Multistage Production–Quality–Maintenance Optimization Under Uncertain Quality-Deviation Propagation: A K-Adaptability Approach

Uncertain quality-deviation propagation complicates the coordination of production, quality, and preventive maintenance in multistage manufacturing systems. This study develops a two-stage K-adaptability robust optimization model for integrated production–quality–maintenance decision-making under limited post-realization flexibility. The production–maintenance structure and a finite set of candidate operating policies are determined before uncertainty realization, while one policy is selected after the physical scenario is observed. Candidate policies are generated through active-scenario refinement, evaluated over the specified physical-scenario set, and compared by exhaustive subset selection within a finite common candidate-policy pool. Under the baseline uncertainty budget Γ = 3, removing zero-effect combinations yields 93 unique physical scenarios. In the four-stage benchmark, increasing the policy limit from one to two reduces the finite-pool certified worst-case total cost from 87,700.48 to 87,630.32 cost units (CU), a reduction of approximately 0.08%. Allowing a third policy does not further reduce this cost but improves Smax, S0.95, and Smean measures by 11.21%, 19.23%, and 18.97%, respectively. A shortage-based lexicographic rule is used to distinguish cost-equivalent policy subsets in the four-stage benchmark. In the eight-stage refinement, increasing the policy limit from one to two reduces the finite-pool certified worst-case total cost by 5.46%, while a third policy provides no further improvement. These results show that the benefits of finite adaptability depend on the distinct scenario-specific responses provided by the candidate policies.