Integrated optimization of business interruption insurance purchase and operational decisions under disruption risk

Although business interruption insurance has been proven effective in mitigating disruption risks for manufacturers, its implementation often underperforms due to the “temporal gap” between indemnity periods and actual recovery times, compounded by a disconnect between insurance decisions and operational planning. To address these issues, we propose a two-stage multi-period integrated optimization model that simultaneously optimizes the insurance coverage amount and indemnity period, alongside operational decisions regarding production, inventory, and capacity recovery. To enhance the robustness of decisions against disruption uncertainty and data scarcity, we adopt a distributionally robust optimization approach based on the Wasserstein ambiguity set. The model is reformulated into a tractable mixed-integer linear program and solved using a customized novel stabilized hybrid Benders decomposition algorithm with exact dual lifting. Extensive experiments based on real-world geographical datasets from the U.S. and China demonstrate that the proposed model significantly improves out-of-sample payoffs and reduces tail risks compared to stochastic and robust benchmarks. Furthermore, our analysis reveals the indemnity period is a rigid survival baseline more critical than the coverage amount. We also demonstrate that high insurance coverage cannot substitute for active operational recovery, thereby validating the necessity of integrated recovery efforts. Overall, this study introduces the temporal dimension into insurance planning for the first time, offering manufacturers a risk response decision framework to align financial protection with operational resilience.