View source for Module 5: Time as an Extrinsic index

[[Category: Analytica Optimizer Guide]]
<breadcrumbs> Analytica Optimizer Guide > Optimizer key concepts: Airline Example> {{PAGENAME}}</breadcrumbs><br /> 

Let’s assume that Base Demand increases by 10% per year. How would that affect our decisions over time. In this example, Analytica will abstract over the system index [[Time]] instead of [[Run]]. The principle is exactly the same as in [[Optimizing_with_Uncertainty#Module_4:_Multiple_Optimizations_of_Separate_Samples_.28MOSS.29|Module 4]]. 

First, we define the system [[Time]] index to represent years from 2011 to 2015. To edit this special index, select '''Edit Time''' from the [[Definition menu]] and enter this definition:
:<code>Index Time := 2011..1015</code>

Starting with the Base Case setup, create a new variable<code>Growth<code>_</code>Rate</code>. Re-define <code>Base_Demand</code> so that it grows exponentially over time using this annual growth rate.

:<code>Variable Growth_Rate := 10%</code>
:<code>Variable Base_Demand := 400k*(1 + Growth_Rate)^(@Time - 1)</code>

This definition uses a positional reference for the [[Time]] index. The first year corresponds to position 1 (making the exponent zero). Thus, <code>Base Demand</code> for the first year will be 400k, and this value increases 10% every year. 

[[Time]] is now an index of <code>Base Demand</code>. The extrinsic index is propagated to the Objective. [[Array Abstraction|Array abstraction]] results in a separate optimization for each year.

:[[File:nlp_mod5_1.png|400px]]

Profit rises in each year as demand increases. A new plane is added in 2014. Wait! Did you forget something? This in an NLP with an extrinsic index. If you remembered to set a [[Using SetContext to efficiently solve NLPs|context variable]] you win a free Grande Analyti-latte! '''Base_Demand''' is the sensible choice.

<pre style="background:white; border:white; margin-left: 1em;">
Variable Opt := DefineOptimization(
     Decisions: Number_of_Planes, Fare,
     Maximize: Profit,
     SetContext: Base_Demand)
</pre>

==See Also==
* [[Time]]
* [[Time index]]
* [[Dynamic]]
* [[Run]]
* [[Implicit Dimensions]]
* [[Array Abstraction]]
* [[Definition menu]]


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