考虑区域容量与需求溢出，用AI优化服务网络分阶段扩展顺序。
Sequential Service Region Design with Capacity-Constrained Investment and Spillover Effect
- 结合期权理论与Transformer的强化学习算法，自动规划最优投资序列。
- 在多区域场景下，比基准方法更快收敛且投资序列选项价值更高。
- 适合需要动态应对需求变化的物流、基建等长期布局决策者。
服务区域设计决定服务网络的地理覆盖范围，影响长期运营表现。受资本和运营约束，大规模部署无法同时进行，必须分阶段推进。核心挑战在于：如何在需求不确定条件下，权衡提前或延迟投资的时机，并考虑各区域间连通性带来的网络效应——每次部署都会重塑未来需求。本文研究一种包含两个现实但未被充分探讨因素的分阶段服务区域设计（SSRD）问题：每期最多投资k个区域的容量限制，以及随机溢出效应带来的需求演化关联。该问题需在不确定性下对区域组合进行序列决策，导致可行投资路径呈组合爆炸。为此，提出融合实时期权分析（ROA）与基于Transformer的近端策略优化（TPPO）的解决方案：ROA评估投资序列的时间价值，而TPPO学习直接生成高期权价值序列，无需穷举。在真实多区域场景的数值实验表明，TPPO收敛速度优于基准深度强化学习方法，且持续识别出选项价值更高的序列。案例研究与敏感性分析进一步验证了方法稳健性，并揭示了在强溢出效应和动态市场下，采用该方法可显著提升自适应扩张收益，明确投资并发性、区域优先级等关键策略。
原文摘要 · Abstract (English)
Service region design determines the geographic coverage of service networks, shaping long-term operational performance. Capital and operational constraints preclude simultaneous large-scale deployment, requiring expansion to proceed sequentially. The resulting challenge is to determine when and where to invest under demand uncertainty, balancing intertemporal trade-offs between early and delayed investment and accounting for network effects whereby each deployment reshapes future demand through inter-regional connectivity. This study addresses a sequential service region design (SSRD) problem incorporating two practical yet underexplored factors: a $k$-region constraint that limits the number of regions investable per period and a stochastic spillover effect linking investment decisions to demand evolution. The resulting problem requires sequencing regional portfolios under uncertainty, leading to a combinatorial explosion in feasible investment sequences. To address this challenge, we propose a solution framework that integrates real options analysis (ROA) with a Transformer-based Proximal Policy Optimization (TPPO) algorithm. ROA evaluates the intertemporal option value of investment sequences, while TPPO learns sequential policies that directly generate high option-value sequences without exhaustive enumeration. Numerical experiments on realistic multi-region settings demonstrate that TPPO converges faster than benchmark DRL methods and consistently identifies sequences with superior option value. Case studies and sensitivity analyses further confirm robustness and provide insights on investment concurrency, regional prioritization, and the increasing benefits of adaptive expansion via our approach under stronger spillovers and dynamic market conditions.
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