Optimal crew groups A column generation heuristic for a combinatorial optimization problem

The studied problem is how to construct groups of cabin crew that will work together for a month. The construction of groups should as far as possible fulfill requests from both the airline and the crew. There is today at Carmen Consulting an application based on Constraint Logic Programming (CLP) that solves the problem. The purpose of this project was to examine whether mathematical optimization methods could improve the construction of crew groups. The new solution method relies on an enumeration of possible groups, where the constraints for group construction is handled by CLP. The selection of groups is then through a set-partition formulation treated as an optimization problem. A heuristic column generation is developed to implicitly consider a large number of possible groups while enumerating a relatively small number of them. Results for the new solution method have been compared to results found with the existing application for a randomly chosen month. The objective value for these test cases improved between 3 and 6%. Solution time was also decreased; especially for a large test case there was a considerable improvement (from 4068 to 1325 seconds). Optimala besättningsgrupper En heuristik för kolumngenerering till ett kombinatoriskt optimeringsproblem