Select Page

## AMPL ASSIGNMENT Case Solution

Decision Variables

Let,

X1 = Volume after felling for crop 1

X2 = Volume after felling for crop 2

X3= Volume after felling for crop 3

X4= Volume after felling for crop 4

X5= Volume after felling for crop 5

X6= Volume after felling for crop 6

The above are the decision variables for the LP optimization problem because we need to choose an optimal felling program at which the net discounted revenue is maximized for the next decade. All the above variables are measured in acres.

Objective Function

Maximize Revenue = X1 (287 + 215 +228 + 292) + X2 (207 + 135 + 148 + 212 + 148) + X3 (157 + 85 + 98 + 162 + 112) + X4 (487 + 415 + 317) + X5 (337 + 265 + 264) + X6 (87 + 15 + 61)

Constraints

All the constraints for the above LP model are shown below:

Subject to the constraints:

X1 + X2 + X3 + X4 + X5 + X6 <= 5000 acres

X4 + X5 <= 3845 acres

X1 + X2 + X3 <= 2.44 million h.ft

X4 + X5 + X6 <= 4.16 million h.ft

X4 + X5 + X6 >= 500 acres

The first constraint shows that the total treated area for all the five crops should not exceed 5000 acres. The second constraint shows that the total area for the newly planted conifer plus the untreated area of the old conifers must not exceed 3845 acres. Constraint 3 shows that the total volume for the felled hardwood should not exceed 2.44 million h. ft. The fourth constraint shows that the total volume for felled conifer and the mixed high forest should not exceed 4.16 million h. ft. Finally, the last constraint shows that minimum 50 acres of crops should be planted with hardwood.

Non-negativity:

The non-negativity constraints show that the values of all the decision variables can be 0 or greater than zero but not less than 0.

X1 + X2 + X3 + X4 + X5 + X6 >= 0

AMPL Codes

First, create a symbolic link to the AMPL interactive solver by typing the following command on any of the Sun workstation:

ln -s /afs/engin.umich.edu/group/engin/priv/ioe/ampl/ampl_interactive ampl

Three additional solvers are also available which are OSL, MINOS and ALPO. The command lines below would create the symbolic link to the various solvers:

ln -s /afs/engin.umich.edu/group/engin/priv/ioe/ampl/solvers_SunOS/osl osl

ln -s /afs/engin.umich.edu/group/engin/priv/ioe/ampl/solvers_SunOS/minos minos

ln -s /afs/engin.umich.edu/group/engin/priv/ioe/ampl/solvers_SunOS/alpo alpo

The LP formulation for the forestry problem has been created above. Now the codes for the model and the data file are as follows:

AMPL Model File: HW5Forestry.mod

set X1;

set X2;

set X3;

set X4;

set X5;

set X6;

param avail {X1,X2,X3,X4,X5,X6} >= 0;

param portion {X1,X2,X3} >= 0;

param price {X4,X5,X6} >= 0;

var Prod {X6} >= 0;

maximize revenue: sum {j in acres} Prod[j] * revenue[j];

subject to acres_avail {i in ACRES}:

sum {j in acres} portion[i,j] * Prod[j] <= avail[i];

AMPL Data File: HW5Forestry.dat

set Treatment := M1 M2 M3 M4 M5 ;

set Acres := X1 X2 X3 X4 X5 X6 ;

param avail := X1 2754 X2 850 X3 855 X4 1598 X5 405 X6 1761;

param portion : A1 A2 A3 A4 A5 A6 :=

M1 287 215 228 292 204

M2 207 135 148 212 148

M3 157 85 98 162 112

M4 487 415 0 0 371

M5  337 265 0 0 264

M6 87 15 0 0 61;

param revenue :=

A1 287 A2 207 A3 157 A4 415 A5265 A6 15;....................

This is just a sample partial case solution. Please place the order on the website to order your own originally done case solution.