Strangely, the small merchants in India are doing a great job when it comes to door delivery of groceries.
Even over 15-20 years back, my mom used to get door delivery of the month's groceries by just making a phone call.
One of the reason's for the success of this model was that most customers did not have a car to transport all of their groceries and phone-order was the easiest option available to them. (I'm talking about the late 90s when Internet was not that common).
Of course, it works on the assumption that the customer exactly knows what they want - rather than making them buying arbitrary items at the store.
Most of the merchants circulate their menu/deals along with newspapers and have a phone number that customers can reach them at. All you do is decide on what you want to order and then call the merchant at the given number. They deliver all the items at your house within a couple of hours. It uses the idea of "Cash on Delivery" i.e., you make your payment in-person to the delivery person. This method has been in practice for so many years that customers are quite used to the entire process and the merchants make sure that the delivery is processed as comfortably as possible.