Just to add to Ralph's comments (which are all correct), having the programs installed locally will give negligible speed improvement. The biggest factor for speed is data transfer across the network. Having the programs on the network rather than local contributes to a far smaller percent of network traffic (and speed) once the programs are loaded.

So to echo Ralph, the Adagio programs and associated files should be installed on the network P drive, rather than 3 separate instances on local computers, to make sure the data file are locked properly. For example, you could have one person working on an invoice batch and a second person post it - not a desirable situation.