近年來，因為國際油價格高漲不下與溫室效應的影響，全球積極提倡節能減碳的活動，鼓勵民眾使用零污染或低汙染之交通運輸工具，以減少交通工具帶給環境的衝擊，而為了能使環境能夠永續發展，標榜綠色交通的自行車租借系統，則於近幾年來在世界各大都會區蔚為風尚。以環保概念所設置的自行車租借系統，標榜騎乘者自助租還，倘若營運單位未針對各租借站配置適當的初始自行車總量，則租借者可能面臨「無車可借」或「無位可還」的情況，因而降低系統服務品質與使用率，甚而導致整個系統的失敗。

針對每日隨時變動的租還需求與不同的租借情境，本研究採用以一啟發式演算法結合模擬最佳化（Optimization via Simulation；OvS）的排序與選擇程序（Ranking and Selection；R&S）方式。在系統數龐大的空間中，搜尋最適解之集合，再以兩階段的選擇機制，先刪除表現值較差的系統，再從剩下的系統增加抽樣數，計算其平均績效表現值，並且考慮租借系統中之各站租借需求比例，從模擬實驗中找出在信心水準之下具有最佳期望績效的初始車輛配置方式與運補車數量，以減少顧客總等待時間或人次，進而提升租借系統整體服務水準。

In order to catch the dynamic traffic of the real-world bike sharing systems in practice, this paper presents simulation models that mimic the movements of bikers generated based on historical rental data. Using these simulation models as a core, we further show how to calculate the optimal initial bike deployment for each rental site by techniques of Ranking and Selection in the fields of Optimization via Simulation. By integrating the procedures of ranking and selection into the Particle Swarm Optimization algorithmic framework, we can converge to a good solution within shorter time. In addition, we also evaluate the performance of the estimated initial bike deployment obtained by a simplified linear programming model, and conclude that our proposed technique gives better deployment, and should be useful for supporting the logistics decision in practice.

王俊偉. 2011. 以系統模擬探討公共自行車租借系統之建置及營運策略. 資訊管理學系碩士論文，國立成功大學.

洪菁蓬. 2011. 公共自行車租借系統之最佳租借站位址設置及車輛運補策略之研究. 工業與資訊管理學系碩士論文，國立成功大學.

傅聖揚. 2011. 考慮單一隨機限制式下之離散型模擬最佳化演算法. 工業與資訊管理學系碩士論文，國立成功大學.

張立蓁. 2010. 都會區公共自行車租借系統之設計與營運方式研究. 工業與資訊管理學系碩士論文，國立成功大學.

龔建宇. 2007. 國軍油料補給管理模式之建構與分析. 資訊管理學系碩士論文，國防大學.

劉奕青. 2003. 自動販賣機存貨途程問題之研究. 工業工程與管理研究所碩士論文,元智大學.

謝東緯. 2000. 遠洋航商空櫃調度問題之研究. 交通管理科學研究所碩士論文,國立成功大學.

Alshamrani, A., Mathur, K., and Ballou, R.H. Reverse logistics: simultaneous design of delivery routes and returns strategies. Computers & Operations Research, 34, 595-619, 2007.

Ai, J. and Kachitvichyanukul, V. A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Computers & Operations Research, 36(5), 1693-1702, 2009.

Bard, J.F. and Nananukul, N. Heuristics for a multiperiod inventory routing problemwith production decisions. Computers & Industrial Engineering, 57, 713-723, 2009.

Branks, J., Chick, S.E.,and Schmidt, C. Selecting a selection procedure. Management Science, 53, 1916-1932, 2007.

Boesel, J., Nelson, B.L., and Kim, S.H. Using Ranking and Selection To “Clean Up” After Simulation Optimization. Operations Research, 51(5), 814-825, 2003.

Bechhofer, R.E., Santner, T.J., and Goldsman, D. Design and Analysis of Experiments for Statistical Selection, Screening and Multiple Comparisons. John Wiley & Sons, New York, 1995.

Bechhofer, R.E. A single-sample multiple decision procedure for ranking means of normal populations with known variances. Annals of Mathematical Statistics, 25, 16-39, 1954.

Chen, C.H., Lee, L.H., Stochastic Simulation Optimization – An Optimal Computing Budget Allocation. World Scientific, Singapore, 2011.

Crainic, T., Gendreau, M. and Dejax, P. Dynamic and stochastic models for the llocation of empty containers. Operations Research, 41(1), 102-126, 1993.

Carson, Y. and Maria, A. Simulation Optimization: Methods and Applications. In Proceedings of the 1997 Winter Simulation Conference, 118- 126, 1997.

DeMaio, P. Bike-Sharing: History, Impacts, Models of Provision, and Future. Journal of Public Transportation, 12(4), 41-56, 2009.

Fu, M., Optimization for Simulation: Theory vs. Practice, INFORMS Journal on Computing, 14(3), 192-215, 2002.

Guner, A. R. and Sevkli, M. A continuous particle swarm optimization algorithm for uncapacitated facility location problem. Ant Colony Optimization and Swarm, 4150, 316-323, 2006.

Goldsman, D., and Nelson, B.L. Comparing systems via simulation. The Handbook of Simulation. John Wiley, New York, 273-306, 1998.

Golden, B.L., Baker, E.K., Alfaro, J.L. and Schaffer, J.R. The vehicle routing problem with backhauling: two approaches. Working paper MS/S 85-017, University of Maryland, College Park, 1985.

Goldsman D. Ranking And Selection In Simulation. Proceedings of the 1983 Winter Simulation Conference, 387-394.

Gupta, S.S. On a decision rule for a problem in ranking means. Doctoral dissertation, Institute of Statistics, Univ. of North Carolina, Chapel Hill, NC., 1956.

Hong, L.J., and Nelson, B.L. A Brief Introduction to Optimization via Simulation. Proceedings of the 2009 Winter Simulation Conference, 75-85.

Kim, S.H., Nelson, B.L., Selecting the best system, Chapter 17 in Elsevier Handbook in Operation Research and Management Science: Simulation, Elsevier., 2005.

Kennedy, J. and Eberhart, R. Particle swarm optimization. IEEI International Conference on Neural Networks, 1942-1948, 1995.

Law, A.M. and Kelton, W.D. Simulation Modeling & Analysis. McGraw-Hill, 1991.

Li, Z. and Tao, F. On determining optimal fleetsize and vehicle transfer policy for a car rental company. Computers and Operations Research, 37, 341-350, 2010.

Lin, J.R. and Yang, T.H. Strategic design of public bicycle sharing systems with service level constraints. Transportation Research Part E, 47(2), 284-294, 2011.

Magoulas,G.D.,Eldabi,T.,and Paul,R.J. Globalnsearch for simulation optimisation. Proceedings of the 2002 Winter Simulation Conference, 1978-1985.

Min, H. The multiple vehicle routing problem with simultaneous delivery and pickup points. Transportation Research A, 23, 377-386, 1989.

Nelson, B.L. Optimiztion via Simulation Over Discrete Decision Variables. Operations Research, 7, 193-207, 2010.

Nelson, B.L., Swann, J., Goldsman, D., and Song, W. Simple Procedures for Selecting the Best Simulated System When the Number of Alternatives Is Large. Operations Research, 49, 950-963, 2001.

Rinott, Y. On Two-Stage Selection Procedures and Related Probability-Inequalities. Communications in Statistics – Theory and Methods, 7, 799-811, 1978.

Shaheen, S., Guzman, S., and Zhang, H. Bikesharing in Europe, the Americas, and Asia: past, present, and future. Transportation Research Record, 2010.

Shu, J., Chou, M., Liu, Q., Teo, C.P. and Wang, I.-L. Bicycle-sharing system: deployment, utilization and the value of re-distribution. Working paper, 2010.

Santner, T.J., and Goldsman D. Design and Analysis of Experiments for Statistical Selection, Screening and Multiple Comparisons. John Wiley, New York., 1995.

Wilcox, R.R. A table for Rinott’s selection procedure. Journal of Quality Technology. 16,97-100, 1984.

Yang, T.H., Lin, J.R. and Chang, Y.C. Strategic Design of Public Bicycle Sharing Systems Incorporating with Bicycle Stocks Considerations. Proceeding of The International Conference on Computers and Industrial Engineering, 25-28, 2010.

Zhang, H., Tam,C.M., Li, H., Shi, J.J., Particle swarm optimization-supported simulation for construction operations. Construction Engineering and Management, 132 (12), 1267–1274, 2006.