Mathematics of Information Technology and Complex Systems

 

 

 

 

 

 

Milestones

·  2001
Development of a pricing bilevel model and initial proof of concept. Complexity results, development of algorithms.

·  2002
Development of the calibration module. New theoretical results on complexity. New branch-and-bound approach. Validation on real life airline data.

·  2003
Extensive testing of the optimization engine on the North American low-cost airline market. Development of specialized solution algorithms for solving instances of practical size. Adaptation of the model to the passenger rail problem.

·  2004
Integration of capacity.  Extensive testing of the model and algorithms on real rail data (provided by a major European railway). Adaptation of the model to the telecom context and pricing of bandwidth.

·  2005
Development of new behavioural model based on the random utility paradigm: connection with previous multiclass model. New algorithms to incorporate these random models. Results on dynamic pricing and real options.

·  2006-2009

Development of a simulator for the airline industry. New algorithms for the calibration of nested logit models. Real life applications in airline and rail. Development of forecaster based on neural networks.

 

And, throughout the entire project, lots of lemmas, theorems and corollaries pertaining to variational inequalities, polyhedral theory, bilevel optimization, optimal control, simulation.