratio is called ROCE.
In divisions, the supplier of capital is the head office and RI ensures that a charge for the use of capital is made. In a company context, suppliers of capital are lenders and equity shareholders. The equivalent to RI would be EVA as a deduction is made at WACC for the capital employed (of course in EVA other adjustments are made also).