本研究以公共自行車租賃系統營運業者立場,在最小化總營運成本的目標下,建構數學規劃模式,求解每日營運前各租賃站應配置之自行車輛數。於研究中首先以時空網路(Time Space Network)描述系統中自行車流動,構建確定性車輛配置模式(Deterministic Vehicle Allocation Model),接著考慮需求不確定情況,以穩健最佳化(Robust Optimization, RO)之技巧,建構穩健車輛配置模式(Robust Vehicle Allocation Model),並延伸考量租賃站自行車輛不足導致顧客流失之情況。本研究根據新北市自行車租賃系統營運數據產生測試範例,利用GAMS的MINOS求解器進行模式求解,並分析購車成本、維護成本、調度成本、車輛租賃站滯留、車輛不足對於求解結果之影響。研究結果可提供業者於自行車租賃系統每日營運前各租賃站車輛配置之參考。此外,本研究探討穩健價格(Robust Price)與避險值(Hedge Value)兩個指標,以瞭解追求穩健解對於原模式最佳解之影響,與穩健解在不確定需求情境下的效益。
This study develops mathematical programming models to determine optimal daily allocation of bicycles to rental stations of a public-bike sharing system. The objective is to minimize the total cost of the system operator. Firstly, a time-space network is built to describe bike flows of the system. A deterministic bike allocation model that considers average historical demand is established based on the time-space network and then is extended to allow customer loss due to insufficient capacities at stations. Moreover, a Robust Optimization technique is adopted to address uncertain demands faced by rental stations and to develop a robust bike allocation model. A set of numerical experiments was conducted based on the New Taipei City’s public-bicycle sharing system to demonstrate the applicability and performance of the proposed models. Problem instances were solved by GAMS’s MINOS solver for the optimal bicycle allocation. The study also analyzed the impact of various cost parameters on the solutions. The findings can provide the operator insights in the daily operation of the public-bicycle rental system. In addition, this study explores two performance indicators, namely Robust Price and Hedge value, in order to understand the tradeoff between robustness and optimality and the benefit of applying robust solutions relative to nominal optimal solutions in uncertain demand situations.