introduction to gams...gams lives for a moment: report writing commands always use values from the...

Introduction to GAMS:Comparative analysis

Dhazn Gillig&

Bruce A. McCarl

Department of Agricultural EconomicsTexas A&M University

Comparative Analysis

Models once built are almost always subjected to comparative analysis where a number of alternative scenarios are run then the analyst compares the results across scenarios to see the effect is of the scenario assumptions.

! Two ways to conduct comparative analysis

• Use multiple GAMS submissions or multiple solves generating report writing output and then manually comparing the analysis results

• Use the GAMS LOOP procedure and set up a comparative scenario analysis system that creates cross scenario comparison tables

Let use an example from McCarl and Spreen book

• GAMS implementation of the Unified MOTAD

example

• Section 14.3.1.3

• Book Chapter 14 - Risk

(http://ageco.tamu.edu/faculty/mccarl/mccspr/new14.pdf)

Example on Unified MOTAD

Example on Unified MOTAD

Suppose we wish to simulate 3 scenarios involved with varying the risk aversion parameter. One will have a zero risk aversion parameter and the others with “1.5” and “5.0”. We could do this using repeated solves at the end of the GAMS program as follows.

… data section …… model structure …RAP=0;SOLVE MTDPortfol USING LP MAXIMIZING OBJ ;

RAP = 1.5 ;SOLVE MTDPortfol USING LP MAXIMIZING OBJ ;

RAP = 5 ;SOLVE MTDPortfol USING LP MAXIMIZING OBJ ;

Multiple GAMS Submissions

The model is first solved at the original RAP = 0.

The RAP is changed to 1.5 and model is solved again

The RAP is changed to 5 and model is solved again

GAMS lives for a MOMENT: Report writing commands always use values from the most recent solution. One must save the data if comparative reports are desired by creating a parameter to store the report data and then actively storing what is needed.

PARAMETER OUTPUT(*) RESULTS FROM MODELVAR Variance ;

VAR = SUM(EVENTS,(POSDEV.L(EVENTS)+NEGDEV.L(EVENTS))**2)/ CARD(EVENTS ) ;

OUTPUT("OBJ") = OBJ.L ;OUTPUT("RAP") = RAP ;OUTPUT(STOCKS) = INVEST.L(STOCKS) ;OUTPUT("VAR") = VAR ;OUTPUT("SHADPRICE") = INVESTAV.M ;OPTION Output:2:0:1; DISPLAY Output;

We will save the calculation parts of this program as another file called report.gms so that it can be used by “$include” command.


Here are steps:

1. Set up and solve the original model

2. Setup parameters

3. Construct a report

4. Alter the risk aversion parameter to 1.5

5. Solve altered model


7. Alter the risk aversion parameter to 5

8. Solve altered model



SOLVE MTDPortfol USING LP MAXIMIZING OBJ ;

PARAMETER OUTPUT(*) Model RESULTS VAR Variance ;

$include report.gms

RAP = 1.5 ;


$include report.gms

RAP = 5 ;


$include report.gms


Output from RAP = 0---- 162 PARAMETER OUTPUT RESULTS FROM MODEL

BUYSTOCK3 17.86OBJ 148.21MEAN 148.21VAR 19709.82STD 140.39SHADPRICE 0.30

Output from RAP = 1.5---- 162 PARAMETER OUTPUT RESULTS FROM MODEL

BUYSTOCK1 2.82BUYSTOCK2 5.62BUYSTOCK3 1.82BUYSTOCK4 8.40OBJ 106.09RAP 1.50MEAN 119.80VAR 83.89STD 9.16SHADPRICE 0.21

This approach does not yield cross scenario comparative report writing and output is widely dispersed. Let’s fix that.

Step 1 Create a parameter in which to save report with a place for a scenario name in the set dimensions


PARAMETER OUTPUT1(*,*) RESULTS FROM MODELVAR Variance ;

Step 2 Compute a report using the scenario name in it’s index position (note that in this example the 2nd set refers to scenarios)


OUTPUT("OBJ","RAP = 0.0") = OBJ.L ;OUTPUT("RAP","RAP = 0.0") = RAP ;OUTPUT(STOCKS,"RAP = 0.0") = INVEST.L(STOCKS) ;OUTPUT("VAR","RAP = 0.0") = VAR ;OUTPUT("SHADPRICE","RAP = 0.0") = INVESTAV.M ;


Step 3 After the second solve statement, Compute a report using the scenario name in it’s index position, but this time use a name indicative of the second scenario such as “RAP = 1.5”

Rap=1.5;



OUTPUT("OBJ","RAP = 1.5") = OBJ.L ;OUTPUT("RAP","RAP = 1.5 ") = RAP ;OUTPUT(STOCKS,"RAP = 1.5 ") = INVEST.L(STOCKS) ;OUTPUT("VAR","RAP = 1.5 ") = VAR ;OUTPUT("SHADPRICE","RAP = 1.5 ") = INVESTAV.M ;


Why do we re-calculate VAR parameter?

Display the output

OPTION OUTPUT:4:1:1 ;DISPLAY OUTPUT;

places of decimals: # of indices in R: # of indices in C


Multiple GAMS Submissions – percentage change

Percentage changes often desirable in a cross scenario comparison. Suppose we use the following code:

! The first conditional ($) prevents us from dividing through by zero and rounds to get rid of excessively small numbers.

! The second conditional tells us where percentage changes couldn’t be calculated because the base solution was zero and uses a special value which is NA.

Output without using conditional ($)

Output with using conditional ($)


Cautions about calculations !!GAMS treats calculations in three distinctly different ways.

! Dynamic – calculations repeated every time the model is generated.

Only calculations in the model .. Statements are dynamic

! Static – calculations executed once only at the place the GAMS instruction appears in the code.

! Repeated Static – static calculations in a loop executed every time we go through the loop

Loop(I, land=land*2; ) ;


Because GAMS lives for the moment, when a calculation is issued then all prior values are overwritten. If you one want to revert to original values then one has to instruct GAMS to do that.


The better way to conduct comparative analysis is to use the LOOP procedure. Here the code contains a LOOP which causes GAMS to repeat execution of statement enclosed in the parentheses defining the LOOP for each value of the defining set.

Using GAMS LOOP Procedure

There are several steps.Step 1: Define Scenario setStep 2: Define parameters that will be altered by scenario

(i.e. risk aversion parameters)Step 3: Define parameters used in the LOOP (i.e. output, sRap)

Using GAMS LOOP Procedure for Comparative Runs

STEP1

STEP2

STEP3

Using GAMS LOOP ProcedureReset RAP values to original values

Set RAP values by scenarios

Using GAMS LOOP Procedure – GAMS output

OPTION Output :4:1:1 ;DISPLAY Output ;

Using GAMS LOOP Procedure – GAMS output

Many comparative studies involve model structure modification. One can introduce context sensitive structure by making constraints or terms conditionals.

sameas(i,j) a statement that is True if text for set element name of I = that for j

sameas(resource, “ Land”) => A statement is true if text for the element of resource is Land otherwise, it is false.

Using GAMS LOOP Procedure – structural modification

ResourceEq(Resource)$( (ResourceAvailable(Resource) GT 100)and sameas(Resource,"Land") ).. would impose the

constraint in a conditional manner.

Base Scenario:

Scenario 1:


OPTION Output :3:2:1 ;DISPLAY Output ;


Increasing run efficiency using the Save and Restart procedure.

In the IDE a box is available just to the right of execute button where we can associate a set of execution time parameters with a file and the IDE will remember these whenever the file is opened in this project.-s = .\t\a1 => save work files-r = .\t\a1 => restart work files

Using GAMS LOOP Procedure

ReferencesMcCarl, B. A. Basic GAMS class.

(http://agecon.tamu.edu/faculty/mccarl/mccarl.htm).

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