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Time-dependent (or temporal) properties may arise in many network-basedplanning problems, particularly in the routing and scheduling of railway trackinspection problems. The availability of tracks depends on the train schedules,maintenance possessions, etc. In the absence of side constraints, this routingand scheduling problem is formulated as a multi-agent rural postman problem ona temporal-directed network; where a given set of rail track sections must bevisited while respecting the temporal attributes due to railway trackunavailabilities. In this work, we adopt a three-index formulation for themulti-agent Rural Postman Problem with Temporal Recurring Unavailabilities(RPP-TRU) and frame it as a Mixed Integer Linear Programming (MILP) problem. Inaddition, we propose relevant theoretical studies for RPP-TRU to ensure thefeasibility of the proposed optimization problem. Two approaches of an exactalgorithm are proposed, based on Benders' decomposition framework, to addressthe disjunctive unavailability constraints occurring in its schedulingsub-problems, alongside the NP-Hard routing (master) problem. A polynomial-timealgorithm is designed to address the scheduling sub-problem, while the NP-Hardmaster problem is solved using MILP toolbox. Comparison results with RPP(without temporal constraints) show a minor compromise with the spatial costsolution with significantly less delay, hence suitable for real-world routingand scheduling applications occurring in a shared network like railways. Asimulation study on a part of the Mumbai suburban railway network demonstratesthe working of the proposed methodology under a realistic setting.

Temporal Recurring Unavailabilities in Multi-agent Rural Postman Problem: Navigating railway tracks during availability time intervals