A bilevel programming and bargaining game approach to negotiations regarding time on track for railway maintenance

Railway maintenance scheduling requires rigorous planning to ensure harmony between the agents involved. The roles of these agents can vary from country to country; however, the infrastructure manager usually oversees the railway operations and controls access to the railway network for maintenance measures. Trackwork requires time free from train traffic — therefore, this will be the main discussion point of this paper. In particular, the negotiations between infrastructure managers and maintenance undertakers regarding time on track in the capacity allocation process. Irrationality in negotiations for time on track is a consequence of the aims and responsibilities of each agent, as well as imbalance of leverage. This paper models the scenario as a Stackelberg game and solves the problem using methods from bilevel optimisation. The model considers factors that affect leverage, such as the urgency of the works and quality of other available options - e.g. outside parties that may be able to provide a better deal, known as the Best Alternative To a Negotiated Agreement. The results from a worked example using synthetic data provide evidence that there is a significant surplus of utility being left on the table due to non-cooperation between agents, and corrective rather than preventative maintenance.