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In this paper, we address the problem of dynamic scheduling of a multipurpose batch process subject to two types of disturbances, namely, processing time variation and demand uncertainty. We propose a rescheduling strategy that combines several ideas. First, when we generate a new schedule, we simultaneously construct a Directed Acyclic Graph (DAG) to represent this new schedule. While each node in the DAG represents an operation, each arc represents the dependency of an operation on another. Based on this DAG, we then use a simple procedure to determine how long an operation is allowed to be delayed without affecting the current makespan. After that, when the new schedule is used for online execution, we trigger a rescheduling procedure only when (1) we infer from the predetermined delayable time information that the current makespan will be extended, or (2) we observe new demands, or (3) the current schedule is not guaranteed to be feasible. In the rescheduling procedure, only the affected operations are allowed to be revised, while those unaffected operations are fixed. By doing this, we can reduce system nervousness and improve computational efficiency. The computational results demonstrate that our method can achieve an order of magnitude of reduction in both the number of operation changes and the computational time with a slightly better long-term makespan, compared to the widely used periodically–completely rescheduling strategy.