We define and investigate quantity-contingent auctions. Such auctions can be used when there exist multiple units of one or more products and the value of a set of units depends on the total quantity sold. For example, a road network or airport will become congested if too many cars or aircraft are admitted. Thus, access to these resources is more valuable as the total usage level is limited. A quantity-contingent auction determines both the number of items sold and an allocation of items to bidders. Since such auctions could be used by bidders to gain excessive market power we impose constraints limiting market power. We focus on the application of such auctions to the allocation of airport arrival and departure slots, which involve multiple products and multiple units of each product. We propose an (approximate) continuous model and an integer programming model for the associated winner determination problem. Using these models, we perform computational experiments that lend insights into the properties of the quantity-contingent auction particularly for the airport slot allocation setting. Co-authors: Alex Estes, Mark Hansen, Yulin Liu
Michael Ball holds the Dean’s Chair in Management Science at the Robert H. Smith School of Business at the University of Maryland. He also has a joint appointment within the Institute for Systems Research (ISR) in the Clark School of Engineering and is a member of the Decision, Operations and Information Technologies Department within the Smith School. Dr. Ball has over 150 scholarly publications, covering a range of subjects including air transportation, revenue management and pricing, supply chain management and system reliability. He is co-Director and principal investigator of NEXTOR-II, an 8-university consortium funded by the FAA to carry out research in aviation operations research. Several of his research and consulting projects have led to implementations in industry and government. In the past five years, he has been a member of various expert panels that have given advice to the United Nations, the FAA, the National Academy of Engineering and multiple airport authorities on aviation policies. Throughout his career, Dr. Ball has been an active member of INFORMS, the Institute for Operations Research and the Management Sciences. He has been area editor for both Transportation and Optimization for Operations Research and is now associate editor for the journals, Operations Research and Transportation Science. In 2008, he was president of the INFORMS Transportation Science and Logistics Society. In 2004, he was named an INFORMS Fellow. Dr. Ball received BES and MSE degrees from Johns Hopkins University in 1972 and a PhD in Operations Research from Cornell University in 1977.
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