Enabling robot teams to execute natural language commands requires translating high-level instructions into feasible, efficient multi-robot plans. While Large Language Models (LLMs) combined with Planning Domain Description Language (PDDL) offer promise for single-robot scenarios, existing approaches struggle with multi-robot coordination due to brittle task decomposition, poor scalability, and low coordination efficiency. We introduce PIP-LLM, a language-based coordination framework that consists of PDDL-based team-level planning and Integer Programming (IP) based robot-level planning. PIP-LLMs first decomposes the command by translating the command into a team-level PDDL problem and solves it to obtain a team-level plan, abstracting away robot assignment. Each team-level action represents a subtask to be finished by the team. Next, this plan is translated into a dependency graph representing the subtasks' dependency structure. Such a dependency graph is then used to guide the robot-level planning, in which each subtask node will be formulated as an IP-based task allocation problem, explicitly optimizing travel costs and workload while respecting robot capabilities and user-defined constraints. This separation of planning from assignment allows PIP-LLM to avoid the pitfalls of syntax-based decomposition and scale to larger teams. Experiments across diverse tasks show that PIP-LLM improves plan success rate, reduces maximum and average travel costs, and achieves better load balancing compared to state-of-the-art baselines.

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