## Math 464 Lecture 24, 04/06/2023
## AMPL Session

ampl: reset; model ProdnBTILO1.15.mod.txt; data ProdnBTILO1.15.dat.txt;
ampl: display ProdAssembly, ProdTesting;
: ProdAssembly ProdTesting    :=
1     0.25         0.125
2     0.333        0.333
;

## We could read data that is presented in text files directly into
## parameters declared in the model file, and whose sizes are set
## (either in a data file or in the ampl: prompt directly).

ampl: read {j in 1..n_Prod} ProdAssembly[j], ProdTesting[j], ProdRawMatl[j], Value[j] < DataMatrix.txt;

j is not defined
context:  read {j in 1..n_Prod} ProdAssembly[j],  >>> ProdTesting[j] <<< , ProdRawMatl[j], Value[j] < DataMatrix.txt;

syntax error
context:  read {j in 1..n_Prod} ProdAssembly[j], ProdTesting[j] >>> , <<<  ProdRawMatl[j], Value[j] < DataMatrix.txt;

## Oops! This is not the correct way to read in a param.  You can read
## in one parameter at a time - all dimensions of it, in fact. It all
## depends on how the data is stored in the file from which we are
## reading.


ampl: read ProdAssembly[1] < DataMatrix.txt;
ampl: read ProdTesting[1] < DataMatrix.txt;
ampl: read ProdRawMatl[1] < DataMatrix.txt;
ampl: read Value[1] < DataMatrix.txt;
ampl: display Value;
Value [*] :=
1  9.2
2  8
;

ampl: read ProdAssembly[2] < DataMatrix.txt;
ampl: read ProdTesting[2] < DataMatrix.txt;
ampl: read ProdRawMatl[2] < DataMatrix.txt;
ampl: read Value[2] < DataMatrix.txt;
ampl: close DataMatrix.txt;

## After you're done reading from a file, you should close that
## file. This is important if you want to read from another file next.

ampl: display ProdAssembly, ProdTesting, ProdRawMatl, Value;
: ProdAssembly ProdTesting ProdRawMatl Value    :=
1     0.25         0.125        1.2      9.2
2     0.333        0.333        3.9      8.4
;

## Notice that the changed values given in DataMatrix.txt have indeed
## been read in.

## Another way to assign parameter values directly at the ampl: prompt
## is using the let command.

ampl: let Value[1] := 10;
ampl: display ProdAssembly, ProdTesting, ProdRawMatl, Value;
: ProdAssembly ProdTesting ProdRawMatl  Value    :=
1     0.25         0.125        1.2      10
2     0.333        0.333        3.9       8.4
;

## The let command is the most convenient option to (re)assign one, or
## a few, parameter values. One could assign the size of a matrix
## parameter at the ampl: prompt using the let command, and then read
## in the matrix values from a text file, for instance.

## We go back to the original problem data by resetting only the data
## file. A simple "reset;" will reset everything including the model.

ampl: reset data;
ampl: reset; model ProdnBTILO1.15.mod.txt; data ProdnBTILO1.15.dat.txt; solve;
CPLEX 20.1.0.0: optimal solution; objective 2808
1 dual simplex iterations (1 in phase I)

## AMPL provides the optimal dual solution once the primal LP is
## solved. We can directly read off the optimal dual variable values
## by 'display'ing the corresponding constraint name in the primal LP.

ampl: display AssemblyCon, TestingCon;
AssemblyCon = 31.2
TestingCon = 0

## We can verify that complementary slackness conditions (CSCs) are
## satisfied at optimality. Note above that the dual variable for the
## TestingCon constraint is zero. We check that this zero value is
## indeed forced by that constraint being non-binding.


ampl: display x;
x [*] :=
1  360
2    0
;

ampl: display sum {j in 1..n_Prod} ProdAssembly[j]*x[j];
sum{j in 1 .. n_Prod} ProdAssembly[j]*x[j] = 90

ampl: display sum {j in 1..n_Prod} ProdTesting[j]*x[j];
sum{j in 1 .. n_Prod} ProdTesting[j]*x[j] = 45

## Note that we are using only 45 out of the 80 hours of Testing
## available. Hence the optimal dual variable for that constraint will
## be zero (due to CSCs).

## But we are using all of the 90 Assembly hours. Hence we could've
## obtained the optimal dual solution value for AssemblyCon also as
## 2808/90 = 31.2