Robust optimization of pharmaceutical inventory under supply and demand uncertainty: a multi-period CVaR model based on the SPD framework

Purpose This study aims to strengthen pharmaceutical inventory resilience under dual supply–demand uncertainties by developing a multi-period robust optimization model embedded in the supply, processing and Distribution (SPD) framework, thereby addressing gaps in risk-sensitive decision-making during volatile healthcare environments. Design/methodology/approach This study develops a multi-period robust optimization framework that embeds conditional value-at-risk (CVaR) within Wasserstein distributionally robust sets to rigorously model tail risks under dual supply–demand uncertainty. Theoretical validation through Hessian analysis confirms convexity and global optimality, while empirical evaluation based on procurement and settlement data of a classical influenza drug from tertiary hospitals and SPD suppliers combines benchmarking, stress testing and sensitivity analysis, thereby demonstrating both methodological novelty and practical relevance for resilient pharmaceutical supply chains. Findings The robust-SPD strategy consistently reduces total costs by 15–25% while sustaining service levels above 0.9 across most periods. Under high-volatility scenarios, shortage penalties decline by over 25% and cost distributions exhibit markedly compressed tails, demonstrating effective tail-risk mitigation. Sensitivity analysis further reveals an optimal risk-aversion range (a ˜0.88–0.90), ensuring robust performance and operational stability without requiring frequent parameter adjustment. Originality/value This study advances the methodological frontier of pharmaceutical inventory optimization by combining Wasserstein sets and CVaR to overcome the conservatism of worst-case models and to explicitly manage tail risks. The SPD outsourcing threshold theorem is proposed to define conditions for economic feasibility, offering a quantitative benchmark for hospital–SPD collaboration. Beyond theoretical innovation, the model provides a practical decision-support tool enabling hospitals to achieve long-term cost stability, risk control, and service reliability under national reimbursement and regulatory constraints.