Campaign continuous manufacturing (CM), characterized by relatively short operational windows such as a few weeks, is being explored as an alternative to traditional batch-wise manufacturing in the pharmaceutical industry. However, optimal operation in campaign CM can be challenging due to the significance of startup and shutdown phases, which can negatively affect on-specification production and plant economy. In this paper, the effectiveness and computational tractability of several known optimization approaches when applied to campaign CM are investigated. Inspired by the turnpike property in optimal control, a new approach is then proposed, which aims to maximize on-specification production directly rather than minimizing the startup/shutdown times as commonly adopted in high-volume industries. A main contribution in the new approach is that the resulting optimization formulation is guaranteed to be differentiable, despite the underlying hybrid dynamic system. Thus, it can be solved reliably using gradient-based algorithms. Case studies are presented to demonstrate the effectiveness of the proposed approach.