I want to auction a set of ASSETS ($A$) and fetch the maximum total price. The bidding is simultaneous and works as follows.
Say I have a collection of BIDDERS ($B$) who, individually, bid to purchase a subset of the assets $A$. Each bidder is constrained by a maximum outlay which is typically less than the total price of their bids. I.e., Bidders can not generally purchase all the assets they bid on. They must settle on a subset as determined by the AUCTIONEER.
What method, algorithm or protocol can the auctioneer follow to ensure he fetches the MAXIMUM TOTAL PRICE? (Your ideal answer would include pseudocode.)
There is a similar assignment problem which the Hungarian Algorithm solves. Here is an online implementation. However, that doesn't exactly solve this problem because more than one asset can be assigned to each bidder subject to their total outlay constraints.
To clarify the question a bit. I am seeking an algorithm or, ideally, computer code or a program that can solve the problem in polynomial time or better.