Using deficit functions for crew planning in aviation

We use deficit functions (DFs) to decompose an aviation schedule of aircraft flights into a minimal number of periodic and balanced chains (flight sequences). Each chain visits periodically a set S of airports and is served by several cockpit crews circulating along the airports of this set. We introduce the notion of "chunks" which are a sequence of flights serviced by a crew in one day according to contract regulations. These chunks are then used to provide crew schedules and rosters. The method provides a simplicity for the construction of aircraft schedules and crew pairings which is absent in other approaches to the problem.