Originally posted by: qtbgo

Hi, there. In a staffing system, we have a demand curve which varies along time. And I defined a cumulative function to represent the number of working employees .

In my model,  sometimes the demand curve is under the cumulative function curve, sometimes the demand curve is above the cumulative function curve.

In my objective function, I want to minimize the area  between these two curves, that is to make them fit best.

How to model this? any idea?

Originally posted by: qtbgo

Let me put it more simply.

In a staffing system, we have a demand curve along time which indicates the number of workers needed at different time slots. We have some workers to execute tasks.

The objective is to minimize the over-staffing and the under-staffing.

How to model this?

Originally posted by: DavidGravot

Naively I would go for a discretization of time, create non-optional intervals a1,a2, ... (typically, create 48 intervals of 15 minutes from 08 am to 08 pm) 

Then you will interpolate each of your two curves at each time point ai with di = heightAtStart(ai, demandCurve) and wi = heightAtStart(ai, workload) 

summing all abs(di-wi) gives you an estimation of the area between the two curves

What would be more interesting instead is to get dynamically the points representing any step of the two curves, but I have no idea how to do so 

Hope this helps

David

Originally posted by: DavidGravot

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