The cloud is extended towards the edge to form a computing continuum while managing resources' heterogeneity. The serverless technology simplified how to build cloud applications and use resources, becoming a driving force in consolidating the continuum with the deployment of small functions with short execution. However, the adaptation of serverless to the edge-cloud continuum brings new challenges mainly related to resource management and scheduling. Standard cloud scheduling policies are based on greedy algorithms that do not efficiently handle platforms' heterogeneity nor deal with problems such as cold start delays. This work introduces a new scheduling policy that tries to address these issues. It is based on multi-objective optimization for data transfers and makespan while considering heterogeneity. Using simulations that vary workloads, platforms, and heterogeneity levels, we study the system utilization, the trade-offs between the targets, and the impacts of considering platforms' heterogeneity. We perform comparisons with a baseline inspired by a Kubernetes-based policy, representing greedy algorithms. Our experiments show considerable gaps between the efficiency of a greedy-based scheduling policy and a multi-objective-based one. The last outperforms the baseline by reducing makespan, data transfers, and system utilization by up to two orders of magnitudes in relevant cases for the edge-cloud continuum.