Business Problem Optimization Using Linear Programming (PuLP)

This project demonstrates how optimization techniques, specifically Linear Programming (LP), can be applied to solve real-world business and supply chain problems using Python and the PuLP library.

Unlike traditional Machine Learning projects that rely on historical data, this project focuses on decision optimization under constraints.

---

📖 Project Overview

The notebook covers two major optimization use cases:

1. Manufacturing Profit Maximization
2. Supply Chain Transportation Cost Minimization

Both problems are modeled mathematically and solved using Linear Programming.

---

🎯 Objectives

• Understand business problems from an optimization perspective
• Formulate objective functions and constraints
• Implement Linear Programming using Python
• Use PuLP to obtain optimal solutions
• Interpret results and extract business insights
• Visualize optimized supply chain flows

---

🧩 Problem 1: Manufacturing Profit Maximization

Business Scenario

A manufacturing company produces two products:

• Product A
• Product B

Each product consumes machine hours and labor hours, which are limited. The goal is to determine the optimal production quantities that maximize total profit.

Optimization Type

• Objective: Maximize profit
• Technique: Linear Programming
• Decision Variables: Units of Product A and Product B
• Constraints: Machine hours, labor hours, non-negativity

---

📦 Problem 2: Supply Chain Optimization

Business Scenario

A company operates:

• 2 Warehouses
• 3 Retail Stores

Each warehouse has limited supply capacity, and each store has fixed demand. Transportation costs vary between warehouse–store pairs.

Optimization Type

• Objective: Minimize transportation cost
• Technique: Linear Programming
• Decision Variables: Units shipped from each warehouse to each store
• Constraints: Supply limits, demand fulfillment

---

📊 Visualization

The optimized supply chain solution is visualized to:

• Show shipment routes
• Display flow quantities
• Improve interpretability of optimization results

Visualization helps bridge the gap between technical solutions and business decision-making.

---

🛠 Tools & Technologies Used

• Python
• Jupyter Notebook
• PuLP (Linear Programming Library)
• Matplotlib (Visualization)

---

📁 Repository Structure

📦 Business_Problem_Optimization_Using_Linear_Programming 
│
├── Business_Problem_Optimization_Using_Linear_Programming.ipynb                                       # Jupyter Notebook with full implementation
└── README.md                                                                                          # Project documentation

---