I have to explain my model a bit  before asking my question on using
a GAMS
command that SUMS OVER A SUBSET. If you have time, please read through
it and
let me know where the model goes wrong. Any help would be appreciated.
Thank you for your attention.
Subbu Kumarappan
In the following, STEP 1 defines a simpler problem which gives me
correct/expected results
after optimization. I use the SAME logic/set up in STEP 2 – I use a
command SUM
over SUBSETS which is the reason for wrong results.
In particular, a number 127012.3237 is calculated repeatedly and
inserted as Supply of
biomass feedstock – even though there is no use for that feedstock
(no ethanol production during those times  please see below to read
more of my problem. It is a big lengthy  but explains the logic/model
set up).
STEP 1:
My COST MINIMIZATION model is as follows:
TIME FRAME: 10 years (40 quarters)
DECISION/CHOICE VARIABLES:
 Corn acreage harvested for stover annually (10 years or 40
quarters) and  Switchgrass planted as a perennial crop (acreage chosen once  and
it stands up to
10 years in the field).
OUTPUT  Cellulosic ethanol  production starts in 8th quarter  13.25
million gallons
per quarter capacity
Other Constraints: Some constraints for inventory requirement, etc
were added.
RESULT: When I modeled the above problem, I got a proper answer (there
is no
demand for stover or grasses in quarters 1 through 7) since ethanol
production started only 8th quarter.
STEP 2:
TIME FRAME: I increased the time frame from 10 years to 20 years (80
quarters)
DECISION VARIABLES: I allowed subsequent planting of switchgrass in
years 2, 3, 4,
5…, 18, 19 and 20.
If the grass is planted in year 1, its productive life ranges from
year 1 to 10,
Switchgrass Planted in year 2  productive life from 2 to 11
…
Planted in year 10  productive life from 10 to 19
Planted in year 11  productive life from 11 to 20
Planted in year 12  productive life from 12 to 20
…
Planted in year 20  productive life from 20 to 20
OTHERS:
All others (corn stover acreage, constraints, ethanol output) remain
the same as
above.
PROBLEM WITH MY CODE:
In year 5, there can possibly be 5 different switchgrass plots  one
that was planted in
year 1, then the others planted in year 2, 3, 4 and 5  so, the
acreage planted in year 1
is not available for year 3 or 4 planting – Note that it is also not
available for corn stover
harvesting.
To model the above mentioned charactersitic, I used a GAMS commands as
following:
SETS
q /q1q80/ “Quarters”
t1 /q1q40/ “Subset of quarters to compute acreage allotted to
switchgrass
planted in year 1”
t2 /q5q44/ “Subset of quarters to compute acreage allotted to
switchgrass
planted in year 2”
…
t20 /q77q80/ “Switchgras planted in year 20”
POSITIVE VARIABLES
vGrassAcresYr1(t1)
vGrassAcresYr2(t2)
…
vGrassAcresYr20(t20)
vStoverAcres(q)
EQUATIONS (only one is given):
eqnAvailableArea(q)…
Sum[t1, vGrassAcresYr1(t1)]

Sum[t2, vGrassAcresYr2(t2)]
… 
Sum[t20, vGrassAcresYr20(t20)]

vStoverAcres(q) =l= AvailableArea(q)
Is the summing over subsets correct? While STEP 1 gave me correct
results (no biomass
demand when ethanol production is ZERO), STEP 2 gives me a number
(127012.3237) repeated wherever it has to be ZERO.
The fundamental difference in model is SUMMING OVER SUBSETS. Please
let me know if you know where the mistake could be…
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