Optimizing Location and Capacity for Multiple Types of Locomotive Maintenance Shops

Thousands of locomotives run in the North America railroad network and each of them must receive periodic maintenance service; meanwhile, the locomotives may break down during shipment operations and demand repair. Maintenance shops are characterized by the types of locomotives they can handle and the level of service they can provide. This article formulates a mixed-integer program model to optimize location and capacity of locomotive maintenance shops. The objective is to minimize the sum of the costs for building new (or shutting down existing) maintenance shops, the costs for capacity expansion (or reduction), and the costs for shipping broken locomotives to a suitable shop. A Lagrangian-relaxation-based heuristic algorithm is proposed to solve the shop location and capacity planning problem. The model and solution techniques are applied to a full-scale real-world case study, while the computational results show that the current maintenance shops are overly built and recommend that two maintenance shops should be closed and an amount of capacities should be reduced from the existing shops. A series of numerical sensitivity analyses are also conducted to draw managerial insights.