I think you should give more information about the relationship between productivity and hours worked. It is too difficult to understand your position.
Saying the relationship is not linear does not tell us what you think the relationship is.
My experience in my own area (software development) is that above working 8h/day people quick start getting chronically tired and tired people make more bugs and more incorrect design decisions, which have to be fixed which is something that consumes far more work than doing things right in the first place - in other words, tired people, alongside doing the work they’re supposed to do, also unwittingly create additional work that needs to be done. As the hours worked per day goes up, this effect quickly eats up the gains from working more hours a day and eventually you’re actually producing less in overall than you would working fewer hours a day.
Whilst were the sweet spot is varies from person to person, in my experience in my area 10h/day is too much for just about everybody and 13h/day would be insane.
On the other directing you get a reverse effect were you lose work done from fewer hours being worked but you gain some per-hour productivity from being rested that increases work being done. Clearly at 0h/day overall productivity is zero so there must be a point somewhere in there were the losses from fewer hours worked exceed the gains from higher productivity per-hour. Further, I have the impression that productivity gains from being rested actually plateau - as in, you can’t really get more rested and productive than a certain level.
As with the other one, I also think it varies from person to person, but I’m less experienced with working shorter hours than working longer hours so don’t really know were the sweet spot would be.
Keep in mind that all this is for long term practicing of a schedule, not for, say, people being very tired from working long hours and then switching to working short hours to rest. Recovery from overwork is a whole different ball game and in my experience the fastest way to recover and get back to maximum rest and hence productivity is to just take one (or more) whole days off work, rather than reducing hours worked per day.
I think you should give more information about the relationship between productivity and hours worked. It is too difficult to understand your position.
Saying the relationship is not linear does not tell us what you think the relationship is.
My experience in my own area (software development) is that above working 8h/day people quick start getting chronically tired and tired people make more bugs and more incorrect design decisions, which have to be fixed which is something that consumes far more work than doing things right in the first place - in other words, tired people, alongside doing the work they’re supposed to do, also unwittingly create additional work that needs to be done. As the hours worked per day goes up, this effect quickly eats up the gains from working more hours a day and eventually you’re actually producing less in overall than you would working fewer hours a day.
Whilst were the sweet spot is varies from person to person, in my experience in my area 10h/day is too much for just about everybody and 13h/day would be insane.
On the other directing you get a reverse effect were you lose work done from fewer hours being worked but you gain some per-hour productivity from being rested that increases work being done. Clearly at 0h/day overall productivity is zero so there must be a point somewhere in there were the losses from fewer hours worked exceed the gains from higher productivity per-hour. Further, I have the impression that productivity gains from being rested actually plateau - as in, you can’t really get more rested and productive than a certain level.
As with the other one, I also think it varies from person to person, but I’m less experienced with working shorter hours than working longer hours so don’t really know were the sweet spot would be.
Keep in mind that all this is for long term practicing of a schedule, not for, say, people being very tired from working long hours and then switching to working short hours to rest. Recovery from overwork is a whole different ball game and in my experience the fastest way to recover and get back to maximum rest and hence productivity is to just take one (or more) whole days off work, rather than reducing hours worked per day.