Assuming, of course, that people actually do the proper thing when removing a container.
@PaulS, man you hit the problem squarely. Still too much human trust in the process.
Personally, I would put microswitches (Hall effect, reed, etc.) Under each bin location. When an Active bin was lifted, the staff would have 15 seconds to use their personal RFID card-tag to log the bin outbound. Reverse for inbound. Siren, red-fladhing lights, or other fun alarms would instill trustworthiness 
Ray