Return on investment (ROI) is an economic evaluation that seeks to justify investment made (in an information service) in terms of the gains or losses (to the organisation) that might be attributed to the investment. (Urquhart and Turner, 2016).
It is a complex method that ideally needs the expertise of an economist. It has been used in large scale studies, most notably in the public library sector (Aabo, 2009).
There are studies in academic library sectors. Across the board the return is similar. For every $1 invested in the library $4-$5 are returned. This suggests that similar returns may be possible in other sectors (Aabo, 2009; Brettle and Maden, 2016).
One of the largest UK studies relates to the British Library. It suggested that the British Library delivers £5 for every £1 invested (Tessler, 2013).
Jemison et al (2009) provides an example and some tools of its use in a hospital library in the US.