摘 要：资源分配问题是现代管理科学与工程领域的重要研究课题，其复杂性和多变性对优化方法提出了更高要求。本文以动态规划为核心工具，探讨其在资源分配问题中的优化策略及其应用潜力。研究旨在通过构建动态规划模型，解决多阶段、多约束条件下的资源分配难题，从而实现资源利用效率的最大化。基于Bellman最优性原理，本文设计了一种改进的动态规划算法，该算法通过状态空间缩减和价值函数近似技术显著提升了计算效率。实验结果表明，相较于传统线性规划和启发式方法，所提算法在求解大规模资源分配问题时表现出更优的性能和更高的精度。本文的主要创新点在于将动态规划与现代计算技术相结合，提出了一种适用于复杂场景的高效优化框架，为实际资源分配问题提供了新的解决方案。研究成果不仅丰富了动态规划理论，还为相关领域的实践应用奠定了坚实基础。
关键词：资源分配；动态规划；Bellman最优性原理；状态空间缩减；价值函数近似
Optimization Strategies of Dynamic Programming in Resource Allocation Problems
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Abstract：Resource allocation problems are crucial research topics in modern management science and engineering, with their complexity and variability imposing higher demands on optimization methods. This study focuses on dynamic programming as the core tool to explore its optimization strategies and application potential in resource allocation problems. The aim is to construct a dynamic programming model to address resource allocation challenges under multi-stage and multi-constraint conditions, thereby maximizing resource utilization efficiency. Based on Bellman's principle of optimality, an improved dynamic programming algorithm is designed, which significantly enhances computational efficiency through state space reduction and value function approximation techniques. Experimental results demonstrate that, compared with traditional linear programming and heuristic methods, the proposed algorithm exhibits superior performance and higher accuracy in solving large-scale resource allocation problems. The primary innovation of this study lies in integrating dynamic programming with modern computational technologies to propose an efficient optimization fr amework suitable for complex scenarios, offering new solutions to practical resource allocation issues. The research not only enriches the theoretical foundation of dynamic programming but also provides a solid basis for practical applications in related fields.
Keywords: Resource Allocation；Dynamic Programming；Bellman Optimality Principle；State Space Reduction；Value Function Approximation
目 录
引言 1
一、动态规划基础与资源分配问题 1
(一)动态规划的基本原理 1
(二)资源分配问题的特性分析 2
(三)动态规划在资源分配中的适用性 2
二、动态规划模型构建方法 3
(一)状态变量的设计原则 3
(二)决策函数的定义与优化 3
(三)目标函数的构造与求解 4
三、优化策略的具体实现路径 4
(一)子问题分解与递推关系建立 4
(二)边界条件的设定与处理 5
(三)算法复杂度分析与改进措施 5
四、实际应用与案例研究 6
(一)资源分配问题的实际场景分析 6
(二)动态规划优化策略的应用效果评估 6
(三)案例研究中的挑战与解决方案 7
结论 7
参考文献 3
致谢 3
