Robust Optimization: Lessons Learned from Aircraft Routing

Abstract

Building robust airline scheduling models involves constructing schedules and routes with reduced levels of flight delays as well as fewer passenger and crew disruptions. In this paper, we study different classes of models to achieve robust airline scheduling solutions, with a focus on the aircraft routing problem. In particular, we compare one domain-specific approach and two general paradigms of robust models, namely, (i) an extreme-value based or robust optimizationbased approach, and (ii) a chance-constrained or stochastic optimization-based approach. Our modeling and solution approach demonstrates the creation of data-driven uncertainty sets for aircraft routing using domain-specific knowledge and develops a completely data-driven simulation-based validation and testing approach. We first demonstrate that additional modeling, capturing domain knowledge, is required to adapt these general robust modeling paradigms to the aircraft routing problem, in order to meaningfully add robustness features specific to aircraft routing. However, we show that these models in their naive forms, still face issues of tractability and solution quality for the largescale networks which are representative of real-world airline scheduling problems. Therefore, we develop and present advanced models that address these shortcomings. Our advanced models can be applied to aircraft routing in multiple ways, through varied descriptions of the uncertainty sets; and moreover,

Robust Modeling and Planning: Insights from Three Industrial Applications

“…The impact of capturing uncertainty, and consequently, the impact of providing robust solutions, can be enormous. In the past two decades, therefore, there has been an exponential growth in developing uncertainty modeling approaches in the context of numerous applications, including finance [4][5][6][7][8], revenue management [9-14], queueing theory [15][16][17][18], transportation [19][20][21][22][23], project management [24], scheduling [25], network optimization [26,27], inventory and supply chain management [28,29] and energy grids [30][31][32][33].…”

“…They may be more comfortable with setting a 'robustness budget' δ -that is, the extent to which the key performance metric's value may be decreased in order to obtain a solution which is more robust than the nominal solution. Marla [72] and Marla, Vaze and Barnhart [73] propose to adapt the CCP model in this direction and suggest introducing a constraint that restricts the loss in the performance metric value by a cost budget δ while maximizing the robustness measure α. Specifically tailored to linear programs, their robust formulation sets the protection level α as a variable, while finding the most protected solution within a robustness budget δ compared to an optimal solution x* to the nominal problem:…”

“…. For details of the linearization of the formulation under right-hand-side uncertainty and special set-partitioning constraints, we refer the reader to Marla [72] and Marla, Vaze and Barnhart [73].…”

“…The selection of an overall robustness budget with respect to the cost may be more intuitive for the decision maker to specify and also eliminates the need to define a priori the robust measure Γ for each constraint. They propose an alternate model, in the same spirit as ECCP for CCP, tailored to large-scale binary integer programs, that sets an allowable 'robustness budget' δ with respect to the cost of the optimal solution x* to the nominal problem and maximize the number of coefficients Δ protected within that budget [72,73]. This formulation therefore is:…”

Robust Aircraft Routing

“…Applying robust optimization to the aircraft routing problem is fairly new. Until now, only one study (Marla and Barnhart 2010) has considered this approach. They compare the performance of three different classes of models: 1) chance-constrained programming, 2) robust optimization, and 3) stochastic optimization (Lan et al 2006).…”