Stochastic capacity expansion models for airport facilities

• Formulating global planning models for optimizing airport facility development.
• Proposing a superior out-approximation technique to existing discrete approximation.
• Providing a tighter formulation which requires less computation.
• Designing efficient interactive framework for finding the global optimum.
• Obtaining considerable savings (18.8% in the example) through the stochastic program.

It is important and also challenging to plan airport facilities to meet future traffic needs in a rapidly changing environment, which is characterized by various uncertainties. One key issue in airport facility development is that facility performance functions (delay levels as functions of capacity utilization rates) are nonlinear, which complicates the solution method design. Potential demand fluctuations in a deregulated aviation market add another dimension to the decision making process. To solve this problem, a deterministic total cost minimization model is proposed and then extended into stochastic programs, by including uncertainties in traffic forecasts. After the exploration of properties of the delay cost function, an Outer-Approximation (OA) technique which is superior to the existing discrete approximation is designed. After model enhancements, an efficient solution framework based on the OA technique is used to solve the model to its global optimality by interactively generating upper and lower bounds to the objective. Computational tests demonstrate the validity of developed models and efficiency of proposed algorithms. The total cost is reduced by 18.8% with the stochastic program in the numerical example.