FedEx ULD Optimization

The Unit Load Device (ULD) optimization problem focuses on enhancing operational efficiency, reducing costs, and improving service reliability in logistics networks. ULDs are standardized air shipment containers with strict weight and volume limits, requiring efficient packing to maximize space utilization, minimize costs, and ensure the timely delivery of Priority Packages.

The challenge is to determine which packages to load into which ULDs while adhering to constraints such as weight limits, package dimensions, and the precedence of Priority Packages. Properly optimized ULDs not only reduce costs and ensure efficient resource utilization but also improve delivery timeliness and contribute to environmental sustainability by minimizing fuel consumption and carbon emissions.

Packing Simulation using Streamlit

We have provided a GUI, deployed using Streamlit, to display the packing sequence in each ULD, along with the packing visualization.

Deployment

Installing the Dependencies

Make sure that you have Python 3.12 installed on your system.

Run the following command in your terminal:

pip install -r requirements.txt

Ensure that your system has a valid Gurobi Named-User License installed.

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Running the Program

1. Command-Line Interface

Run the following command in the repository folder:

python main.py

For advanced usage, an optional timeout parameter t (in seconds) can be added to control the runtime. Here t is not the total runtime, but the time the MIP solvers will run for:

python main.py t

2. Streamlit Web Application

To run the Streamlit app, use one of the following commands in the terminal inside the repository folder:

streamlit run Streamlit_App.py

If the above doesn't work, try:

python3 -m streamlit run Streamlit_App.py

Or:

python -m streamlit run Streamlit_App.py

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Streamlit App Usage Guide

Main Page

When you first launch the app, you will see the main page with two input options:

• Upload File: Upload CSV files for ULDs and packages.
• Manual Input: Enter ULD and package data directly into the app.

Input Methods

File Input Method:

Prepare two CSV files:

• ULDs: Contains ULD data with columns: ULD_id, length, width, height, and weight_limit.
• Packages: Contains package data with columns: Package_id, length, width, height, weight, package_type, and penalty (for economy packages; enter - for priority packages).

After that, you can choose the runtime t. Here t is not the total runtime, but the time the MIP solvers will run for.

Example ULDs CSV:

U1, 100, 100, 100, 2500
U2, 100, 150, 125, 3000

Example Packages CSV:

P1, 99, 53, 55, 61, Economy, 176
P2, 56, 99, 81, 53, Priority, -
P3, 42, 101, 51, 17, Priority, -
P4, 108, 75, 56, 73, Economy, 138
P5, 88, 58, 64, 93, Economy, 139

Manual Input Method:

Manually enter details for:

• ULDs: ULD_id, length, width, height, weight_limit.
• Packages: Package_id, length, width, height, weight, package_type, penalty (for economy packages; enter - for priority packages).

Click on Add ULD or Add Package after entering data for each ULD/package.

After that, you can choose the runtime t. Here t is not the total runtime, but the time the MIP solvers will run for.

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Visualization

After input, the app will:

• Solve package placement optimization.
• Create interactive 3D visualizations of package placement.
• Display progressive packing sequences.
• Show detailed metrics, including:
  • Free space percentage.
  • Free weight percentage.
  • Total number of packages.
  • Priority vs. economy packages packed.
  • Total packages loaded.
  • Total cost of shipment.

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Solution Pipeline

Overview of Optimization Strategy

The solution pipeline employs a multi-stage approach to efficiently pack packages into Unit Load Devices (ULDs), combining heuristic methods and Mixed Integer Programming (MIP) techniques.

Pipeline Stages

1. Initial Data Preprocessing

   • Reorder ULD and package data using custom heuristics.
   • Prepare data for an efficient placement strategy.

2. Package Classification

   • Separate packages into:
     • Priority Packages: High-importance items.
     • Economy Packages: Standard items.

3. Initial Package Assignment

   • Extreme Points Filling: Assign packages using extreme point placement to optimize spatial utilization.
   • Tri-Planar Projection: Analyze and optimize placements along three axes (X, Y, Z).

4. Space Defragmentation

   • Reorganize package placements to minimize unused space and improve ULD efficiency.

5. Second Projection and Refinement

   • Repeat tri-planar projection for further optimization.

6. First Mixed Integer Programming (MIP) Stage

   • Attempt to fit unassigned packages using mathematical optimization.
   • Execute for a predefined number of iterations.

7. Second MIP Stage

   • Focus on package swapping and optimizing assignments.
   • Run additional iterations to maximize placement efficiency.

Optimization Objectives

• Maximize ULD space utilization.
• Prioritize critical (priority) packages.
• Minimize transportation costs.
• Reduce the number of unused or partially filled ULDs.

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Potential Future Enhancements

• Advanced space fragmentation techniques.
• Enhanced MIP formulations.
• Machine learning-based placement predictions.