Linear Metal Part Optimizer

A web-based calculator that optimizes metal purchasing decisions to minimize costs and waste. This tool determines the most cost-effective combination of metal lengths to purchase while providing detailed cutting plans.

Mathematical Foundation

The LMP-Optimizer uses a combination of mathematical approaches:

Cost Minimization Function

Minimize: Σ(Ci × Qi)
Subject to: Σ(Li × Qi) ≥ Σ(Pj × Qj)
Where:
- Ci = Cost per unit of option i
- Qi = Quantity of option i to purchase
- Li = Length of option i
- Pj = Length of required part j
- Qj = Quantity of required part j

Backtracking Algorithm

The algorithm explores all possible combinations using:

• State Space: Each state represents a partial solution with remaining material needs
• Pruning: Eliminates branches where current cost exceeds the best known solution
• Optimization: Minimizes total cost while ensuring all parts can be produced

Cutting Optimization

For each purchased piece, the algorithm:

1. Sorts parts by length in descending order: P1 ≥ P2 ≥ ... ≥ Pn
2. Fits parts using a greedy approach: remaining_length ≥ part_length
3. Calculates waste: waste = piece_length - Σ(used_parts)
4. Minimizes total waste across all pieces

Efficiency Metrics

• Cost per foot: CPF = price / length
• Waste percentage: WP = (total_waste / total_purchased) × 100
• Material utilization: MU = (total_used / total_purchased) × 100

#Use

1. Add Required Parts

• Enter the length of each part needed (in feet)
• Specify the quantity required
• Click "Add Part" to add to your list
• You can add unlimited parts

2. Define Purchasing Options

• Enter available metal lengths and their prices
• The calculator shows cost per foot for easy comparison
• Add multiple purchasing options from different suppliers

3. Calculate Optimal Purchase

• Click "Calculate Optimal Purchase" to run the LMP-Optimizer
• View the optimal combination of metal to buy
• See detailed cutting instructions for each piece

4. Review Results

• Purchase Plan: Shows exactly what to buy and total cost
• Cutting Plan: Visual guide for cutting each piece
• Material Summary: Total needed vs purchased vs excess
• Chart: Visual breakdown of material usage

Algorithm Details

LMP-Optimizer (Linear Metal Part Optimizer)

The calculator uses the LMP-Optimizer algorithm that:

1. Sorts Options: Orders purchasing options by cost per foot
2. Explores Combinations: Tests different combinations of metal lengths
3. Minimizes Cost: Finds the combination with the lowest total cost
4. Allows Excess: Permits some excess material to find better deals

Cutting Optimization

The cutting plan algorithm:

1. Sorts Parts: Orders parts by length (largest first) for efficiency
2. Fits Parts: Tries to fit as many parts as possible into each piece
3. Minimizes Waste: Reduces scrap material through smart placement
4. Visual Guide: Shows exactly how to cut each piece

Example Use Case

Scenario: Manufacturing Project

• Parts Needed:
  • 10 pieces of 8 ft metal
  • 15 pieces of 6 ft metal
  • 20 pieces of 4 ft metal
• Purchasing Options:
  • 20 ft pieces at $50 each
  • 12 ft pieces at $35 each
  • 8 ft pieces at $25 each

Result:

The LMP-Optimizer will determine the optimal combination (e.g., 2×20ft + 3×12ft + 1×8ft) and show exactly how to cut each piece to minimize waste and cost.

Features in Detail

Cost Optimization

• Compares cost per foot across all options
• Finds the best combination even if it means buying more than needed
• Considers bulk discounts and supplier variations

Waste Minimization

• Shows exact waste from each cut
• Calculates waste percentage
• Suggests uses for excess material

Visual Cutting Guide

• Color-coded segments show different cuts
• Blue segments: Parts to be cut
• Red segments: Waste material
• Proportional sizing based on actual lengths

Real-time Updates

• Add/remove parts and options dynamically
• Instant recalculation when inputs change
• Live preview of cost implications

Customization

Styling

The application uses CSS custom properties that can be easily modified:

• Color scheme can be changed by updating CSS variables
• Layout can be adjusted for different screen sizes
• Typography can be customized for brand consistency

Functionality

• Algorithm parameters can be adjusted for different optimization strategies
• Chart types can be changed for different data visualization needs
• Additional input validation can be added as needed

Contributing

This is a standalone application designed for metal purchasing optimization. The code is well-documented and modular, making it easy to extend with additional features.

License

This project is open source and available for educational and commercial use.

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LBO Metal Purchasing Calculator - Optimize your metal purchasing decisions with precision and efficiency using the LMP-Optimizer algorithm.