Hybrid Value Function Approximation for Solving the Technician Routing Problem with Stochastic Repair Requests

Abstract

We investigate the combined planning problem involving the routing of technicians and the stocking of spare parts for servicing geographically distributed repair tasks. The problem incorporates many operational uncertainties, such as future repair requests and the required spare parts to replace malfunctioned components. We model the problem as a sequential decision problem where decisions are made at the end of each day about the next day’s technician route and spare part inventory in the van. We show that exact methods are intractable because of the inherent high-dimensional state, decision, and transition spaces involved. To overcome these challenges, we present two novel algorithmic techniques. First, we suggest a hybrid value function approximation method that combines a genetic search with a graph neural network capable of reasoning, learning, and decision making in high-dimensional, discrete decision spaces. Second, we introduce a unique state-encoding method that employs multiattribute graphs and spatial markers, eliminating the need for manually designed basis functions and allowing efficient learning. We illustrate the general adaptive learning capacity by solving a variety of instance settings without instance-specific hyperparameter tuning. An extensive numerical study demonstrates that our hybrid learning technique outperforms other benchmark policies and adapts well to changes in the environment. We also generate a wide range of insights that not only shed light on the algorithmic components but also offer guidance on how to execute on-site repair tasks more efficiently. The techniques showcased are versatile and hold potential for application in other dynamic and stochastic problems, particularly in the realm of transportation planning. Funding: This work was supported by Deutsche Forschungsgemeinschaft (DFG). The Research Training Group 2201 [Grant 277991500], “Advanced Optimization in a Networked Economy,” funded by the DFG, has provided partial support for this work. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0434 .