At VideoIQ we had a number of Goodwill stores as customers that used video analytics along with remote live monitoring for this exact problem.
You can also try an automated/pre-recorded message, though many times that quickly becomes ineffective when people realize there is no threat behind it.
The basic idea is that you have a camera setup to monitor the area around the donation drop-off, and send an alert to a remote monitoring center. The monitoring center will do a live audio talk-down, telling the person the store is closed, they need to leave, etc. The live audio tends to be very effective because people know they are being watched, it's not just a basic "get lost" message. If it's an extreme problem you can also add a PTZ that the remote operator can use to get license plate details.
If the person does not leave just from the audio talk-down, local police are called. Response times are generally better than average, because the police dispatcher is being told by the remote monitoring center that the crime is in-progress, they can also give details on how many people are there, etc.
From an analytics standpoint, this is a fairly basic problem. You may have some problems with stray animals, but for the most part there should be multiple vendors that could tackle this.
For the remote monitoring, something like this is probably going to cost the customer $150-$250/mo. per location (based on rates in the US). It will mostly be dependent on how many alarms are generated overall, so reducing false alarms is important as it will cut costs down.
I would suggest finding a monitoring company first, and then asking them what products they prefer to monitor vs. buying a camera or analytics package and then trying to find someone who can monitor that device.
Glean from this (or this) what you can. Good luck.
Pro Focus LLC | 05/05/16 12:30pm
How about a change in business hours to accommodate late drop offs, a secure bin to have late drop offs accepted, where they cannot be pilfered, or placing a really large dumpster where people normally dump stuff at night.