An approval matrix sets who may approve what, at which value, for which part of the organisation. It grows because each exception seems reasonable at the time, and a matrix nobody can explain is one nobody maintains, which means it eventually routes requests to people who left and thresholds that no longer reflect any policy anybody agreed.
Start from delegated authority
Most organisations already have a delegation of authority written for contracts or capital spend, and invoice and order approval usually fall under it implicitly. Starting there keeps the matrix consistent with the rest of the organisation and makes it far easier to get agreed, because you are documenting existing policy rather than proposing new rules.
Route by cost centre and value
Stable, matches how budgets are held, and answerable by the approver, who is being asked whether their budget should carry this. Routing by supplier feels natural and ages badly, because supplier relationships move between departments and one supplier often serves several parts of the organisation at once.
Name deputies and a default owner
Absence is the largest single cause of approval delay, so every position in the matrix needs a deputy, and everything the rules cannot place needs a named default rather than a limbo queue. An item that routes nowhere is the one discovered weeks later when a supplier telephones about it.
Publish it
A requester who knows in advance what their request will need plans accordingly. One who finds out afterwards experiences the process as arbitrary and starts splitting requests to stay under thresholds, which is exactly the behaviour the matrix exists to prevent. Publishing costs nothing and removes most of the friction.
Questions people ask about approval matrix
How many levels should there be?
As few as your delegated authority allows. Each level adds elapsed time and dilutes responsibility, and two approvers each assuming the other looked is a documented failure.
How often should it be reviewed?
Annually and after any reorganisation, since cost centre structures change more often than approval matrices get updated.
Who owns it?
Whoever owns the delegated authority, with finance implementing it. A matrix maintained only in a system configuration drifts from the policy it was meant to encode.