Linear location-inventory models for service parts logistics network design

• Location-inventory models for spare parts with time-based service levels.
• Difficulty due to demand uncertainty and nonlinear service constraints.
• Linear formulation for the nonlinear part-warehouse service constraints.
• Approximate linear formulation for the nonlinear part service constraints.
• New linear formulations are effectively solved by a commercial optimizer.

We present two integrated network design and inventory control problems in service-parts logistics systems. Such models are complicated due to demand uncertainty and highly nonlinear time-based service level constraints. Exploiting unique properties of the nonlinear constraints, we provide an equivalent linear formulation under part-warehouse service requirements, and an approximate linear formulation under part service requirements. Computational results indicate the superiority of our approach over existing approaches in the literature.