I'm not sure if this is really applicable to your case, but this is my guess.

｢便」 usually refers to some kind of delivery service.

「代行」 usually refers to some kind of service that does your job for you, i.e. substitute worker, etc.

In Japan, there is a very popular service called 「運転代行屋」 which is a service that drives your car home for you when you've had too much (or even just a little) to drink. You (the owner of the car) sit in the passenger seat, and the driver drives your car home and parks your car in your garage, and you pay him, just like you would pay a taxi. Of course the question is, how does the driver get back? The service comes with another car+driver who follows the customer's car to the customer's home, and after they dropped off the customer and his car, the two drivers ride back in their own car. So, you can drink as much as you like and get home in your own car without driving under the influence.

Anyway, this ｢代行便」 appears to be a similar service, except, its for trucks, and its not for drunk drivers. Its a service offered to trucking companies if they are suddenly short of drivers, or for anyone who owns a truck, but is short of truck drivers.