A minimum charge is the floor under every bill. However small the job, the customer pays at least that amount. It exists because a ten-minute job costs nearly as much to deliver as a one-hour job: the drive, the parking, unloading, the paperwork and the drive to the next one are the same either way. It is usually stated as a dollar figure that includes a set amount of time on site, or as a minimum number of hours, such as a one-hour minimum for a trade or a four-hour minimum for a machine with an operator.
A minimum charge is not the same as a call-out fee. A call-out fee is added on top of the work; a minimum charge is the least the whole visit can come to. Some businesses use both, with a call-out fee and a minimum of one hour of labour after it. That is defensible but harder to explain, and a single clear minimum usually goes down better with customers.
In practice
An electrician sets a minimum charge of $180, covering travel and the first 45 minutes on site, with labour after that at $110 an hour. Replacing a broken light switch takes 15 minutes, and the bill is $180. Fitting a new power point in the same kitchen takes 75 minutes, so the bill is $180 plus 30 minutes at $110, which is $235, plus the part. Both customers heard "$180 minimum, which covers the first 45 minutes" on the phone, so neither bill is a surprise.
The two places a minimum charge goes wrong are silence and inconsistency. A minimum that is first mentioned on the invoice reads as a penalty. A minimum that applies to some customers and not others gets talked about. Say it when the job is booked, put it on the quote, and apply it every time. The guide to minimum charges for small jobs covers how to set the figure.
In Quote Desk
Add the minimum to your price list as one item priced each. A job that falls under it becomes a single-line quote, and a job that runs over gets the extra labour as further lines.