Originally it is the idea from Charnes, Cooper and Rhodes who did a brilliant job using Linear Programming Problem formulation for a non-linear efficiency problem.
You will find some of the links here of some interest. Depending on the number of DMUs, you have to formulate as much LPPs. Hence manual solution may be difficult considering that one has multiple inputs and multiple outputs,
A spreadsheet solver (LP solver in Excel) or the solver in Google spreadsheet can be used.
Some links are given here .