Nowadays, the airlines use discrete optimization in many fields in order to plan and control resources like crews and aircraft. The biggest recent problem is a growing number of delays and delayed flights what significantly increases operational costs and harms goodwill of the airline. Therefore growing importance lies in robust optimization that can provide more stable solutions, with respect to delays, so to minimizes operational costs of the airline. In our project, we focus on one part of the planning, namely on Tail assignment.

Aim of the robust optimization is to deal with problems with uncertainty in data, what is the case of the most real world problems because input data are usually inaccurate or only estimated. To solve such a problem is difficult task. Especially, for discrete problems small change in input data can cause big change in quality of the solution. Here arises the question what an optimal solution for such a problem is. Robust optimization is widely studied topic in literature. Unfortunately, known solution methods produce too conservative solutions for practical usage and do not suite to discrete problems.

Tail assignment problem is the problem of assigning flights to individual aircraft in order to satisfy number of constraints like airport curfews, minimal connection times between flights and maintenance constraints.

In our problem uncertainty we deal with are flight departures and arrivals influenced by delays.For non robust schedule can small delay on one flight cause avalanche of delays on connecting flights, passangers can miss their connecting flight or, even worse, end up by cancellation of another flight much later. Aircraft assignment plays important role in robustness of airlines scheduling process, because aircraft rotation is one of the major sources of delays.

Our goal is to develop more robust aircraft rotations by solving set partitioning model by column generation algorithm.