A Method for Optimally Solving the Rostering Problem

Abstract

This paper presents a prototype method for optimally solving the rostering problem, i.e., constructing work schedules for airline crew members. The main goal is to show the possibilities of solving the rostering problem using optimal methods. The prototype uses a column generation approach embedded in a branch and bound algorithm to solve the rostering problem. To the knowledge of the authors, this prototype is the first optimal method for solving the rostering problem.

The prototype is first tested for the construction of two-week schedules for pilots. Then, a strategy for accelerating the column generation process is discussed. The strategy consists in generating “disjoint columns”, i.e., columns with no or few activities in common, during optimization. This strategy is shown to decrease solution time by almost half in test problems. The use of disjoint columns shows great promise for generalized set-partitioning problems.

In the rostering problem, employees usually make requests such as a specific rest period, a flight that goes to a specific city, etc. All methods existing in the literature satisfy such requests before constructing schedules. One approach presented in this paper, by contrast, includes the assignment of requests in the optimization process. This approach and the conventional approach to rostering are both evaluated with respect to their ability to satisfy requests and the number of employees needed to cover all tasks to be performed during the schedule period. An analysis of the tradeoff between those two factors is also presented. It appears from this analysis that it is important to reconsider the preassignment of some desirata because it has a direct effect on productivity.