客服中心為企業組織和顧客聯繫時的主要方式，在全球各地都具有一定程度的發展。近年來對於客服中心問題的研究也日益增加，由於資訊設備的進步，因此硬體設備在客服中心裡並非最主要的成本，客服中心大部分的成本來自於服務人員成本，根據相關研究約為60%至70%，所以如何能在滿足一定程度的服務水準(Service level)下，使得服務人員總成本最小，為客服中心問題主要探討的部分。

　　在相關文獻中，有許多學者利用模擬方法，發展不同的演算法以處理客服中心問題，且所搭配使用的數值分析方法也不同，各自擁有不同的優缺點和適用情況。而本研究針對幾個能運用於此問題的演算法進行分析與討論，第一個為切面模擬演算法，主要以整數規劃處理樣本平均近似問題並輔以切面法加入切面限制式的方式求解。第二個為拉格朗日模擬演算法，使用拉格朗日乘數法簡化原始問題為一無限制式的模擬最佳化問題，並搭配區域搜尋求解。第三個為模擬迭代演算法，以模擬為基礎，取代傳統等候模型求解服務人員配置的方式，在考慮連續時間的到達率變動情況下進行求解。本研究主要目的為討論各個模擬演算法的優缺點以及執行績效，並設定各種情境及變因進行實驗，分析各個模擬演算法在不同設定下的表現會有何變化，以及其適用範圍。

　　切面模擬演算法以及模擬迭代演算法的表現相近，都有著不錯的目標成本以及PFS。整體來說，切面模擬演算法在加入可行性判定程序後，在目標成本以及可行解機率的綜合績效是最好的，但必須花費最多的模擬成本。拉格朗日模擬演算法則是改變拉格朗日乘數的計算方法後，績效表現能得到有效的改善，但較其他兩個演算法差一些。而模擬迭代演算法則是能夠在不耗費太多模擬成本的情況下，得到良好的目標成本及可行解機率。

　　We propose and improve three Simulation-based algorithms, the Cutting Plane Algorithm, Lagrangian Algorithm, and Iterative Algorithm, to solve the agent staffing problem in a single-skill call center. This problem aims to minimize the total costs of agents subject to service-level requirements that are estimated by simulation. The first algorithm combines the Cutting plane method and integer programming, then we improve it by using the Multiple Feasibility Check Procedure (MFCP). The second algorithm combines the Lagrange method and local search, then we improve it by updating lagrange multipliers. The third algorithm combines the queueing method for staffing, then we improve it by adjusting transform method of service-level. In our numerical experiments, all three algorithm perform better with new setting, though each of them has some strengths and weaknesses, the Cutting Plane Algorithm and the Iterative Algorithm perform better under most scenarios.

Aksin, Z., M. Armony, V. Mehrotra. 2007. The modern call center: a multi-disciplinary perspective on operations management research. Production Oper. Management 16 665-688.

Andradóttir, S., S.H. Kim. 2010. Fully sequential procedures for comparing constrained systems via simulation. Naval Res. Logist. 57 403-421.

Atlason, J., M.A. Epelman, S.G. Henderson. 2004. Call
center staffing with simulation and cutting plane methods. Ann. Oper. Res. 127 333-358.

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

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

Avramidis, A.N., W. Chan, M. Gendreau, P. L'Ecuyer, O. Pisacane. 2010. Optimizing daily agent scheduling in a
multiskill call center. Eur. J. Oper. Res. 200 822-832.

Batur, D., S.H. Kim. 2010. Finding feasible systems in
the presence of constraints on multiple performance measures. ACM Trans. Model. Comput. Simulation 20 1-26.

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

Bhulai, S., G. Koole, A. Pot. 2008. Simple methods for
shift scheduling in multiskill call centers. Manufacturing Service Oper. Management 10 411-420.

Boschetti, M.A., V. Maniezzo, M. Roffilli. 2011. A fully distributed lagrangean solution for a peer-to-peer overlay network design problem. INFORMS J. Comput. 23 90-104.

Buffa, E.S., M.J. Cosgrove, B.J. Luce. 1976. An
integrated work shift scheduling system. Decis. Sci. 7 620-630.

Cezik, M.T., P. L'Ecuyer. 2008. Staffing multiskill call centers via linear programming and simulation. Management Sci. 54 310-323.

Cooper, R.B. 1981. Introduction to Queueing Theory. 2nd ed. Elsevier, North-Holland, New Work.

Feldman, Z., A. Mandelbaum, W.A. Massey, W. Whitt. 2008.
Staffing of time-varying queues to achieve time-stable performance. Management Sci. 54 324-338.

Fu, M.C. 2006. Gradient estimation. S.G. Henderson, B.L. Nelson, eds. Handbooks in Operations Research and Management Science: Simulation. Elsevier Science, Amsterdam, 575-616.

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

Green, L., P. Kolesar. 1991. The pointwise stationary
approximation for queues with nonstationary arrivals.
Management Sci. 37 84-97.

Green, L.V., P.J. Kolesar, J. Soares. 2001. Improving
the SIPP approach for staffing service systems that have cyclic demands. Oper. Res. 49 549-564.

Green, L.V., P.J. Kolesar, J. Soares. 2003. An improved
heuristic for staffing telephone call centers with limited operating hours. Production Oper. Management 12 46-61.

Halfin, S., W. Whitt. 1981. Heavy-traffic limits for
queues with many exponential servers. Oper. Res. 29 567-588.

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

Hong, L.J., B.L. Nelson. 2009. A brief introduction to optimization via simulation. M. D. Rossetti, R. R.
Hill, B. Johansson, A. Dunkin, R.G. Ingalls, eds. Proc. 2009 Winter Simulation Conf., Institute of Electrical and Electronics Engineers, Piscataway. NJ, 75-85.

Ingolfsson, A., F. Campello, X. Wu, E. Cabral. 2010.
Combining integer programming and the randomization method to schedule employees. Eur. J. Oper. Res. 202 153-163.

Izady, N., D. Worthington. 2012. Setting staffing requirements for time dependent queueing networks: The case of accident and emergency departments. Eur. J. Oper. Res. 219 531-540.

Kleywegt, A.J., A. Shapiro, T. Homem-de-Mello. 2002. The
sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12 479-502.

Koole, G., A. Mandelbaum. 2002. Queueing models of call
centers: An introduction. Ann. Oper. Res. 113 41-59.

Luo, Y., E. Lim. 2013. Simulation-based optimization over discrete sets with noisy constraints. IIE Trans. 45 699-715.

Mason, A.J., D.M. Ryan, D.M. Panton. 1998. Integrated
simulation, heuristic and optimization approaches to staff scheduling. Oper. Res. 46 161-175.

Mehrotra, V., J. Fama. 2003. Call center
simulations: call center simulation modeling: methods, challenges, and opportunities. S. Chick, P.J. S'anchez, D. Ferrin, D.J. Morrice, eds. Proc. 2003 Winter Simulation Conf., Institute of Electrical and Electronics Engineers, Piscataway. NJ, 135-143.

Melo, W.A., M.H. Fampa, F.M. Raupp. 2012. A stochastic
local search algorithm for constrained continuous global
optimization. Int. Trans. Oper. Res. 19 825-846.

Nelson, B.L. 2010. Optimization via simulation over discrete decision variables. Tutorials in Operations Research. 7 193-207.

Pichitlamken, J., B.L. Nelson. 2003. A combined procedure
for optimization via simulation. ACM Trans. Model. Comput. Simulation 13 155-179.

Pirkul, H. 1987. Efficient algorithms for the capacitated concentrator location problem. Comput. Oper. Res. 14 197-208.

Pot, A., S. Bhulai, G. Koole. 2008. A simple staffing
method for multiskill call centers. Manufacturing Service
Oper. Management 10 421-428.

Shapiro, A. 1991. Asymptotic analysis of stochastic programs. Ann. Oper. Res. 30 169-186.

Whitt, W. 1991. The pointwise stationary approximation for Mt/Mt/s queues is asymptotically correct as the rates increase. Management Sci. 37 307-314.

Whitt, W. 2007. What you should know about queueing models to set staffing requirements in service systems. Naval Res. Logist. 54 476-484.

Xu, W.L., B.L. Nelson. 2013. Empirical stochastic branch-and-bound for optimization via simulation. IIE Trans. 45 685-698.

Zhang, Y., M.L. Puterman, M. Nelson, D. Atkins. 2012. A
simulation optimization approach to long-term care capacity planning. Oper. Res. 60 249-261.