What would be the best mathematical approach to devise a payment distribution method among three people for two separate billable services and if one of the three people did not use the services for the full billable period?
For example Service A had a total cost of 120 dollars , Service B had a total cost of 65 dollars. Service A had a total billing day cycle of 31 days, Service B had a total billing day cycle of 33 days. Out of the 3 people, only 1 used Services A and B for a total of 15 days, where as the other two individuals used Services A and B until the end of the billing cycle.
Would the best approach be splitting the cost in the following manner:
((days used / total days) * (total cost) / 3 people))
For that 1 person of 15 days:
Service A: ((15 / 31) * (120) / 3) = 19.35
Service B: ((15/33) * (65) / 3) = 9.85
Or
((Days used per individual / total days for all individuals) * total cost)
Service A: (15 / (15+31+31)) = 23.38
Service B: (15 / 15+33+33) = 12.04
Which of the two methods is better to use in terms of a more fair distribution?
The answer depends on how the billable service is charged. If the service has a fixed daily price independent of use (for example - unlimited internet at price 3.87 per day), then the first method is probably the fairest. But if the service is charged by amount of 'stuff' used (for example gas used for cooking in a house at fixed price per kJ equivalent) and the three people each use similar amounts when they are cooking, then the second method is more reasonable.