Lowest fare of the day or lowest logical fare as it was used to be called in our company is a waste of time and will not yield savings to the organisation. It is a cop out straegy that makes procurement feel like it is enforcing saving approach, but it doesn't and adds cost by the workforce spending hours calculating how they can get around it to end up on the airline they want. As others have mentioned, there are many ways around lowest fare.
The only way to save significant sums on large company corporate travel is to commit to a sole supplier with the only exception being where they literally do not fly to that destination or there isn't a flight within a 3 hour window of need to travel. Yes, there will be times when the preferred airline is more expensive, however at the end of the year the savings will be there, and your staff won't be spending an hour trying to work out how to get around the lowest fare problem.
What is needed is solid leadership around the change in policy.It won't work unless senior management lead the way. Rest assured that in the current environment people won't leave a company becuase of an airline choice. If they do, they should be pleasantly sent on their way. When we changed domestic carriers the excuses heard around why it was a bad idea were humorous. I even had one indicating that the 737s of the preferred airline were an hour slower to Perth than the A330's or 767s of the other.
Ulimately in an environment where employees coffee machines and fruit bowls are being eliminated is it right to stick with the more expensive airline when over 1 mill of savings are on the table with a disciplined sole supplier approach?
I was one of the biggest skeptics around the change. I had over 2 mill FF points on the previous airline, but after time and some good change management it made sense to me and most others in the company. Most people are now content and the preferred airline is doing a great job for us.