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Time-dependent (or temporal) properties may arise in many practical staticnetwork search problems, for example routing and scheduling of railway trackinspection where availability of track for inspection depends on therail-schedule. In the absence of side constraints this routing and schedulingproblem is a multi-agent rural postman problem on a temporal directed network;having temporal attributes motivated from railway track unavailabilities. Thiswork presents a novel Mixed Integer Linear Programming (MILP) formulation modelfor a Multi-agent Temporal Rural Postman Problem (MTRPP), and proposes theoryfor temporal graphs to support the model. A modified Benders' decompositionalgorithm is also proposed to address the non-convex unavailability constraintsoccurring in its sub-problems. Furthermore, a polynomial time algorithm isdesigned to address this sub-problem, while restraining the NP-Hard part to themaster problem. A simulation study showing application in rail-track inspectionusing track-based-agents is presented, alongside comparison study showingimproved results in smaller and sparser graphs compared to Time-Dependent RuralPostman Problem (TDRPP) which is developed over temporal attributes arising dueto congestion in roadway networks.

Optimal routing and scheduling in a time-dependent and directed multi-graph: a multi-agent temporal rural postman problem