To the extent other parts of the convention need consumable materials to function, a Supplies system must be established by the Executive Committee. The simplest way would be to set up a reimbursements method with the treasurer, whereby people make purchases from their own funds, the treasurer determines the validitiy of the purchase for a convention purpose, and then pays the purchaser from the convention funds.
A more rigorous (but absolutely necessary in large conventions) method would be to designate one or more Buyers for the convention. Person(s) in this position would make regular shopping trips and provide the items to the requestor. Payment would be arranged between the buyer, the treasurer and the various vendors.
The reason that purchasing in larger, and in many smaller, conventions is centralized is that if every department needs office supplies, do you send one person or each department head/buyer? Conventions that have established a corporate entity can also get purchasing cards from Visa/MC/Amex, which can make the treasurer's job a lot easier.