NBA franchise management is not a sequence of independent tasks, but a single dynamic control problem in which roster construction, cash-flow discipline, media strategy, external market shocks, and player-health uncertainty interact over time. Using the New York Knicks as a case study, this paper develops a unified decision architecture for franchise management under competitive, financial, and regulatory constraints. The core layer is formulated as a rolling-horizon stochastic mixed-integer program augmented with distributionally robust optimization and conditional value-at-risk constraints, so that long-run franchise value can be optimized while downside exposure remains explicitly controlled. On top of this core layer, we construct coordinated modules for transaction execution, league-expansion shock transmission, media-rights regime transition, and injury-triggered re-optimization. This integrated design reframes multiple managerial mechanisms inside one research problem: how should an NBA franchise allocate resources and update decisions when performance objectives and commercial objectives are jointly determined under uncertainty? The manuscript is organized around problem formulation, model architecture, empirical validation, robustness analysis, and managerial interpretation.

翻译：NBA球队管理并非一系列独立任务的简单组合，而是一个动态控制问题，其中阵容构建、现金流纪律、媒体策略、外部市场冲击以及球员健康不确定性随时间相互交织。本文以纽约尼克斯队为案例，构建了一个在竞争、财务与监管约束下进行球队管理的统一决策架构。该架构的核心层被建模为一个经分布鲁棒优化和条件风险价值约束增强的滚动时域随机混合整数规划模型，从而在明确控制下行风险的同时，实现球队长期价值的优化。在此核心层之上，我们构建了用于交易执行、联盟扩张冲击传导、媒体版权制度转换以及伤病触发重新优化的协同模块。这种集成设计将多种管理机制重新纳入同一研究问题：当绩效目标与商业目标在不确定性下共同决定时，NBA球队应如何分配资源并更新决策？本文围绕问题建模、模型架构、实证验证、鲁棒性分析及管理诠释展开论述。