A method and apparatus allow the computer based implementation of an auction of heterogeneous types of items wherein one or more types of the items may include plural items. At any point in the bidding process, the set of feasible assignments of the items, given the bidding state, is the set of all possible allocations of the available quantity of the types of items to the bidders, subject to satisfying all the constraints on the assignment of the items, the constraints on the bidding process and the constraints posed by the bidding state. There may be a time in the auction when, based on the bidding state, one or more items (of one or more types) can only be assigned to one particular bidder in any feasible assignment, i.e., the particular bidder is guaranteed to be assigned the item. Such item is assigned to such bidder at such time.