Drivers generally don't get company phones or anything like that so if they are ringing you etc they are doing it out of their own pockets.
I'm shocked that you don't issue them with phones. I would've thought this would be mandatory.
Can you not issue them with mobile phones and customer telephone numbers? It would make your service that much better and would also reduce the number of parcels that your drivers have to bring back to the depot.
You could even use the fact that your drivers have company mobiles and phone customers (if no answer at the door), as a marketing trick to gain clients.
If I were a client and you added this feature to your company profile, I would definitely give it a go. The big gripe that most customers have with delivery companies is that "I was in, the driver didnt ring, he didnt leave a card", etc. Having a feature where the driver phones the customer if they fail to answer the door, would be a fantastic feature.
What you DO occasionally get is a driver who says he attempted when he didn't, this does nothing but cause me aggro and I wish they'd just be honest and admit that they ran out of time.
This is my biggest gripe with delivery companies. Don't lie or make up stories as it usually elongates the procedure of getting my parcel delivered.
You'd be surprised when push comes to shove how many "I WAS HOME ALL DAY!" stories eventually turn into "Well, I did nip out for half an hour, and I popped down the garden for a bit, so I suppose he might have come then..."
If you issued the driver with mobile phones, they could give the customer 1 call. If no answer, then leave the card and take a photo of the door, on their mobile phone (to prove that they did actually attend the property, should a customer complain and the driver be investigated).
Phoning may sound like time wasting, but when you consider that some delivery locations are quite remote - it makes no sense for sake of a 1 minute phone call, to driver all the way back to your depot and then drive out the next day, to the same remote location. A simple 1 minute phone call could save this. Your company would save fuel, driver time and extra resources which will be required to check the parcel back in, when the driver returns it to depot.
The phone call would also reduce the amount of occurrances where a driver can't find the delivery address or cards the wrong address. I remember when I was kid and delivered newspapers - some addresses are almost impossible to find unless you have been shown previously, by someone else how to get to the front door.