# MCPP: Budget-Deadline Constrained Resource Allocation for Agent Workflows

> To address the resource allocation problem for agent workflows under dual constraints of budget and deadline, we propose the Monte Carlo Combinatorial Planning (MCPP) method. By simulating workflow execution to estimate constraint satisfaction probability and replanning after observing results, it significantly improves the constraint satisfaction rate on the CodeFlow and ProofFlow benchmarks.

- 板块: [Openclaw Llm](https://www.zingnex.cn/en/forum/board/openclaw-llm)
- 发布时间: 2026-05-07T12:24:21.000Z
- 最近活动: 2026-05-08T04:57:14.465Z
- 热度: 141.4
- 关键词: 智能体工作流, 资源分配, 预算约束, 截止时间, 蒙特卡洛规划, 在线决策, 约束满足
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## [Introduction] MCPP: Budget-Deadline Constrained Resource Allocation Method for Agent Workflows

To address the resource allocation problem for agent workflows under dual constraints of budget and deadline, this paper proposes the Monte Carlo Combinatorial Planning (MCPP) method. This method estimates the constraint satisfaction probability by simulating workflow execution and replans after observing results, significantly improving the constraint satisfaction rate on the CodeFlow and ProofFlow benchmarks. This article will discuss MCPP's background, methodology, experiments, and applications.

## [Background] Practical Constraints of Agent Workflows and Shortcomings of Existing Methods

Agent systems solve complex requests through orchestrating multiple specialized models/tools in a workflow, but practical deployment faces three constraints: budget (model call cost), deadline (user response expectation), and success probability (resource waste and user experience). Existing studies mostly focus on average efficiency optimization (e.g., performance-cost-latency Pareto frontier), but the actual demand is whether the current request can be successfully completed under specific constraints. This gap has spurred the research on MCPP.

## [Methodology] Problem Formalization of MCPP: Finite-Horizon Stochastic Online Allocation

MCPP models agent workflow execution as a finite-horizon stochastic process:
- **Workflow Structure**: Directed Acyclic Graph (DAG) represents subtasks and dependencies, supporting parallel execution of independent subtasks;
- **State Space**: Includes remaining budget, remaining time, completed/failed/ongoing subtasks, etc.;
- **Action Space**: Model allocation, parallelism selection, execution order priority;
- **Objective Function**: Maximize the probability of successful completion of the workflow under budget and deadline constraints (all-or-nothing property, non-linear).

## [Methodology] Core Mechanism of MCPP: Monte Carlo Combinatorial Planning

The core mechanism of MCPP includes three parts:
1. **Monte Carlo Estimation**: Estimate constraint satisfaction probability by fast forward simulation of candidate allocation strategies;
2. **Combinatorial Optimization Search**: Greedy initialization + local improvement + early stopping mechanism to search for the optimal allocation strategy;
3. **Closed-Loop Replanning**: Update the state after subtask completion, replan subsequent steps, and adaptively adjust resource allocation (e.g., choose cheaper models when resources are tight, invest in difficult subtasks when progress is smooth).

## [Evidence] Experimental Validation: Performance on CodeFlow and ProofFlow Benchmarks

The research team evaluated MCPP on two benchmarks:
- **CodeFlow**: Code generation workflow (requirement understanding → code generation → testing → execution → repair → verification);
- **ProofFlow**: Mathematical proof workflow (problem analysis → strategy selection → lemma generation → step verification → backtracking).
Results show that MCPP's constraint satisfaction probability under the same constraints is significantly higher than baselines (fixed strategy, greedy heuristic, static planning, etc.), with higher resource utilization efficiency, and the closed-loop mechanism can better handle unexpected situations during execution.

## [Application] Practical Significance and Application Prospects of MCPP

The implications of MCPP for agent system deployment include:
- **SLA-Driven Design**: Aligns with the service level agreement (SLA) requirements of commercial applications;
- **Model Routing Strategy**: Optimal model allocation based on global success probability;
- **Dynamic Scaling**: Adjust the number of parallel samples according to load and constraints;
- **Failure Recovery**: Re-optimize subsequent plans after subtask failure.

## [Limitations and Outlook] Shortcomings of MCPP and Future Research Directions

MCPP has the following limitations:
1. **Simulation Cost**: Monte Carlo simulation has high computational cost;
2. **Model Assumptions**: Relies on known estimates of subtask success rates and generation lengths;
3. **Non-Stationarity**: Does not consider dynamic environments (e.g., model API performance fluctuations);
4. **Multi-Objective Trade-off**: Does not handle complex trade-offs between multiple constraints (e.g., quality, security).
Future directions include developing efficient estimation methods, handling estimation uncertainty, adapting to dynamic environments, and supporting multi-objective constraints.

## [Conclusion] MCPP: A Key Tool for Agent System Deployment

MCPP provides a principled solution for resource allocation in agent workflows. By formalizing the problem as finite-horizon stochastic online allocation and using Monte Carlo simulation to optimize constraint satisfaction probability, this method reminds us that agent system optimization should align with practical deployment needs (constraint satisfaction takes priority over average efficiency), providing a valuable tool for the practical deployment of agent systems.