Assignment Problems Topic Review summary

Key learning points

• Balance the matrix if needed (dummy row/column of zeros).
• Row reduce then column reduce to create zeros.
• Cover zeros with minimum lines; adjust if an assignment is not yet possible.
• Read off an optimal assignment from independent zeros.
• Maximisation: subtract each entry from the largest, then minimise.

Worked example 1 — Reduce

First step of Hungarian on a cost matrix?

Working

Creates zeros for assignment.

Worked example 2 — Max → min

How to maximise profit with Hungarian?

Working

Then run minimisation.

Worked example 3 — Practice point 1

Apply this idea from the Topic Review: Balance the matrix if needed (dummy row/column of zeros).

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Practice point 2

Apply this idea from the Topic Review: Row reduce then column reduce to create zeros.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.