AMPL (A Mathematical Programming Language) is an algebraic modeling language designed for solving optimization problems, particularly linear and nonlinear programming problems. It was first developed by Robert Fourer, David M. Gay, and Brian W. Kernighan in the 1980s and has since become a widely used language in the operations research and management science communities. In this guide, we will provide an introduction to AMPL, including how to write it with an example and what the best applications for it are.
Writing AMPL
AMPL is a high-level language that is designed to be intuitive and easy to use. Its syntax is similar to that of a mathematical equation, making it easy for users to translate real-world problems into mathematical models. An AMPL program consists of three parts: the model, the data, and the commands. The model defines the mathematical problem that needs to be solved, the data provides the values for the model parameters, and the commands specify how to solve the problem.
Let us look at a simple example to demonstrate how to write an AMPL program. Consider the following linear programming problem:
Maximize 2x1 + 3x2
Subject to
2x1 + x2 <= 10
x1 + 3x2 <= 12
x1, x2 >= 0
To write this problem in AMPL, we first define the model using the 'subject to' keyword. We then define the objective function and the constraints. Finally, we specify the command to solve the problem using the 'solve' keyword.
Here's what the AMPL code for this problem would look like:
```
# Define the model
param n = 2;
var x {1..n} >= 0;
maximize obj: 2*x[1] + 3*x[2];
# Define the constraints
subject to c1: 2*x[1] + x[2] <= 10;
subject to c2: x[1] + 3*x[2] <= 12;
# Solve the problem
solve;
```
Applications of AMPL
AMPL is widely used in operations research and management science to model and solve optimization problems. Some of the areas where AMPL is applied include finance, transportation, manufacturing, logistics, and energy. AMPL is particularly useful in industries that involve complex supply chain management, such as food and beverage, pharmaceuticals, and retail.
One of the strengths of AMPL is its ability to handle large and complex optimization problems. It can handle a variety of problem types, including linear programming, nonlinear programming, integer programming, and mixed-integer programming. AMPL also supports a wide range of solvers, including CPLEX, Gurobi, and MINOS, making it a versatile language for solving optimization problems.
Conclusion
AMPL is a powerful algebraic modeling language that is widely used in operations research and management science. Its intuitive syntax and ability to handle complex optimization problems make it a popular choice among researchers and practitioners. In this guide, we provided an introduction to AMPL, including how to write it with an example and what the best applications for it are. We hope this guide has been helpful in getting you started with AMPL and solving optimization problems.