Serverless computing is an appealing model for the edge-cloud continuum, but its stateless assumption breaks down once functions need persistent data: fetching state from a distant cloud store erases the latency benefit of running at the edge. Keeping data close means replicating it, and replication forces a placement decision that is coupled with where functions execute and with the consistency each application demands. We study this joint problem of function scheduling and data placement under two consistency models, strong and eventual replication. We first formulate it as a Binary Linear Program that yields the optimal placement for a given system snapshot, and use it as a reference point. Because the solver does not scale past a few hundred nodes, we add two heuristics with progressively less information: a Global-View greedy method that works from the same complete snapshot, and an Aggregated-View heuristic in which each node decides from locally observed demand alone. Across a range of system sizes the Global-View heuristic stays within a few percent of the optimum while scaling to over $10^4$ nodes. The Aggregated-View heuristic sacrifices some solution quality, but adapts continuously to each invocation. Under client mobility, centralized policies suffer from stale snapshots and recurring latency spikes, while the Aggregated-View maintains low and stable client-observed latency. Across all experiments, data placement proves more influential than function scheduling in determining the outcome.

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