Optimizing behaviour

[Stormyman]

I am building a model where players maximize their cumulated payoff. The payoff depends on the players investments.
Conditions change over time thus early investments are more profitable than late investments, both have a cost.

In each period a player asks : What is the optimal investment in the actual period to maximize my cumulated payoff at the end ?
I want to find an optimal investment path...
if I(t) is investment in period t ..say I*(1) = 3 , I*(2) = 2.32 , I*(3) =2.01 maximizes the payoff at the end of period 3. Any other stragy is worse.
For another player with different characteristics, the optimal path differs.

I want to do this for larger simulation with about 80 periods.
What is the easiest way for doing this in Vensim ??

I let Vensim try out all thinkable investment paths in sensitivy simulations, but their number is much too large... 10 strategies and 3 periods already produce 10*10*10 options.
Is there an easier way for this optimization problem ?

Is it possible to compute that in vensim ? I was wondering if it works with VMAX, subscribts and matrizes...

What commands are useful ?? Does it work with the Vensim optimization tool ?

Thank you for help !
Greetings

[LAUJJL]

Hi

I do not fully understand your problem.
It would be better to make a little model to explain it.
Suppose that the whole period has say 10 years.
We are at the year 1.
One player has to decide what he will invest at year 1.
But can he choose between an investment that lasts 3 years and another one
That lasts until the period is over.
Is the investment valuated at the end of the period.
Does the player has a limit of investment possible over the whole period?
The question about the optimal payoff at the end of the period is not clear.
Is the payoff the percentage of profitability or the brutto profitability?
The question you are asking looks like if the player had to decide today what he will
invest later on. Is it the case?
You should better explain the problem eventually with a model.
Regards.
JJ

[bob@vensim.com]

I am not sure I understand this either but you have described an optimization problem so I do not understand why you would use senstivitiy simulations.

You might be able to code externally a dynamic programing algorithm to solve this efficiently. Alternatively, just subscript your optimization variable by the number of periods and switch by time. The following equations do this:

investment= SUM(investment by time[TimePeriod!]*is this time period[TimePeriod!]) ~$/Year
investment by time[TimePeriod]= 1000 ~%/Year ~ This is what is optimized over
is this time period[TimePeriod]= IF THEN ELSE(INTEGER(Time) = TimePeriod-1,1,0) ~ Dmnl ~ Changing when time changes to 2,3, and so on


I hope that helps.

[Stormyman]

Thank you for the help, I figured out how to do it - at least partially !! It works !!

I am new to dds, I used Vensim standard before thats why I tryed to solve with sensitivity simulations.

I am just wondering how to define the [TimePeriod] subscript... what exactly should I write into the subscript equation so it uses the time ?

[bob@vensim.com]

For the above you would just use

TimePeriod : (TP1-TP20)

or however many you have. The variable "is this time period" manages the switching over time.