A minimum charge is the least a business will bill for attending, regardless of how little work is done.
What it is covering
The visit itself costs something before any work happens: the drive there, the drive back, the vehicle, and the paid time of a person who could have been somewhere else.
That cost is the same whether the job takes ten minutes or two hours — see labour cost and tickets per route.
Setting it
The floor is what a visit costs to make, including travel time and the overhead share the job should carry.
A minimum set below that guarantees a loss on every small job, and the losses are invisible because they average out against larger work — see job margin.
Why it should be stated up front
A minimum disclosed at booking is a term. Disclosed on the invoice it is a dispute, and it is a common cause of a chargeback or a poor review over an amount that was entirely fair.
Call-out fees applied to the work
A common arrangement is charging to attend, then crediting that amount against the repair if the customer proceeds.
It covers the wasted visit where they do not, and removes the objection where they do. It also filters enquiries from people who wanted a free opinion rather than the work.
Where the fee is for the diagnosis rather than the trip
That is a distinct charge with its own reasoning — see diagnostic fees.
Reviewing it
Minimums drift out of date as wages and fuel rise. A figure set three years ago is being charged against today's costs, which is the same problem as any other stale price — see pricing adequacy.