I think "restock" or "restock the inventory" or "replenish the inventory" sound ok. I used to work in the retail industry in the UK, and the word "buyer" was used as the job title of people who went out to seal deals with suppliers. For example, I knew a "buyer" who would travel to French vineyards and make deals for the supermarket she worked for to buy wine from the vineyard. So it's likely that restaurants have "buyers", too, or at least the role of "buyer", which may be performed by management or kitchen staff depending on the size of the enterprise.