Cornwallis
What may help, is for the rostering/crewing manager to speak with other airlines rostering/crewing managers and to visit their departments to see how they run their show. Take a look at the computer systems they use and discuss their scheduling agreements.
Some airlines may not want to discuss some sensitive commercial points, but in my time I have seen airlines visit other airlines departments and not just rostering and crewing.
First stop should be TCX and FCA both appear to be doing well. They use AIMS and have a scheduling agreement.
Just my thoughts.