After-Sales Service Network Design Under Demand Uncertainty: A Two-Stage Stochastic Program with Interchangeable Resources

Before failures are known, an after-sales provider must decide where to open service centers, how to staff and cross-train technicians, how much spare-part throughput to reserve, and how much service capacity to keep in-house. Two features of this planning problem require separate attention. Technicians with the same primary skill can be relabeled without changing the network, whereas conservative service-time reservations can make in-house capacity appear smaller and increase outsourcing. We study these issues with a two-stage stochastic mixed-integer program in which each demand scenario is covered by reserved in-house bundles or by outsourcing. For homogeneous primary-skill pools, we identify the technician-relabeling group and show that a simple hiring-order rule preserves the optimal objective while removing only the active/inactive selection symmetry. The computational study uses a frozen campaign of 113 MIP runs in IBM ILOG CPLEX Optimization Studio 22.1 (64-bit). It retains six valid censored observations, repeats four representative Size-2 instances under four categorical solver seeds, and audits 54 designs with exact service times for ρ∈{0,0.5,1}. All 113 MIP rows and all 54 audits pass the registered structural checks, and 107 MIPs reach their size-specific target. The hiring-order rule is not a general accelerator. Its median PAR10 ratios (on/off) are 1.231, 0.885, and 0.832 for Sizes 1–3, and the direction of the effect changes across solver seeds for three of the four Size-2 diagnostic instances. Automatic solver symmetry gives a Size-2 median ratio of 0.861, although the bootstrap interval extends to 1.024; the Size-3 result is mixed. Stronger reservation protection increases total cost and reduces exact-time overload. The Size-3 minus Size-1 difference in outsourcing cost share is uncertain at ρ=0, but positive at ρ=0.5 and ρ=1. The group-theoretic tools are classical. The contribution lies in certifying their role in this after-sales model and evaluating them with explicit treatment of variability and censoring. Solver-side symmetry handling is the tested default, the model-side rule is cost-preserving but its computational effect is conditional, and outsourcing results should be interpreted together with reservation reliability.