Linear Programming Part 1 - Where LP Fits Into AI Systems

What LP is and where it fits in AI systems*

1. LP is not AI

Linear Programming (LP) is an optimization technique, not an AI model.

AI/ML typically learns patterns from data and uses those patterns to make predictions, classifications, or scores.

LP does something different. It finds the best possible decision while satisfying a set of constraints.

LP is introduced here because, in a real AI system, the AI/ML model is often only one part of the overall system. Other components may be responsible for turning predictions into actual decisions.

A simplified AI system might look like:

Data
  ↓
AI / ML Model
  ↓
Predictions / Scores
  ↓
Optimization / Rules
  ↓
Final Decision
  ↓
Application

LP is one optimization technique that can be used in this broader system.

The goal here is not to treat LP as AI, but to understand where LP can fit into an AI system and what role it can play.

2 What Does LP Actually Do?

LP answers practical questions such as:

How many products should we produce?
How should we allocate a limited budget?
How should available workers be assigned?
How should limited materials be distributed?
How should delivery capacity be allocated?

The basic idea is:

Choose the values of some decision variables so that an objective is optimized while all constraints are satisfied.

For example, a company produces two products:

Product A makes $10 profit
Product B makes $15 profit

But the company has limited materials and labor.

LP can determine:

How many A and B should we produce to maximize profit without exceeding our available resources?

So LP is mainly about decision-making under constraints.

concept

3. AI Predicts, LP Optimizes

A useful way to distinguish them is:

AI/ML	Linear Programming
Learns patterns from data	Optimizes decisions
Makes predictions or scores	Finds the best feasible solution
"What is likely to happen?"	"What should we do?"
Example: predict product demand	Example: decide how much to produce

They can also work together.

AI might predict that demand for a product will be 1,000 units next month.

LP can then use that prediction, together with production capacity, labor, materials, and costs, to determine how much to actually produce.

4. Real AI Systems Contain More Than the AI Model

A real-world AI application is rarely just an ML model.

A simplified system might look like:

Data
  ↓
AI / ML Model
  ↓
Predictions / Scores
  ↓
Optimization / Rules
  ↓
Final Decision
  ↓
Application

The AI model provides information that helps the system make a decision.

Optimization can then determine what action should actually be taken while respecting practical constraints.

LP is one possible optimization technique used in this supporting layer.

5. Example: Movie Recommendation System

Suppose a movie recommendation system uses an ML model to predict how much a user may like each movie:

Movie A → 0.91
Movie B → 0.87
Movie C → 0.84
Movie D → 0.81
...

The ML model answers:

Which movies is the user likely to enjoy?

But the application may need to select only 10 movies and follow additional rules:

Maximum 3 movies from the same genre
At least 2 new releases
Maximum 5 movies the user has already watched

An optimization model can use the ML scores and these constraints to decide which 10 movies to show.

So the roles are different:

ML
  ↓
Predict how much the user may like each movie
  ↓
LP / Optimization
  ↓
Select the best combination subject to constraints

The important distinction is:

AI/ML can provide predictions or scores. LP can use those results to make an optimized decision under constraints.

This is why LP is useful to understand even though LP itself is not AI.

Relevant Link(s)

AI in Context Main Page