How It Works - Detailed Guide
Understanding the matching algorithm with examples
📚Quick Navigation
🧮The Hungarian Algorithm
The Hungarian Algorithm solves the assignment problem: Given N officers and N positions, find the optimal one-to-one assignment that maximizes total satisfaction.
Why Use This?
- ✓Optimal: Best possible outcome
- ✓Fair: Considers all preferences
- ✓Fast: Handles 100+ officers instantly
- ✓Proven: Used in economics & logistics
Builds a "reward matrix" where each cell = how good a pairing would be, then finds the assignment that maximizes total reward.
🎯Scoring System
Each officer-position pairing gets a reward score:
⚠️ The -99 penalty ensures officers rotate to new roles instead of staying in place.
📝Basic Example: 3 Officers, 3 Positions
Input Data
Officer Preferences
| Officer | Current | Wants |
|---|---|---|
| Alice | A | B,C,A |
| Bob | B | C,A,B |
| Carol | C | A,B,C |
Position Preferences
| Position | Wants |
|---|---|
| Pos A | Carol,Bob,Alice |
| Pos B | Alice,Carol,Bob |
| Pos C | Bob,Alice,Carol |
✨ Result
Everyone got 1st choice!
Reward Matrix (How Scores Are Calculated)
| Officer | Pos A | Pos B | Pos C |
|---|---|---|---|
| Alice | -99 current | 6 both 1st | 4 both 2nd |
| Bob | 4 both 2nd | -99 current | 6 both 1st |
| Carol | 6 both 1st | 4 both 2nd | -99 current |
Algorithm picks assignments with highest scores while ensuring each officer gets exactly one position.
🔧Org Preferences Example
Use org bonuses to influence assignments for strategic reasons:
Scenario: Succession Planning
Groom David for leadership by assigning to Manager (Finance).
| Officer | Position | Bonus |
|---|---|---|
| David | Mgr (Finance) | +3 |
Impact on Scoring
Without:
+2 (David 2nd)
+1 (Pos 3rd)
+0 (org)
= 3 pts
With Bonus:
+2 (David 2nd)
+1 (Pos 3rd)
+3 (org) ⭐
= 6 pts
Result: Bonus doubles the score, making this assignment much more likely!
⚠️Edge Cases
1.More Officers than Positions
10 officers, 8 positions → 2 officers unassigned
Fix: Add positions or keep some in current roles
2.More Positions than Officers
8 officers, 10 positions → 2 positions vacant
Fix: Recruit or consolidate positions
3.Everyone Wants Same Position
All 5 officers want "Manager (Finance)"
How resolved: Position preferences break the tie
4.No Mutual Preferences
Officer and position don't prefer each other
Result: Score = 0. Use org bonuses to guide
💡Best Practices
DO
- • Collect honest preferences
- • Use org bonuses sparingly
- • Review and iterate
- • Communicate the process
- • Keep names consistent
DON'T
- • Override all preferences
- • Use extreme bonuses carelessly
- • Forget positions in file
- • Have duplicate names
- • Ignore results blindly
🔄Iterative Approach
- 1.Run with basic prefs
- 2.Review results
- 3.Add org bonuses
- 4.Run again & compare
- 5.Repeat until satisfied