GNU MathProg

Key takeaways

GNU MathProg belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect GNU MathProg to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of GNU MathProg from memory before moving on to harder problems.

Reference excerpt

GNU MathProg is a high-level mathematical modelling language designed for creating and solving linear programming (LP), mixed integer programming (MIP), and other related optimisation problems. It is a subset of the AMPL (A Mathematical Programming Language) and is primarily used with the GNU Linear Programming Kit (GLPK).

Overview GNU MathProg provides a structured definition of data, decision variables, constraints, and objective functions. It allows users to describe complex optimisation problems in a human-readable form, separate from the solution algorithm. The language supports sets, parameters, variables, constraints, and objective functions, and offers features for reading external data and generating reports. Because of its syntactical similarity to AMPL, MathProg enables easy transition to commercial solvers for larger or more complex problems, while maintaining compatibility with free and open-source software tools.

Features Support for linear and mixed-integer linear programming AMPL-like syntax for easy model formulation Built-in data section for embedding problem data Compatibility with GLPK for solving and analysis Ability to import external data using table statements

Usage MathProg models are typically written in .mod files (sometimes .mpl) and solved using the GLPK solver via the glpsol command-line tool, a desktop or online interface. The general command-line usage pattern is: glpsol --math my-model.mod --data my-data.dat MathProg is particularly suited for educational purposes, small-scale optimisation, and rapid prototyping of models before deployment in more robust optimisation environments.

Example We want to maximise the profit of two products (A and B). The profit for one pallet of A is £80, and £100 for B. Both products rely on the same resources (time and materials). It takes two hours to produce one pallet of product A and four hours for B. The time is limited to 80 hours (per day). To produce one palette of A, we need 80 kg of material. Similarly, 60 kg of material is needed for one pallet of B. The common material for A and B is limited to 2400 kg. How many pallets of A and B must be produced to maximise the profit? The mathematical problem formulation is:

max x 1 , x 2 80 x 1 + 100 x 2 subject to 2 x 1 + 4 x 2 ≤ 80 80 x 1 + 60 x 2 ≤ 2400 {\displaystyle {\begin{aligned}&{\underset {x_{1},x_{2}}{\text{max}}}&&80x_{1}+100x_{2}\\&{\text{subject to}}&&\\&&&2x_{1}+4x_{2}\leq 80\\&&&80x_{1}+60x_{2}\leq 2400\\\end{aligned}}}

The advantage of the MathProg is its similarity to the mathematical formulation.

This example demonstrates the similarity of the MathProg model to the mathematical formulation. It contains an output code section, allowing the formatted display of essential values such as the objective and optimal decision values. For instance, the above output code generates:

The optimal production per day is: 24.0 pallets of product A, 8.0 pallets of product B This will return a profit of 2720.00 pounds

History GNU MathProg was developed as part of the GNU Linear Programming Kit (GLPK) by Andrew Makhorin. It serves as an interface for users who prefer a declarative style of optimisation modelling without delving into the C API of GLPK.

See also Linear programming Operations research

External links GLPK official website MathProg Online solver

References

Worked examples

Example 1 — a first encounter with GNU MathProg

Start with the simplest possible case. Write down what GNU MathProg claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to GNU MathProg before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about GNU MathProg ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of GNU MathProg

In research: GNU MathProg appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses GNU MathProg in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: GNU MathProg is common in secondary-school and first-year university syllabi. It links to neighbouring topics GNU Project, Mathematical modeling, so understanding it makes those chapters shorter.
In everyday life: Look for GNU MathProg outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study GNU MathProg in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what GNU MathProg means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain GNU MathProg out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is GNU MathProg in simple terms?

GNU MathProg is a high-level mathematical modelling language designed for creating and solving linear programming (LP), mixed integer programming (MIP), and other related optimisation problems. It is a subset of the AMPL (A Mathematical Programming Language) and is primarily used with the GNU Linea…

Why does GNU MathProg matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study GNU MathProg?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on GNU MathProg.