公共自行車在世界各都會區逐漸成為熱門的短程接駁代步工具，成功的自行車租借系統必須在給定之地理範圍內決定合適的租借站位址與容量，並在營運期間做好車輛在不同時段於各站的配置與運補。為能更符合實際狀況，本研究一共分成兩個部分，首先為最佳租借站位址設置問題，在考量行人在各路段的行走或騎乘時間服從特定機率分配的情況下，據此發展出一套可處理隨機性節線長度之隨機性混整數規劃模式，經過進一步之推導後，模式可轉換成二次混整數規劃模式，接著再以兩類粒子群演算法以加速解得更合理的最佳租借站位址、容量及自行車配置方式。本論文之第二部分為自行車租借車輛配置運補問題，在保證租借者總旅行時間能滿足給定的服務水準假設下，我們依據不同程度的租借資訊，分別提出三種不同情境的最小成本多元商品網路流量模式來求解營運期間各站在各期應配置的自行車數及最小成本的運補方式，並發展粒子群演算法加速求解最佳的運補車路線。

Recently, short-term bicycle rentals at a network of unmanned locations in metropolitan areas around the world become popular. A successful manager of a bike-sharing system has to decide suited location and capacity of a bike rental station, deploy the bike fleet, and conduct bike repositioning between stations in a way that minimizes the total cost while satisfying a given service level. This paper investigates two problems encountered in the design and management of urban public bike sharing systems. In order to better meet the real behavior of customers, the first network design problem considers different walking and riding time at every arc for different customer that obeys specific probability distribution. Based on the stochastic traveling time assumption, we propose a stochastic mixed integer model to decide the best station locations, capacity and amount of initial bicycles to be put for each station. We explain how to convert this problem as a Quadratic mixed integer program, which consumes much computational time by CPLEX. Then we propose two particle swarm optimization(PSO) algorithms to solve larger network design cases in shorter time.
Our second problem deals with a dynamic bike repositioning problem. In particular, with guarantees on the number of customers to be served and their total travel time not exceeding a specified threshold, we provide three specialized minimum cost multi-commodity network flow formulations based on different levels of available rental information. We recommend using our third formulation that assumes the customers follow historical trend of traveling, and seek the best route and repositioning decisions for each transit vehicle that travels between stations to load or unload bikes. Due to the complexity of the MIP formulation, we propose PSO algorithms to deal with dynamic bike repositioning problems of larger scale.

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