Globalization and the resultant complexity of today's supply chains require that enterprises be agile and proactive. This communication looks at a refinery supply chain where disruptions such as crude arrival delay could make the current schedule infeasible and necessitate rescheduling of operations. Existing approaches for generating (near) optimal schedules for a real-world refinery typically require significantly large amounts of time. This is undesirable when rectification decisions need to be made in a short time. Further, when the problem data given to the existing scheduling approaches are changed, as is the case during a disruption, the optimizers follow different solution paths and result in substantially different schedules. A heuristic rescheduling strategy is proposed that overcomes both these shortcomings. The key insight exploited here is that any schedule can be broken into operation blocks. Rescheduling is performed by modifying these blocks in the original schedule using simple heuristics to generate a new schedule that is feasible for the new problem data. Our strategy avoids major operational changes by preserving—as far as possible—the blocks in the original schedule. The major advantages of the proposed method are its real-time computational performance and the minimal changes to the operations as compared to total rescheduling. Further, the proposed strategy can also identify many feasible schedules and allow refinery personnel to select one by considering other factors that cannot be adequately modeled in a scheduler. Our method is illustrated using five types of disruptions occurring in a refinery. The various factors that affect the robustness of a supply chain in the face of disruptions are also discussed.