We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 06 July 2010
This chapter presents several applications of integer linear programming: combinatorial auctions, the lockbox problem, and index funds. We also present a model of integer quadratic programming: portfolio optimization with minimum transaction levels.
Combinatorial auctions
In many auctions, the value that a bidder has for acquiring a set of items may not be the sum of the values that he has for acquiring the individual items in the set. It may be more or it may be less. Examples are equity trading, electricity markets, pollution right auctions, and auctions for airport landing slots. To take this into account, combinatorial auctions allow the bidders to submit bids on combinations of items.
Specifically, let M = {1, 2, …,m} be the set of items that the auctioneer has to sell. A bid is a pair Bj = (Sj, pj) where Sj ⊆ M is a nonempty set of items and pj is the price offer for this set. Suppose that the auctioneer has received n bids B1, B2, …, Bn. How should the auctioneer determine the winners in order to maximize his revenue? This can be done by solving an integer program. Let xj be a 0,1 variable that takes the value 1 if bid Bj wins, and 0 if it looses.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
