An integrated heuristic and mathematical modelling method to optimize vehicle maintenance schedule under single dead-end track parking and service level agreement

Inspired by real life maintenance operations, we introduce a vehicle maintenance scheduling problem in an urban light rail line which considers service level agreement (SLA), preventive maintenance cycles and corrective jobs on a single dead-end track. We show that the problem is strongly NP-Hard. Experts in real life make use of a heuristic. Yet, the heuristic calls vehicles in their preventive maintenance cycles as early as possible, which increases the number of maintenance calls in the long term. We build a mixed integer linear programming (MILP) model that handles all aspects of this problem. To improve the quality of the model, we modify it based on the structure of the problem and call MILP2. We enhance the heuristic and name ImprHeur. We introduce ImprHeur to provide a starting solution for the MILP2 model and call ImprHeur + MILP2. We perform computational experiments on random test instances and show that the ImprHeur + MILP2 drastically heightens the solution quality of the MILP model. We define key performance indicators (KPI) to assess the system behavior. We create a discrete-event simulation framework for different problem parameters to test the performance of these heuristics and ImprHeur + MILP2. We conclude that ImprHeur + MILP2 improves the real life heuristic by 74.72% with regard to the objective function value of the MILP model.

Automated summary

This study explores a vehicle maintenance scheduling problem in an urban light rail line, proving its NP-hardness and proposing a mixed integer linear programming model to address it. By enhancing a heuristic method and introducing the ImprHeur + MILP2 combination, the quality of solutions for the MILP model is significantly improved, with ImprHeur + MILP2 increasing the objective function value by 74.72% compared to the MILP model.