We present a case study that introduces a systematic framework for designing an automated guided vehicle (AGV) order fulfillment system. The multi-stage framework integrated discrete event simulation (DES), super-efficiency data envelopment analysis (S-DEA) model, and Design of Experiments (DOE) methodologies for the design of an AGV system in an existing large-scale surgical complex within a comprehensive hospital in Singapore. Performance metrics derived from this model were consolidated into a single relative efficiency score using the S-DEA model. This efficiency score was then utilized in a DOE methodology, combined with a post-hoc model selection process, to robustly identify appropriate models for evaluating alternative system designs. The proposed framework optimizes AGV deployment by first identifying opportunities for AGVs to add value within the surgical system through a value-stream mapping approach. It then derives the optimal system design by balancing cost efficiency, manpower reallocation, and order fulfillment rates, facilitated by the S-DEA model augmented with the DOE approach and post-hoc model selection. Application of this framework to the surgical complex revealed several insights that can significantly enhance AGV efficiency prior to actual deployment. However, a key limitation of this case-study-based approach is its limited generalizability across different systems. Despite this, the methodology provides a robust foundation for AGV system design in similar healthcare environments.