Most of the fatigue science research talks about all the negative outcomes associated with fatigue. It usually sounds something like “if you don’t manage fatigue you will crash more planes, trains and automobiles”.
It is a little more difficult to find good science that shows a strong link between better fatigue management and positive outcomes. What I do is, I flip the literature around. If there is a causal link between fatigue and a negative outcome, it implies that you should be able to see a positive outcome if you reduce fatigue. With a flip, you can see that managing fatigue pays for itself in improved safety, health and performance metrics.
A flip I did a while ago showed that you can put $4 million back into your budget by improving the sleep of your 24/7 workforce. This tidy little ROI came from reducing sick leave by 28%. The link here was that people with sleep problems take more sick leave and the flip implies that if you improve their sleep, you reduce the expense of sick leave. Here’s the article: http://sleepanddreams.com/?p=2682
Here’s another good flip. Fatigued people have longer reaction times. Put a fatigued person in a car and send them down the road and what you would see is that they brake late and then hit the gas hard. This is because a fatigued person’s brain reacts too slowly and the driver does not realize they need to brake until they are too close to cars in front of them. Then it takes the fatigued driver’s brain longer to realize it is safe to speed up again, and, rather than becoming a slow moving obstacle, the driver puts the pedal to the metal to keep up with traffic speeds. Hard braking, then flooring it is very inefficient driving and it burns a lot more fuel than steady speed driving. Burning fuel costs money, sometimes a lot of money.
In a study of train operators they showed that fatigued operators use more heavy brake applications and less dynamic brake and throttle manipulations than alert operators. This style of train operation burns 9% more fuel and for one train route this resulted in $183,000 more fuel being burned annually by fatigued train operators than alert operators. Here’s the flip, by reducing fatigue you will improve operational efficiency and reduce fuel costs by 9%. This can put $183,000 back into your budget annually. Not a bad ROI.
Although this ROI flip came from research in railway operations, any industry that relies on people to efficiently use fuel would see a fuel savings by reducing fatigue. The ROI might not be 9% or $183,000 per year, it might be even greater!
 Dorrian, J., Hussey, F., Dawson, D. (2007). Train driving efficiency and safety: Examining the cost of fatigue. Journal of Sleep Research, 16, 1-11.