View source for Module 7: Embedding an NLP in a Dynamic Loop

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

The solution in [[Module 6: Time as an Intrinsic Index|Module 6]] advises the airline to decrease the number of planes in service between 2014 and 2015. What if the airline has a lease agreement that does not allow them to return planes? In this case we would like to impose a constraint that requires the Number of Planes to increase or stay the same from year to year. 

The lower bound of the constraint depends on <code>Number of Planes</code> in the previous year. The constraint is based on a dynamic quantity. You can embed an [[NLP_Characteristics|NLP]] inside a dynamic loop to impose dynamic constraints. There is only one restriction:

* Bounds on Decision variables cannot be recursively dependent on [[Time]] (or other index on which the [[Dynamic]] loop is based). To impose recursively time-dependent bounds, they must be entered as constraints instead of Decision bounds attributes.<br />
<br />
Let’s try it! Starting with [[Module 6: Time as an Intrinsic Index|Module 6]], create a new variable titled <code>Previous Number of Planes</code>. (We will have to use a dynamic definition since we are referring to a previous time step.) Then create the constraint based on the new variable.

<pre style="background:white; border:white; margin-left: 1em;">
Variable Previous_Planes := Dynamic(0, Number_of_Planes[Time - 1])
Constraint No_Plane_Decrease := Number_of_Planes >= Previous_Planes
Variable Opt := DefineOptimization(
     Decisions: Number_of_Planes, Fare,
     Constraints: No_Plane_Decrease
     Maximize: NPV_Profit)
</pre>

:[[File:nlp_mod5_4.png|300px]]

The [[dynamic]] constraint is satisfied.

==See Also==
* [[DefineOptimization]]
* [[NLP Characteristics]]
* [[Dynamic]]
* [[Time]]


<footer> Module 6: Time as an Intrinsic Index / {{PAGENAME}} / Controlling Engine Selection and Setting</footer>