Acceleration strategies of the column generation method for the crew scheduling problem

Abstract

Crew scheduling is an important optimization problem in the railway industry. In last decades, the extension of computational resources made it feasible to address real-life problems generating large-scale set covering problems. Broadly used is the concept of shift frames, which is well suited current practice of several railway operators. In the case when the problem is described by one complete model, which covers all characteristics of the crew scheduling problem, it may lead to a large linear programming problem formulation, which can attack the limits of a common IP-solver. To overcome this obstacle, column generation technique can be used. Column generation technique can reduce the size of solved model. Despite the fact that it cannot find the optimal solution, it can enable to solve larger instances. In this contribution we explain the concept of frames used in design of periodic timetable and analyze the property of the particular frame networks. We explain the column generating principle in connection with the crew scheduling problem. We present improving methods to accelerate the column generation method that are able to find solution of the solved sub-problem faster and different strategies of producing the initial collections of columns, which enable to make the column generation process more effective. Although the computational time in the scheduling problems is not an critical issue, the reduce of the computational time can enable to use this method in the decision supporting tool for the crew schedule design under practical conditions, especially in large scale problems. To test proposed improvements we use various benchmarks of real problems from crew scheduling in railway transportation systems.