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

TL;DR

This paper develops a novel sequential service region design framework incorporating capacity constraints and spillover effects, using a combination of real options analysis and advanced reinforcement learning to optimize investment timing and location under demand uncertainty.

Contribution

It introduces a new SSRD model with practical constraints and spillover effects, and proposes a TPPO algorithm that efficiently learns optimal investment sequences without exhaustive search.

Findings

TPPO converges faster than benchmark DRL methods.

The approach identifies investment sequences with higher option value.

Results show robustness and strategic insights under various market conditions.

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.