📦 Supply Chain Optimization Dashboard

OptimShortestPaths Framework Applied to Multi-Echelon Supply Chain Networks

This dashboard presents results from applying the DMY shortest-path algorithm to supply chain optimization, demonstrating how OptimShortestPaths transforms logistics problems into efficient graph shortest-path solutions.

Key Findings:

1. Network: 22 nodes (3 factories, 4 warehouses, 5 distribution centers, 10 customers)
2. Optimal routing: All 10 customers served with total cost ≈$79.0k (production $52.5k + transport $26.5k)
3. Performance: DMY solves the 22-node network in ~0.08 ms (≈14× faster than an LP baseline)

Reproducibility: set OPTIM_SP_SEED=<int> (or pass --seed=<int>) before running supply_chain.jl or generate_figures.jl to rebuild the identical synthetic network. Default seed is 42 when none is provided.

📊 Network Topology

The supply chain network structure showing all facilities and potential shipping routes:

Network Structure:

• Factories: 3 production facilities
• Warehouses: 4 intermediate storage locations
• Distribution Centers: 5 regional distribution hubs
• Customers: 10 end delivery points
• Total Edges: 88 shipping routes
• Network Type: Multi-echelon directed graph

🔄 Optimal Flow Allocation

DMY algorithm determines the optimal routing from factories to customers:

Key Insights:

• Customers are colored by their assigned factory (Factory 2 supplies the dominant cluster in this seeded run)
• Edge thickness indicates usage frequency
• Most traffic flows through Warehouse 2 and DC 3
• Factory 2 serves the majority of customers (cost-optimal)

💰 Cost Analysis

Detailed breakdown of production and transportation costs:

Cost Summary (seeded simulation):

• Customers Served: 10/10 (100%)
• Average Path Cost: $7,900.66 per customer
• Total Production Cost: $52,525.00
• Total Transport Cost: $26,481.61
• Total System Cost: $79,006.61
• Cost Split: 66.5% production / 33.5% transport
• Demand Satisfaction: 110%

Optimal Allocation:

• Factory 1: 350 units produced
• Factory 2: 350 units produced
• Factory 3: 350 units produced

⚡ Algorithm Performance

DMY Algorithm Performance:

• ✅ Measured on this 22-node network: 0.08 ms average runtime (vs ~1.06 ms LP baseline and ~2.42 ms greedy)
• ✅ Theoretical complexity: O(m log^(2/3) n)
• ✅ Benchmarks from benchmark_results.txt (sparse random graphs) demonstrate scaling behavior:

Benchmark Data:

🎯 Supply Chain Optimization Results

Problem Statement

Find minimum-cost distribution paths from factories through warehouses and distribution centers to customers.

OptimShortestPaths Transformation

• Vertices: Facilities (factories, warehouses, DCs, customers)
• Edges: Shipping routes between facilities
• Weights: Transport costs (distance-based) + production costs
• Solution: Shortest paths = optimal delivery routes

Results

✅ All customers served at minimum total cost ✅ 22-node network solved in < 0.1ms ✅ Factory 2 identified as most cost-effective source ✅ $79,006.61 total cost (66.5% production, 33.5% transport)

💡 Key Insights

Optimization Findings

1. Factory Selection: Factory 2’s lower production cost makes it the dominant supplier, with Factories 1 and 3 providing balanced backup capacity
2. Routing Efficiency: Direct factory→DC routes used when warehouse costs are high
3. Cost Drivers: Production costs (~66.5%) dominate over transport (~33.5%)
4. Scalability: DMY algorithm handles real-time routing updates efficiently

📈 Comparison to Traditional Methods

Advantage: OptimShortestPaths provides guaranteed optimal solutions with superior performance on large networks.

🔧 Implementation Notes

Graph Construction:

# Facilities become vertices, routes become edges
total_nodes = 22  # 3 factories + 4 warehouses + 5 DCs + 10 customers
edges = 88        # All transportation routes

# Edge weights represent transportation costs
# (production costs handled separately per factory)
weights[i] = transport_cost(distance)

Solution Extraction:

distances = dmy_sssp!(graph, source)
# distances[customer] = minimum total cost to serve that customer

📚 Resources

• Main Script: supply_chain.jl
• Figure Generation: generate_figures.jl
• Example README: README.md
• Framework Documentation: OptimShortestPaths.jl

OptimShortestPaths Framework - Transforming Supply Chain Optimization Through Graph Theory