scholarly journals Discrepancy distances and scenario reduction in two-stage stochastic mixed-integer programming

2008 ◽  
Vol 4 (2) ◽  
pp. 363-384 ◽  
Author(s):  
René Henrion ◽  
◽  
Christian Küchler ◽  
Werner Römisch ◽  
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Mixed Integer ◽  
Two Stage ◽  
Scenario Reduction ◽  
Stochastic Mixed Integer Programming

scholarly journals Two-Stage Stochastic Mixed-Integer Programming with Chance Constraints for Extended Aircraft Arrival Management

2020 ◽  
Vol 54 (4) ◽  
pp. 897-919
Author(s):  
Ahmed Khassiba ◽  
Fabian Bastin ◽  
Sonia Cafieri ◽  
Bernard Gendron ◽  
Marcel Mongeau
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Benders Decomposition ◽  
Chance Constraints ◽  
Mixed Integer ◽  
Chance Constrained Programming ◽  
Management Problem ◽  
Two Stage ◽  
Acceleration Techniques ◽  
Stochastic Mixed Integer Programming

The extended aircraft arrival management problem, as an extension of the classic aircraft landing problem, seeks to preschedule aircraft on a destination airport a few hours before their planned landing times. A two-stage stochastic mixed-integer programming model enriched by chance constraints is proposed in this paper. The first-stage optimization problem determines an aircraft sequence and target times over a reference point in the terminal area, called initial approach fix (IAF), so as to minimize the landing sequence length. Actual times over the IAF are assumed to deviate randomly from target times following known probability distributions. In the second stage, actual times over the IAF are assumed to be revealed, and landing times are to be determined in view of minimizing a time-deviation impact cost function. A Benders reformulation is proposed, and acceleration techniques to Benders decomposition are sketched. Extensive results on realistic instances from Paris Charles-de-Gaulle airport show the benefit of two-stage stochastic and chance-constrained programming over a deterministic policy.

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