Items (click to toggle selection)
Knapsack State
0
Total Value
0
Total Weight
Optimal Solution
Items: A + B + D
Weight: 15 | Value: 38
Weight Flow (capacity consumption over time)
Value Flow (value accumulation over time)
Strategic Analysis
Run ODE simulation to see analysis
How It Works
The 0/1 Knapsack Problem is modeled as a Petri net where:
- Places represent item availability and knapsack capacity
- Transitions represent taking each item
- Arc weights encode item weights as capacity consumption
The ODE simulation uses mass-action kinetics:
flux = rate × [item] × [capacity]^weight
Items with higher efficiency (value/weight) have higher rates, causing them to flow faster into the knapsack. The continuous approximation reveals which items compete most effectively for limited capacity.