Incomplete order and no refund

I had an order delivered but not all items were delivered. I contacted them and they had informed me that they could not get stock of the item. They did not inform me of this before hand or rather did not inform me of this at all, the full order had already been payed for as well. I then requested a refund and was told it would be sent through to their billing department and I have not heard back since and have not received the refund for the non-received items.