Constraint Programming & Optimization

Constraint Programming (CP) is a powerful paradigm for solving combinatorial optimization problems. Unlike brute-force search, CP uses intelligent constraint propagation to dramatically reduce the search space.

Why Constraint Programming?

Many real-world problems involve constraints:

• Staff must work specific shifts
• Resources have limited capacity
• Tasks must complete before deadlines
• Supply chains must meet demand

Constraint Programming models these naturally and solves them efficiently.

What You Will Learn

| Chapter | Topic | Application | |:-------:|-------|-------------| | 1 | ILP with PuLP | Production planning, resource allocation | | 2 | Staff Scheduling | Shift assignment, labor rules | | 3 | Resource Allocation | Multi-project resource balancing | | 4 | Supply Chain Optimization | Inventory, logistics, demand planning | | 5 | Optimization API | Deploy optimization as a web service |

Course Outline

Each chapter covers:

• Why: The business problem this technique solves
• What: The mathematical model and algorithm
• How: Implementation with Python code
• Next: Transition to the next chapter

Prerequisites

• Basic Python programming
• Familiarity with loops, lists, and functions
• No prior optimization knowledge needed

The Vibe Coding Approach

Describe your optimization problem to AI:

"I need to schedule 20 employees across 7 days with shift preferences, overtime rules, and minimum coverage requirements. Use OR-Tools CP-SAT."

The AI will generate the complete constraint model.

Let us begin!