An index policy for routing agricultural machinery repairs

We study dynamic routing in an agricultural machinery repair network where mobile repair teams travel to spatially dispersed breakdowns and both travel and on-site repair times are stochastic and comparable. We formulate a finite-horizon Markov decision process tracking each team’s job list and service path, and derive a tractable index-based policy via Whittle-style Lagrangian relaxation that decomposes the original problem into team-wise subproblems. For each team, we obtain a closed-form index, prove indexability, and show that indices preserve their cross-team ordering under finite horizons, ensuring consistent decision rules without additional computation. On the analytical side, the Lagrangian dual yields a computable lower bound against which the index policy is asymptotically optimal. A case study and extensive experiments demonstrate that the index policy achieves the lowest average cost in most tested instances, with an average optimality gap of 1.72% and up to 67% cost reduction over heuristic benchmarks. Sensitivity analysis further confirm robustness under varying system loads, service imbalance, spatial distributions, and other extensions.