Integrated train scheduling and routing in the UK network

We consider an integrated train scheduling and routing problem in tactical and operational level. The train scheduling and routing problem is formulated as a modified parallel machine job shop scheduling problem. The aim is to determine train routes among alternative options whilst simultaneously identifying their timing and relative ordering. The model can be solved in both tactical planning level and in respond to disruptions in operational level. We try to minimise delay propagation in the network subject to a set of operational and safety constraints. A generic Mixed Integer Linear Programming (MILP) model of the problem is developed which can be adapted to different rail networks. A novel algorithm based on the Shifting Bottleneck (SB) heuristic is introduced to solve the integrated train scheduling and routing problem. We explore the performance of the suggested algorithm with a case study based on the part of the UK railway network. Analyses of the mentioned critical corridor with a complex infrastructure and congested traffic indicates the computational advantages and viability of the suggested method.