共享單車存量流程之隨機建模與利潤最佳化應用

Abstract

本研究針對單一共享單車站點之營運情境，提出一套基於分數歐斯坦–烏倫貝克過程（fractional Ornstein-Uhlenbeck process, fOU）之損益分析模型，隨著共享單車逐漸成為城市交通運輸系統中不可或缺的一環，個別站點因車輛數量分布不均勻所導致的營運挑戰日益顯著，不僅影響使用者滿意度，亦降低整體系統效能。為了因應此問題，本研究建構一套以 fOU 模型為基礎之隨機模擬方法，透過 Hurst 指數（H）刻畫需求波動的長期依賴性，並引入均值回復率（λ）與波動強度（σ）以模擬站點車輛數隨時間之動態調整行為。 本模型可結合實際觀測資料進行參數估計與驗證，並用以分析站點營運的關鍵績效指標，包括未滿足需求量、營運成本，以及潛在收益損失或增益等。雖然本研究以單一站點為對象，然而所提出之方法具高度擴展性，未來可應用於多站點系統，作為優化整體營運績效之決策支援工具。

This study presents a loss and revenue analysis model based on the fractional Ornstein–Uhlenbeck (fOU) process for the operation of a single bike-sharing station. As bike-sharing becomes an integral part of urban transportation systems, operational challenges—particularly the uneven distribution of bicycles at individual stations—have become increasingly prominent, impacting user satisfaction and overall system efficiency. To address these issues, we develop a stochastic simulation model using the fOU process, which incorporates the Hurst index (H) to capture long-range dependence in demand fluctuations, the mean-reversion rate (λ), and the volatility parameter (σ) to describe dynamic adjustments in bike inventory over time. The model can be calibrated with real-world data and used to evaluate key performance indicators such as unmet demand, operational costs, and potential revenue loss or gain. Although the focus is on a single station, the proposed method is highly scalable and can be extended to multi-station systems, providing a comprehensive framework for optimizing system-wide performance.