A Noncompact Formulation for Job-Shop Scheduling Problems in Traffic Management

Vehicle scheduling is a central problem in transportation. As railways and the airspace become increasingly congested, it is crucial to develop mathematical tools to better schedule trains and airplanes off-line (timetabling) and online (dispatching). These traffic-management problems can be modeled as job-shop scheduling problems, which, in turn, can be solved using mixed-integer linear programming (MILP). The two most successful and widespread formulations in the past decades are the big-M and the time-indexed methods, each with its strengths and weaknesses. However, there have been few advancements in either approach in recent years. In this paper, we introduce an alternative formulation, obtained by strengthening and lifting the Benders' reformulation of a natural initial formulation. This new approach improves performances on our real-life test bed and opens up interesting research directions.