We study stochastic integer programming models for assigning delays to flights that are destined for an airport whose capacity has been impacted by poor weather or some other exogenous factor. In the existing literature, empirical evidence seemed to suggest that a proposed integer programming model had a strong formulation, but no existing theoretical results explained the observation. We apply recent results concerning the polyhedra of stochastic network flow problems to explain the strength of the existing model, and we propose a model whose size scales better with the number of flights in the problem and that preserves the strength of the existing model. Computational results are provided that demonstrate the benefits of the proposed model. Finally, we define a type of equity property that is satisfied by both models.
In this paper, we define and investigate quantity-contingent auctions. Such auctions can be used when there exist multiple units of a single product and the value of a set of units depends on the total quantity sold. For example, a road network or airport will become congested as the number of users increase so that a permit for use becomes more valuable as the total number allocated decreases. A quantity-contingent auction determines both the number of items sold and an allocation of items to bidders. Because such auctions could be used by bidders to gain excessive market power, we impose constraints limiting market power. We focus on auctions that allocate airport arrival and departure slots. We propose a 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.
This paper provides a model-based approach to planning ground delay programs. Previous research on automated planning of ground delay programs has involved the use of mathematical programming techniques. This paper proposes a data-driven method that models the problem of choosing a traffic management initiative by using the framework of the multiarmed bandit decision problem. This approach makes greater use of the available data, and suggestions made by this procedure can be shown along with data that informed the decision. This combination of tools allows decision makers to more easily evaluate suggested decisions. The paper also provides simulations of the procedure on the basis of data from Newark (New Jersey) International Airport to evaluate its effectiveness.
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