Sequential Service Region Design with Capacity-Constrained Investment and Spillover Effect

2026-03-09

AI Summary

This study addresses the challenge of sequentially determining the timing and location of service region expansions under demand uncertainty and regional investment capacity constraints, while accounting for cross-regional demand spillovers induced by investment. To this end, the paper proposes a novel sequential service network design framework that integrates real options analysis (ROA) with a Transformer-based proximal policy optimization (TPPO) algorithm. This approach is the first to explicitly model concurrent investment constraints across k regions and stochastic spillover effects. ROA is employed to evaluate the intertemporal option value of investment sequences, while TPPO efficiently learns the optimal sequential investment policy. Experimental results demonstrate that TPPO converges faster than baseline deep reinforcement learning methods and consistently identifies investment sequences with higher option value, particularly under strong spillover effects and dynamic market conditions.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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.

Problem

• sequential service region design
• capacity-constrained investment
• spillover effect
• demand uncertainty
• intertemporal trade-offs

Innovation

• Sequential Service Region Design
• Real Options Analysis
• Transformer-based PPO
• Spillover Effect
• Capacity-Constrained Investment