Integration of Nursing and Pharmacy Inventory Decisions with DDD-Based EOQ: UK Institutional Calibration and Robustness Analysis

Background: This study develops a transparent, decision-focused framework that integrates the World Health Organization’s defined daily dose (DDD) standard with the planned-backorder economic order quantity (EOQ) model to manage nursing and pharmacy workflows within a unified economic and operational scale. Method: Demand was expressed in DDD per year, and process-based costs were monetized according to National Health Service (NHS) workflow steps, where the holding cost was computed as H = r × cu and the delay cost B was derived from the target fill rate via a closed-form shadow-price relationship. The model was calibrated for a typical NHS acute-care hospital with 600 beds (D ≈ 130,305 DDD/year). Results: Calibration resulted in an ideal order quantity of 7554 DDD, an inter-order interval of 21 days, and a minimum annual total cost of £451. In the national conceptual scenario, the fill rate is about 99.4%, and the minimum annual total cost is £26,366. At this optimum, cost components are symmetrically balanced, with order cost and combined holding–delay cost contributing equally. Conclusions: This repeatable framework, based on the DDD scale, enhances management visibility regarding the cost–service balance, thereby confirming the policy’s robustness.