A Stochastic Integer Program with Dual Network Structure and Its Application to the Ground-Holding Problem

Abstract

In this paper, we analyze a generalization of a classic network-flow model. The generalization involves the replacement of deterministic demand with stochastic demand. While this generalization destroys the original network structure, we show that the matrix underlying the stochastic model is dual network. Thus, the integer program associated with the stochastic model can be solved efficiently using network-flow or linear-programming techniques. We also develop an application of this model to the ground-holding problem in air-traffic management. The use of this model for the ground-holding problem improves upon prior models by allowing for easy integration into the newly developed ground-delay program procedures based on the Collaborative Decision-Making paradigm.

Applications of Operations Research in the Air Transport Industry

“…For example, one of the most critical problems in the planning of GDPs continues to be the determination of airport acceptance rates (AAR) for several hours into the future and in the presence of uncertainty about airport capacity and air traffic demand. The efficient stochastic integer program developed for this purpose by Ball et al (2003) can be viewed as a direct descendant of the pre-CDM model proposed by Richetta and Odoni (1993).…”

“…Examples of some topics, along with occasional recent references, include: identifying (as an airline) flights that should be cancelled or delayed (and by how much) in connection with GDPs, recovering (as an airline) from irregular operations (cf. §2) resulting from GDPs or other ATFM interventions, ensuring equity of access to airports and ATM resources (Vossen et al 2003), collaborative routing of aircraft through congested airspace (Ball et al 2002), introducing bartering and possibly market-based mechanisms in the allocation of airport slots (Vossen andBall 2001, Hall 1999), and developing efficient simulation environments for the testing of alternative ATFM strategies.…”

Ground Delay Program Planning Under Uncertainty Based on the Ration-by-Distance Principle

“…see (Inniss and Ball 2004), (Liu et al 2006) and (Wilson 2004). Ball et al (2003) proposed an aggregate version of the Richetta and Odoni model that directly sets the PAAR without assigning delays to specific flights. This model was designed for use in a CDM context where other processes that take equity into account and that accept airline preferences to determine the actual flight-to-slot assignment.…”

A General Approach to Equity in Traffic Flow Management and Its Application to Mitigating Exemption Bias in Ground Delay Programs

“…We take as a given in this paper the need to restrict the geographical scope of a GDP and that TFM exercises this option at their discretion on a program-by-program basis (see [ 5], [ 6], [ 7] for a treatment of stochastic planning issues in GDPs). Instead, our interest lies in the ramifications of the exemptions.…”

“…fewer exemptions) may lead to an inequitable distribution of (in hindsight) unnecessary delay, if the predicted reduction in capacity does not materialize, while a small scope may lead to an inequitable distribution of actual delays if the capacity reductions do materialize. As such, integrating the approach described here with GDP models that incorporate uncertainty ( [4], [6]) presents a topic for further research.…”