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An tutorial to AMPL

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Introduction

Mathematical programming is a technique for solving

certain kinds of problems --- notably maximizing

profits and minimizing costs --- subject to constraints

on resources, capacities, supplies, demands, and

the like

AMPL is a language for specifying such optimization

problems

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A two-variable linear program

Tons per hour : Bands 200

Coils 140

Profit per ton : Bands $25

Coils $30

Maximum tons : Bands 6000

Coils 4000

If 40 hours of production time are available, how many tons of

bands and how many tons of coils should be produced to bring

in the greatest total profit?

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A two-variable linear program

X : the number of tons of bands to be produced

Y : the number of tons of coils to be produced

Maximize 25X+30Y

Subject to :

0=<X<=6000

0=<Y<=4000

(X/200)+(Y/140)<=40

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The two-variable linear program in AMPL

Var X;

Var Y;

maximize Profit : 25*X+30*Y;

subject to Time : (1/200)*X+(1/140)*Y<=40

subject to X_limit : 0<=X<=6000

subject to Y_limit : 0<=Y<=4000

The file – call it prod0.mod

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The two-variable linear program in AMPL

Solve prod0.mod ampl : model prod0.mod;

ampl : solve;

MINOS 5.5 : optimal solution found.

2 iterations, objective 192000

ampl : display X, Y;

X=6000

Y=1400

ampl : quit;

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The two-variable linear program in AMPL

Each variable is named in a var statement

Each constraint by a statement that begins with

subject to and a name like X_limit or Time for the

constraint

Multiplication requires an explicit * operator

≦ relation is written <=

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The two-variable linear program in AMPL

model : reads the file into AMPL

solve : to have AMPL translate your linear program, sends it to a linear program solver, and then return the answer

MINOS 5.5 : indicates that AMPL uses version 5.5 of a solver called MINOS

Often there is more than one solution that achieves the optimal objectives, however, in which case different solvers may report different optimal values for the variables

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A linear programming model

Figure 1-1 shows the production problem in algebraic notation

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The linear programming model in AMPL

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The linear programming model in AMPL

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AMPL interfaces

Refer to AMPL web site, www.ampl.com, for more up

to date information and resources

For GUI

– http://www.ampl.com/GUI/expermt.html