Relay Leg Assignment Optimizer
Find a minimum-time distinct-athlete assignment for an entered leg-time matrix.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use exact subset dynamic programming to assign every leg once with each athlete at most once.
Minimize sum(assigned athlete time on each leg)+(legs−1)×common transition seconds
Worked example
For the entered example, Alex on Leg 1, Blair on Leg 2 and Casey on Leg 3 total 181 seconds plus two 1-second transitions, giving 3:03.
Assumptions and input details
Up to 10 distinct legs and 12 candidates; at least as many candidates as legs. One optimum is shown if several tie. This optimizes a supplied deterministic matrix, without eligibility, fatigue, exchanges, recovery, event regulations or future performance assumptions.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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