1. A Mathematical Programming Language
AMPL:
A Mathematical Programming Language
9-Dec-18

2. Introduction Language for large-scale mathematical computing
Generally used for large-scale optimization and scheduling-type problems
Syntax closely resembles the symbolic algebraic notation that is often used to describe mathematical programs
Model linear programming, integer programming, and nonlinear programming, etc.

3. Language Features Sets and indexing Objectives and constraints
Simple sets
Compound sets
Computed sets
Objectives and constraints
Linear
Piecewise-linear
Nonlinear
Integer
Network

4. Syntax Constants: N Variables: i, j, p, x, y
Keywords: param, var, let, in, minimize, subject to
Operators: :=, *, etc.
Expressions: i * j
Statements: ;
Comments: #
Control: for
Commands: solve, printf, display

5. Syntax Example
File: Mult.mod
Run using “model Mult.mod”

6. AMPL Files Each problem instance is coded in AMPL using three files:
A model file (extension .mod): contains the mathematical formulation of the problem
A data file (extension .dat): contains the numerical values of the problem parameters
A run file (extension .run): specifies the solution algorithm (external and/or coded by the user in the AMPL language itself).

7. Linear Problem Example
Tons per hour (rate): Bands Coils 140
Profit per ton (profit): Bands $ Coils $30
Maximum tons (market): Bands 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?

8. Linear Problem Example: Cont.
bands: the number of tons of bands to be produced
coils: the number of tons of coils to be produced
Maximize: $25 * X + $30 * Y
Subject to:
0 <= X <= 6000
0 <= Y <= 4000
(X / 200) + (Y / 140) <= 40 hours

9. Linear Problem Example: Data
File: steel.dat
Tons per hour (rate): Bands Coils 140
Profit per ton (profit): Bands 25 Coils 30
Maximum tons (market): Bands 6000 Coils 4000
bands: the number of tons of bands to be produced
coils: the number of tons of coils to be produced

10. Linear Problem Example: Model
File: steel.mod

11. Linear Problem Example: Run
File: steel.run
Run by calling “include steel.run”

12. AMPL IDE
Download:

13. References: AMPL Website: http://ampl.com/
AMPL Book:

14. The End