Modeling Fatigue

[Cheryl and Bill Harris]

Kevin,

On Tue, 14 Dec 1999 kevin.a.agatstein@us.arthurandersen.com wrote:

> To account for the fact that workers may be less productive the sixth forty hour
> week versus the fourth, I hypothesize one could have cumulative overtime hours
> drive productivity, as opposed to workweek (overtime). I further speculate that
> one could also smooth the cumulative overtime to account for the delay between
> working long hours and "getting tired." Is this a valid approach to solving
> this problem? Does anyone one know of a study, anecdote, or data which supports
> or refutes the use of cumulative overtime versus workweek as a driver of
> fatigue?

Well, I know that, when Ive had to work very long hours for a very long
time, Ive gotten increasingly stressed because things at home (normal
upkeep, relationships, etc.) begin to decay after a while. For a simple
example, the grass grows (linearly?) with time. I can maybe avoid cutting
it for 10 days, but after 2 or 3 weeks its getting more than a bit
unsightly. When thats happening to multiple things simultaneously,
stress begins to build. That wears on productivity.

Maybe thats a way out of your dilemma. Dont estimate the type of curve
you expect and then look for a suitable structure; find a mechanism (such
as, but probably better than , the grass growing) that causes the
effect.

Hope that helps.

Bill
--
Bill Harris 3217 102nd Place SE
Facilitated Systems Everett, WA 98208 USA
mailto:bill_harris@facilitatedsystems.com phone:(425) 338-0512

[Bruce Campbell]

Kevin,

The iThink program and manuals have an example model of "burnout" which
answers your question.

Essentially, the extra hours each week contribute to a Burnout stock.
The longer the period of excess hours, the greater this stock. The value
of this stock is then used to calculate the loss of productivity. This,
then, allows for your problem of the 6th week of 60hrs creating a
greater loss to productivity than the 4th week.

You could also include the effects of annual leave, or reduced working
hours, which reduces the burnout stock (make sure the flow to burnout is
bi-directional).

I gave this problem to a class last year. One student was very
interested in it. At the time she was 8 months pregnant, working full
time at a job where the culture required regular unpaid overtime and was
trying to complete her course. She understood the problem! She also
missed the final exam due to burnout.

Regards,

Bruce Campbell

--
Bruce Campbell
Joint Research Centre for Advanced Systems Engineering
Macquarie University 2109
Australia

E-mail: Bruce.Campbell@mq.edu.au
Ph: +61 2 9850 9107
Fax: +61 2 9850 9102

[Keith Linard]

1. My experience in construction project management (many years back)
working day labour gangs 10 hrs per day x 6 days per week indicated
virtually no drop in overtime or increase in rework in the first 2 weeks.
Thereafter there was a steady increase in absenteeism (on Monday), a
decrease in productivity and an increase in rework. Net productivity
probably bottomed out after about 6 weeks. A reduction of pressure over 2
to 3 weeks would result in a rebound (not necessarily 100%) in
productivity. Anecdotal evidence in the construction industry in the
literature would seem to support this. Subsequent experience in the
bureaucracy would suggest a similar pattern, although generally experienced
staff will work with little fall in productivity for about 4 to 5 weeks
straight. This, of course, ignores all other factors and simply relates
productivity & working hours. Especially in the service sector my
experience suggest that excessive working hours for staff is more a
reflection of managerial incompetence (managers getting involved in task
activity rather than in managing resources&workloads) and poor personal
time management (which is likely to be causally related to poor management
oversight). If this is the case then we have multiple causal relationships
... lousy management fostering poor attitudes to quality ... fostering poor
morale etc etc etc

How to model the falling productivity over time ... One (simplified)
approach is to set up a boolean control stock, e.g.
Moving_Average_Weeks_Over_60 as, say, a 6 level array. Input at
Moving_Average_Weeks_Over_60(1) is (say) Working_Hours_Per_Week >= 60.
Output is the value of Moving_Average_Weeks_Over_60(6).
ARRSUM(Moving_Average_Weeks_Over_60) is then your input to
Effect_of_Moving_Average_Weeks_Over_60_ON_PRODUCTIVITY. The graph might
show zero effect if the value of Moving_Average_Weeks_Over_60 is 1 or 2,
and increase from a small effect at 3 and asymptoting at 6.

Keith Linard
Australian Defence Force Academy
From: Keith Linard <k-linard@adfa.edu.au>

[kevin.a.agatstein@us.arthurander]

Dear SD Community,

I am attempting to build a project model which fatigue is playing a significant
role in productivity reduction. (Some of you may be feeling this right now as
we scramble to get things done by the upcomming vacation and / or exams). As a
starting point I used Jim Hiness Fatgue molecule, equations below, which treat
fatgue as a smooth of overtime.

Effect of fatigue on PDY = Effect of fatigue on PDY f(Fatigue)
Units: dmnl
Effect of fatigue on PDY f ( )
Units: dmnl
Fatigue = INTEG(GettingFatigued,1)
Units: Fraction
GettingFatigued = (Overtime - Fatigue) / TimeToGetFatigued
Units: Fraction / Month
Overtime =
Units: Fraction
TimeToGetFatigued =
Units: Month

If I am interpreting this formulation correctly, a sudden increase in overtime
above the norm will have some effect on productivity, and this effect will be
approached asymptotically. What troubles me about the formulation is that
overtime is not cumulative. For example, neglecting the transient effects of
reaching the goal, the productivity reduction of the fourth 60 hour week is the
same as the sixth 60 hr week. I am not certain I want to model this assumption.

To account for the fact that workers may be less productive the sixth forty hour
week versus the fourth, I hypothesize one could have cumulative overtime hours
drive productivity, as opposed to workweek (overtime). I further speculate that
one could also smooth the cumulative overtime to account for the delay between
working long hours and "getting tired." Is this a valid approach to solving
this problem? Does anyone one know of a study, anecdote, or data which supports
or refutes the use of cumulative overtime versus workweek as a driver of
fatigue?

Warmest regards,
Kevin Agatstein
kevin.a.agatstein@us.arthurandersen.com

["Jim Hines"]

The **intent** of the fatigue molecule is to do what Kevin describes. The
table function shows the maximum effect of working, any given amount of
time - say 60 hours per week. After working a single day at that rate one
would not feel very fatigued, of course. But, after working, say, three
months of 60 hour weeks, the average person finally would be as fatigued as
he would get from working 60 hour weeks. (In this case the time constant on
the smooth would be three months). Now, if you move up to 80 hour weeks,
the average worker will get even more fatigued, but again the additional
fatigue will take time to build up.

The molecules are intended to be a sketch of a good formulation, a source of
inspiration. Someone of Kevins caliber will likely tailor it to a specific
situation. (Kevin, if you do develop some neat alternatives, please send
them to me, I will fold them into the molecules, with proper attribution, of
course).

On the other hand the molecules are not intended to be **bad**
formulations - so if there is a problem here, let me have it! Another
purpose of the molecules is to get common modeling wisdom out on the table
so that we all can improve on it.

One final note: This particular formulation is interesting for another
reason beside the one that Kevin flagged. In the formulation, fatigue is
just a smooth of overtime. A common first impulse would be to run overtime
through a table function to get "indicated fatigue", which would be mesured
on some made-up scale where 1 might represent being "totally fatigued" and
"0" would represent being totally rested. Indicated fatigue would then be
be smoothed to get fatigue. And then that fatigue would go through another
table function to affect productivity. The problem would then come when
the modeler wanted to actually formulate the table functions. First shed
need to find out how a 60 hour week translated onto her new fatigue scale.
Then she would need to translate from the fatigue scale into the effect on
productivity. No one could do that. Its much easier to ask a client,
"what is the ultimate impact of working 80 hour weeks, week after week;
Whats the ultimate impact of working 60 hours a week, week after week" etc.
The modeler would have a very good chance of finding experienced managers
able to answer that question. And thats the strategy taken by this
formulation.

There is a general pattern here: Whenver you take two or more table
function to get from a "real" variable (like overtime) to an effect that you
care about (like the effect on productivity) try to eliminate all but one
table function.

One final, final note: There is a high liklihood that I learned this
formulation at Pugh Roberts. Naturally, if Kevin has found a problem with
the formulation, then Id have to say that I learned it from .... Just
kidding: Any flaws are from me.

Regards,
Jim
From: "Jim Hines" <jimhines@interserv.com>