Rework Cycle Assignment problem

[John Wayne]

Hello Vensim Fanatics.
I am a student working on system dynamics looking for advice on a project.
I am replicating the task of an mit course which I will provide the link to https://ocw.mit.edu/courses/sloan-schoo ... 3_ass4.pdf and im currently on the first section A. I have replicated the model but unfortunately unable to find my models outputs believable. I have consulted websites such as this one http://systems-sciences.uni-graz.at/ete ... /work.html for advice on the equations and I believe my error/mistake in modelling occurs at the Work to do and maximum work rate variables. This is because the task states that the maximum work rate is 1 task per month and yet I have a potential work rate of 400 tasks per month. Please let me know how to solve this or whether there are existing models to gain inspiration from. Thank you!

[tomfid]

I think we'd have to see your model to make a diagnosis (you can attach an mdl file).

[John Wayne]

Here it is

[tomfid]

OK - I think your diagnosis is correct - the potential work rate is too high. Since this is a course, I'll offer just a hint first.

Your equation is:

Potential work rate=
Maximum work rate*Productivity*Staff Level
Units: Tasks/Month

This responds in the right direction, i.e. the work rate increases with increases in any of the inputs. The question is whether these should be combined multiplicatively. You might think of a simple task. Suppose you have a person locked in a room stuffing envelopes until they finish a stack of material. Adding a second person should double the work rate. Giving them coffee should increase productivity, and therefore the work rate, by x%. But for a fixed productivity and staff, would increasing the size of the stack make the work go faster?

[John Wayne]

Hello Tom, Thank you for your response.
I also meanwhile figured productivity is in the units tasks/person*months, and I think your analysis suggests that staff and productivity should be multiplied together but not Maximum work rate. I am currently conflicted since the unit: task/month can only be maintained if they are added or subtracted from each other and I am very unsure if that's the right thing to do.
Furthermore, in the explanation given it states that the employees work at a rate of at best 1 task per month. Therefore my thought process would be to have a potential work rate somewhere near 4 tasks per month. Please let me know if I have interpreted this wrong. Thanks again for the quick response.

[tomfid]

Good catch on the units issue.

There are some other functions that preserve units like addition and subtraction. You might consider the MIN function for example. https://en.wikipedia.org/wiki/Leontief_ ... n_function

[John Wayne]

Thank you Tom. I must say I did not consider any sort of function as an input for potential work rate but this makes a lot of sense.

[tomfid]

You're welcome. At the risk of beating it to death ...

Uses of MIN like this are a fairly common pattern. It also shows up here, for example: https://metasd.com/2019/11/the-importance-of-fonfoo/

It's easy to imagine hybrids. For example,

envelope stuffing = MIN( envelopes avail/min stuffing time, bob stuff rate + mary stuff rate )

Here, Bob and Mary are perfect substitutes, and therefore their stuffing rates contribute additively. But both are constrained by the availability of inputs.

+ and MIN() are extremes of a continuum of possibilities. The CES production function interpolates between them, getting close to the min function for low elasticity of substitution, and close to the sum for high elasticity. However, it's often a bit obscure.

A more transparent formulation might be something like:

work rate = Min( work avail/min task time, staff * productivity )
with
productivity = normal productivity * f( work avail/staff / (normal work per staff) )

In this way, you could capture an effect of work availability on work rate that isn't either/or, but includes effects like congestion of the work area or extra time needed to access the next task. None of this is needed for your exercise of course. Hope it works now!