help in modeling demand in disasters

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anjomshoae
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Joined: Thu Oct 23, 2014 1:08 pm
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help in modeling demand in disasters

Post by anjomshoae »

Hi,

I want to model disaster demand and I have the following description for modeling it using Vensim:


The easiest way to model the disaster-generated demand is as an instantaneous constant G at the beginning (time step n=0). So you would have D(0)=G.
It is also often realistic to use a disaster-generated demand function G(n) to model the fact that a disaster may continue to generate additional demand after the initial time step. Two common expressions for this function are:

exponential decay G(n) = G_0*exp(-k*n), and
uptake-decay G(n) = G_0*n*exp(-k*n),
where G_0 and k are parameters that can be calibrated to model the dynamics of the disaster-generated demand. In this case, this function must be added to the outstanding demand function at each time step, so D(n) = D(n-1) +G(n).

It is also possible to add a “residual demand” term (G_r) to any of the formulas above to model the reality that the disaster-generated demand often never really goes away.


I have tried to model this using vensim. I modeled this formulation:

"G(n)"= G 0*n*exp(-k*n*Time)+"(G r)"

Using the above formulation I get a negative exponential graph, which is different from what I need to get. I attached the model together with the result that I want to get. I am not sure which part of my model is wrong? anyone can help please?

Kind regards,
Attachments
demand.mdl
model
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anjomshoae
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Posts: 46
Joined: Thu Oct 23, 2014 1:08 pm
Vensim version: DSS

Re: help in modeling demand in disasters

Post by anjomshoae »

I forgot to add the graphs. I add them to this post.
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anjomshoae
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Posts: 46
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Vensim version: DSS

Re: help in modeling demand in disasters

Post by anjomshoae »

for some reason, I cant upload two pictures in one post. I add the result that I want to get to this post.
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Re: help in modeling demand in disasters

Post by Administrator »

so D(n) = D(n-1) +G(n).
This indicates that a level should be used.

Where do these equations come from? The description of them is terrible, I'm really struggling to follow it. The graph that you are trying to match, that also looks like real data rather than calculated output. Have you tried modifying the constants in the model as suggested to calibrate (G_0 and k)?
Advice to posters seeking help (it really helps us to help you)
http://www.ventanasystems.co.uk/forum/v ... f=2&t=4391

Units are important!
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anjomshoae
Member
Posts: 46
Joined: Thu Oct 23, 2014 1:08 pm
Vensim version: DSS

Re: help in modeling demand in disasters

Post by anjomshoae »

Yes, calibrating parameters will not generate the graph that I want. The descriptions are the authors response to my email regarding how to model a disaster demand.

Graph that I want to match shows the solution of his model and I realized that it’s actually “wrong” to match the model output to this graph. The question still remains: how to generate a disaster demand? Based on my understanding from literature, the function should produce the following graph:




p.s: The graph comes from the following article. I am not able to upload the full article here as it is not permitted. Here is a link to the article:
Quantifying communication effects in disaster response logistics: A multiple network system dynamics model
https://www.emeraldinsight.com/doi/full ... -2014-0031

The paper presents a discrete mathematical system dynamics (SD) model to study the role of communication and logistical coordination between actors in an emergency disaster response operation, and to measure their impact on the number of lives saved and dollars spent.

The author response to my email after not getting a similar results from the model:
"Figure 2a in the paper shows the solution of the model. To obtain it, you must input the user-defined parameters (such as the function G(n) you chose) into the model, and solve the model.



I am not familiar with Vensim, but you can solve the model using any software that can solve a system of recurrence relations (you can even use Microsoft Excel for example). Equations 6-14 are the recurrence relations that define the variables in terms of their value at the previous time step. The solution of this system gives you the curves that appear in figure 2."
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demand 1.PNG
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anjomshoae
Member
Posts: 46
Joined: Thu Oct 23, 2014 1:08 pm
Vensim version: DSS

Re: help in modeling demand in disasters

Post by anjomshoae »

I revised the demand model in the previous post and attached the new version to this post.


it looks like parameter "n" actually refers to "time". so previous formulation was wrong. the new formulation for G(n) is:


G 0*Time*exp(-k*Time)+"(G r)"

it shows an overshoot and collapses behavior, but starts from an initial value of 0. this is wrong based on my understanding. demand at the onset of a disaster is a value greater than 0. so I think this function can not be used for demand in disaster.



would you please help? How to generate the graph for "item 2" using a SD function?
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demand.mdl
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demand 1.PNG
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