In short, a distribution centre gives you:
* improved pick efficiency (depending on the level of automation), offset somewhat by maintenance costs and the cost of capital.
* increased delivery/transport costs (stores are generally closer to the customer than the cross dock point / outbase, vehicles are already going to the store for the main delivery)
\ flowing more product through existing retail points reduces waste (expiring products).
* increased property cost (you have to pay for a distribution centre at c£9 per square foot incl rates etc, while in retail the space is more expensive but you are already* renting it).
The one thing a fulfilment centre does give you is better service though. You can hold more range, better track dates/batches so you can give your customers the expiry dates on the website and increase availability.
So the honest answer is that delivery from a central point isn’t a slam dunk, and can definitely work but probably won’t be cheaper.