How e dey work, well well
Each person rank di options. Wish of rank 1 cost 1, rank 2 cost 2, and so on: na so dem build di cost matrix.
Dem dey find di assignment wey make di TOTAL cost small pass, exploring all di possible combinations with sense — never one by one, wey no go possible.
Important thing: di calculation fit sacrifice one person to help several. Di optimum na collective, and na exactly wetin dem ask am to do.
Example wey get figures
Three people, three assignments. Di boxes show di rank of di wish.
| Audit | Redesign | Support | |
|---|---|---|---|
| Chloé | 1 | 2 | 3 |
| Ali | 1 | 3 | 2 |
| Bruno | 2 | 1 | 3 |
- To give everybody dia first wish no possible: Chloé and Ali both want Audit.
- Chloé→Audit, Bruno→Redesign, Ali→Support: total cost 1 + 1 + 2 = 4.
- Ali→Audit, Bruno→Redesign, Chloé→Support: total cost 1 + 1 + 3 = 5.
Dem take di first combination: for similar wishes, e cost di group less. No other arrangement fit beat 4.
Where e come from
Na di « assignment problem », classic work for operations research. Harold Kuhn publish efficient solution for 1955 and call am « Hungarian algorithm », to honour di Hungarian mathematicians Dénes Kőnig and Jenő Egerváry wey im work follow.
Later dem come find say Carl Gustav Jacobi don solve di problem for di 19th century, for work wey dem publish after im death for 1890 — sixty-five years before dem rediscover am.
Today di algorithm na normal industrial tool: to assign crews to flights, tasks to machines, vehicles to trips. Every application wey dey pair two sets while optimising total cost na im pikin.
Where dem dey use am
- To share assignments or files across team while maximising overall satisfaction.
- To assign pupils to workshops, options or projects.
- To assign on-call or duty slots.
- To plan crews, routes or machines — di historic industrial use.
Limits and wahala
- Di best total satisfaction wey possible
- No draw involved
- Exact result, no be approximate
- E fit sacrifice one person for common good
- Tactical rankings dey possible
- E no too easy to explain
Questions wey people dey ask
How e take better pass serial dictatorship?
On average, di group dey more satisfied: di algorithm dey see all di combinations one time, while serial dictatorship dey suffer di running order. Di price na readability — and di chance for people to lie.
Wetin happen if two assignments tie?
Several solutions fit reach di same minimum cost; dem go pick one. If di matter heavy, announce di tie-break rule before, or switch to serial dictatorship, wey mechanics dey reproducible.
I need as many places as people?
No, but di gap get price: if places no reach, somebody no go get assignment; if dem plenty pass, some go remain empty. Di calculation still valid both ways.