🏗️ Construction Cost Optimizer

Linear Programming solution for minimizing construction material costs while meeting engineering specifications.

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Problem Statement

A construction company needs to produce a concrete mix using two raw materials with specific cost and property characteristics:

Materials Overview

Material	Cost/Unit	Strength	Durability	Water Resistance
Cement	$20	2 units	1 unit	1 unit
Sand	$10	1 unit	1 unit	3 units

Requirements

• ✅ Minimum Strength: 30 units
• ✅ Minimum Durability: 20 units
• ✅ Minimum Water Resistance: 40 units

Objective

Minimize the total cost while meeting all engineering specifications.

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✅ Solution

Using Linear Programming optimization:

🎯 Optimal Mix:
   • Cement: 10 units
   • Sand: 10 units
   • Total Cost: $300

All constraints satisfied:

• Strength: 2(10) + 10 = 30 units ✓
• Durability: 10 + 10 = 20 units ✓
• Water Resistance: 10 + 3(10) = 40 units ✓

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📐 Mathematical Model

Decision Variables

• x₁ = Units of Cement
• x₂ = Units of Sand

Objective Function

Minimize: Z = 20x₁ + 10x₂

Constraints

Subject to:
   2x₁ + x₂  ≥ 30    (Strength)
   x₁  + x₂  ≥ 20    (Durability)
   x₁  + 3x₂ ≥ 40    (Water Resistance)
   x₁, x₂    ≥ 0     (Non-negativity)

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📂 Project Structure

construction-cost-optimization/
├── src/
│   ├── solver.py          # Custom LP Algorithm Implementation
│   ├── visualizer.py      # Matplotlib Visualization Tools
│   ├── gui.py             # Tkinter User Interface
│   └── main.py            # Application Entry Point
│
├── docs/
│   ├── problem_statement.md      # Detailed Problem Description
│   ├── mathematical_model.md     # Complete LP Formulation
│   ├── user_guide.md             # Usage Instructions
│   └── presentation.pdf          # Project Presentation
│
├── screenshots/           # Application Screenshots & Plots
├── requirements.txt       # Python Dependencies
└── README.md             # This File

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Installation

Prerequisites

• Python 3.8 or higher
• pip package manager

Quick Setup

# Clone the repository
git clone https://github.com/abdelrahmanelsafty75/construction-cost-optimization.git
cd construction-cost-optimization

# Install dependencies
pip install -r requirements.txt

# Verify installation
python src/main.py

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Usage

Option 1: Interactive Menu

python src/main.py

Launches an interactive menu with options:

1. CLI Mode - Command-line interface
2. GUI Mode - Graphical user interface
3. Run Examples - Pre-configured scenarios
4. Generate Visualizations - Create plots

Option 2: Direct GUI Launch

python src/gui.py

Opens the graphical interface immediately with:

• Input fields for costs and requirements
• Real-time optimization solving
• Interactive result visualization
• Parameter adjustment controls

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✨ Features

Core Capabilities

• Custom Manual Solver - Corner point method implementation from scratch
• PuLP Integration - Verification using industry-standard solver
• Interactive GUI - User-friendly Tkinter interface
• Advanced Visualizations - Professional matplotlib charts
• Sensitivity Analysis - Test parameter variations
• Batch Processing - Run multiple scenarios

Visualization Tools

• Feasible Region Plot - Shows constraints and optimal solution
• Cost Comparison - Compare different scenarios
• Sensitivity Analysis - Price variation impact
• Property Breakdown - Material contribution charts

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🖼️ Screenshots

GUI Interface

Feasible Region Visualization

Optimization Results

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📚 Documentation

Comprehensive documentation available in the docs/ folder:

• Problem Statement - Business context and problem description
• Mathematical Model - Complete LP formulation and solution methods
• User Guide - Installation, usage, and troubleshooting
• Presentation - Original project presentation

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🔬 Technical Details

Algorithm Implementation

• Method: Corner Point (Graphical) Method
• Approach: Find constraint intersections, evaluate objective at each
• Verification: Compare with PuLP Simplex solver
• Complexity: O(n²) for n constraints

Technologies Used

• Python 3.8+ - Core programming language
• NumPy - Numerical computations
• Matplotlib - Data visualization and plotting
• Tkinter - GUI framework (built-in with Python)
• PuLP - LP solver for verification (optional)

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🎓 Academic Context

Course: Operations Research
Institution: October 6 University
Semester: Fall 2025

This project demonstrates practical applications of Linear Programming in:

• Construction management
• Resource allocation
• Cost optimization
• Constraint satisfaction problems

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🤝 Contributing

Contributions are welcome! Please:

1. Fork the repository
2. Create a feature branch (git checkout -b feature/AmazingFeature)
3. Commit your changes (git commit -m 'Add some AmazingFeature')
4. Push to the branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

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Contact

For questions, suggestions, or collaboration:

• Email: [abdelrhmanelsafty74gmail.com]
• LinkedIn: [www.linkedin.com/in/abdelrahmanelsafty75]

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Made with ❤️ by the Construction Optimization Team
_{Operations Research Project - Fall 2025}