The Cloud-Edge-IoT computing continuum requires mechanisms for grouping heterogeneous nodes into logical clusters capable of jointly hosting application workloads under multi-resource constraints. The core difficulty is selecting a subset of nodes that can collectively satisfy an application’s concurrent, multi-dimensional task demands, where aggregate resource sufficiency does not guarantee a feasible task-to-node assignment. Existing orchestration frameworks and simulators conflate node selection with task scheduling and cannot natively represent indivisible multi-resource joint feasibility under controlled demand stress. We address this gap with LCF-Bench, a reproducible benchmark for feasibility-aware logical cluster formation. It formalizes logical cluster formation as a feasibility-first node-selection problem, decoupled from runtime scheduling, and packages a parameterized instance generator, a Kubernetes-compatible export, and a standardized evaluation protocol spanning node scaling, task scaling, and demand-load scaling. Using the benchmark, we find that feasibility exhibits sharp phase transitions under increasing demand. The region of exact-optimization hardness is workload-dependent, concentrating near the feasibility transition under balanced and compute-heavy workloads yet largely vanishing under storage-dominated ones. Single-objective heuristics incur a heterogeneity-induced over-provisioning anomaly on skewed resource distributions. We report reference results for five representative methods: Round- Robin, First-fit, Best-fit, a Mixed-Integer Linear Program (MILP) exact reference, and the Kubernetes default scheduler. Best-fit offers the strongest practical trade-off, retaining full feasibility to the highest demand overload of any heuristic (roughly 80% in the reference run), while the MILP reference is optimal but intractable at scale. LCF-Bench provides a common, extensible reference point for the systematic evaluation of logical cluster formation methods under identical conditions.