臺灣博碩士論文加值系統

客服中心為企業和顧客聯繫時的主要方式，且在全球各地都具有一定程度的發展。近年來在作業研究和管理科學方面，對於客服中心問題的研究也日益增加。客服中心主要是勞力密集的經營模式，由於資訊設備的快速發展，因此硬體設備不再是客服中心主要的成本。目前客服中心主要的成本花費60%至70%為人員僱用成本，故考量如何能在滿足一定程度的服務水準(service levels)之下，使得人員僱用成本最小，此為客服中心最主要探討的問題。由於在估計服務水準(service levels)時的複雜度較高，因此適合利用系統模擬建構模型，並且估計客服中心問題的服務水準限制式。Atlason et al.(2004,2008)利用系統模擬建構客服中心模型，再分別使用切面法及中心切面法求解客服中心問題，此二種方法在樣本數夠大時演算法都能收斂至近似最佳解，但在模擬成本受限之下，並不能保證所得到的解為可行解，且一般樣本數目愈大代表花費的成本愈大。

有鑑於此，本研究以離散型模擬最佳化(DOvS)演算法中之隨機搜尋(Random Search)為基礎，利用Hong and Nelson(2006)COMPASS演算法中MPA(Most Promising Area)概念，增加隨機搜尋的收斂速度，並結合排序與選取程序(R＆S)中Batur and Kim (2010)發展之多重可行性驗證程序(MFCP)，針對多重隨機限制式進行可行性驗證，進而挑選出可行解集合，再從可行解集合中依照確定性目標式選出最適解，在1-α信心水準之下保證所找到的解為可行解。

Call center is an important way of businesses to communicate with their customers, and have a certain degree of development around the world. In recent years the research of call center is also increasing in operations research and management science. The call center is labor-intensive business model, due to the rapid development of information technology equipment, so the hardware is no longer the major cost of call center.

The major cost of the call center to spend 60 % to 70 % for the cost of labor, so the most important of call center is considered how to satisfy certain service levels under the staffing level. It’s complexity to estimate the service levels, therefore we use simulation to construct the model and estimate the call center service level constraint. Atlason et al (2004, 2008) use of simulation to construct the call center model, using the cutting plane method and the center cutting plane method for solving the problem of call center, respectively. In the number of samples is large enough for two kinds of methods can converge to optimal solution but in the simulation costs limited, does not guarantee the solution is feasible solution, and in general the more number of samples representative the more costs.

We use the random search in the discrete optimization via simulation, based on the MPA of Hong and Nelson (2006) COMPASS concept to increase the convergence rate of random search, combined with Batur and Kim(2010) ranking and selection procedure (R＆S), the development of multiple feasibility check procedure (MFCP) for the case of multiple stochastic constraints, pick out the feasible solution into a feasible solution set, according to the deterministic objective function selection the optimal solution from the feasible solution set with 1 - α confidence level guarantee to find the solution as a feasible solution.

摘要i
英文摘要ii
誌謝iv
目錄v
圖目錄vii
表目錄viii

第一章緒論1
1.1 研究背景與動機1
1.2 研究目的4
1.3 論文架構.4

第二章文獻探討5
2.1 客服中心人員配置問題(Call Center Staffing Problem)5
2.2 模擬最佳化(Optimization via Simulation; OvS) 11
2.2.1 隨機搜尋(Random Search)12
2.2.2 排序與選擇程序(Ranking and Selection; R＆S)17
2.3 小結23

第三章研究方法24
3.1 客服中心人員配置問題與問題假設24
3.2 客服中心問題之離散型模擬演算法27

第四章實驗情境與分析33
4.1 實驗評估33
4.2 實驗假設34
4.3 MPA 之建構及參數設定35
4.4 實驗情境與結果37
4.5 小結42

第五章結論與未來研究方向43
5.1 結論43
5.2 未來研究方向43

參考文獻45

Aksin, Z., Armony, M., Mehrotra, V., 2007. The modern call center: a multidisciplinary perspective on operations management research. Production and Operations Management, 16, 665-668.

Alrefaei, M. H., Andrad´ottir, S., 1999. A simulated annealing algorithm with constant temperature for discrete stochastic approximation. Management Science 45, 748-764.

Alrefaei, M. H., Andrad´ottir, S., 2001. A modification of the stochastic ruler method for discrete stochastic optimization. European Journal of Operational Research 133(1), 160-182.

Alrefaei, M. H., Andrad´ottir, S., 2005. Discrete stochastic optimization using variant of the stochastic ruler method. Naval Research Logistics, 52, 344-360.

Andrad´ottir, S., 1999. Accelerating the convergence of random search methods for discrete stochastic optimization. ACM Transactions on Modeling and Computer Simulation 9 (4), 349-380.

Andrad´ottir, S., 2006 Simulation optimization with countably infinite feasible regions: Efficiency and convergence. ACM Transactions on Modeling and Computer Simulation 16 (4), 357-374.

Andrad´ottir, S., Prudius A.A., 2009. Balanced explorative and exploitative search with estimation for simulation optimization. INFORMS Journal on Computing, 21, 193-208.

Andrad´ottir, S., Kim, S.H., 2010. Fully sequential procedures for comparing constrained systems via simulation. Naval Research Logistics 57, 403-421.

Atlason, J., Epelman, M.A., Henderson, S.G., 2004. Call center staffing with simulation and cutting plane methods. Annals of Operations Research 127, 333-358.

Atlason, J., Epelman, M.A., Henderson, S.G., 2008. Optimizing call center staffing using simulation and analytic center cutting-plane methods. Management Science 54 (2), 295-309.

Avramidis, A.N., Chan, W., L Ecuyer, P., 2009. Staffing multi-skill call centers via search methods and a performance approximation. IIE Transactions 41, 483-497.

Batur, D., Kim S. H., 2010. Finding feasible systems in the presence of constraints on multiple performance measures. ACM Transactions on Modeling and Computer Simulation 20 (3), 1-26.

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

Bhulai, S., Koole, G. and Pot, A., 2008. Simple methods for shift scheduling in multi-skill call centers. Manufacturing ＆ Service Operations Management, 10, 411-420.

Butler, J. C., Morrice, D. J. and Mullarkey, P., 2001. A multiple attribute utility theory approach to ranking and selection. Management Science 47, 800-816.

Castillo, I., Joro, T., Li,Y., 2009. Workforce scheduling with multiple objectives.European Journal of Operational Research 196, 162-170.

Cezik, M.T., L Ecuyer,, P., 2008. Staffing multiskill call centers via linear programming and simulation. Management Science 54 (2), 310-323.

Fukunaga, A., Hamilton, E., Fama, J., Andre, D., Matan, O., Nourbakhsh,I., 2002.Staff Scheduling for Inbound Call Centers and Customer Contact Centers. AI Magazine 23(4), 30 40.

Gans, N., Koole, G. M., Mandelbaum, A., 2003. Telephone call centers: Tutorial, review, and research prospects. Manufacturing ＆ Service Operations Management, 5, 79-141.

Garnett, O., Mandelbaum, A., Reiman, M., 2002. Designing a call center with impatient customers. Manufacturing ＆ Service Operations Management, 4, 208-227.

Gong, W. B., Ho, Y. C., Zhai, W., 1999. Stochastic comparison algorithm for discrete optimization with estimation. SIAM Journal on Optimization 10, 384-404.

Green, L., P. Kolesar., J. Soares., 2001. Improving the SIPP approach for staffing service systems that have cyclic demands. Operations Research 49 (4), 549-564.

Gurvich I, Luedtke J, Tezcan T., 2010 Staffing call-centers with uncertain demand forecasts: a chance-constraints approach. Management Science 56, 1093-1115.

Henderson, S.G., Nelson, B. L. 2006. SIMULATION. Handbooks in Operations Research and Management Science, 13

Hong, L. J., Nelson, B. L., 2006. Discrete optimization via simulation using COMPASS. Operations Research 54, 115-129.

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

Ingolfsson, A., Haque, M., Umnikov A., 2002. Accounting for time-varying queueing effects in workforce scheduling. European Journal of Operational Research 139, 585-597.

Ingolfsson, A., Campelloa, F., Wub, X., Cabralc, E., 2010 Combining integer programming and the randomization method to schedule employees. European Journal of Operations Research 202, 153-163.

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

Kleijnen, J.P.C., Beers, W. van, Nieuwenhuyse,I. van., 2010. Constrained optimization in expensive simulation: novel approach. European Journal of Operational Research 202 (1), 164-174.

Koole, G. M., Mandelbaum,A., 2002. Queueing models of call centers: An introduction, Annals of Operations Research 113, 41-59.

Mandelbaum A., Zeltyn S., 2006. Service Engineering of Call Centers: Research, Teaching, Practice. IBM SSME conference. Mandelbaum A., 2003. Call Centers. Research Bibliography with Abstracts. Version6.

Mason, A., Ryan, D., Panton, D., 1998. Integrated simulation, heuristic and optimisation approaches to staff scheduling. Operations Research, 46 (2), 161-175.

Nelson, B. L., 2010. Optimization via simulation over discrete decision variables. Tutorials in operations research. INFORMS, 193-207.

Pichitlamken, J., Nelson, B. L., 2003. A combined procedure for optimization via simulation. ACM Transactions on Modeling and Computer Simulation, 13, 155-179.

Pot, S. A., Bhulai, S., Koole, G. M., 2008. A simple staffing method for multiskill call centers. Manufacturing ＆ Service Operations Management, 10(3), 421-428.

Robbins, T., Harrison, T., 2010. A stochastic programming model for scheduling call centers with global service level agreements. European Journal of Operational Research 207(3), 1608-1619.

Shi, L., Olafsson,S., 2000. Nested partitions method for stochastic optimization. Methodology and Computing in Applied Probability, 2, 271-291.

Tien,J., Kamiyama, A., 1982. On manpower scheduling algorithms. SIAM Review 24 (3), 275-287.

Yan,D., Mukai, H., 1992. Stochastic discrete optimization. SIAM Journal on Control and Optimization 30, 594-612.