Optimal balanced control for call centers

In this paper we study the optimal assignment of tasks to agents in a call center. For this type of problem, typically, no single deterministic and stationary (i.e., state independent and easily implementable) policy yields the optimal control, and mixed strategies are used. Other than finding the optimal mixed strategy, we propose to optimize the performance over the set of “balanced” deterministic periodic non-stationary policies. We provide a stochastic approximation algorithm that allows to find the optimal balanced policy by means of Monte Carlo simulation. As illustrated by numerical examples, the optimal balanced policy outperforms the optimal mixed strategy.

[1]  Bruce E. Hajek,et al.  Extremal Splittings of Point Processes , 1985, Math. Oper. Res..

[2]  E. Altman.  Constrained Markov Decision Processes , 1999 .

[3]  Xi-Ren Cao,et al.  A note on the relation between weak derivatives and perturbation realization , 2002, IEEE Trans. Autom. Control..

[4]  Avishai Mandelbaum,et al.  Telephone Call Centers: Tutorial, Review, and Research Prospects , 2003, Manuf. Serv. Oper. Manag..

[5]  Noah Gans,et al.  A Call-Routing Problem with Service-Level Constraints , 2003, Oper. Res..

[6]  Eitan Altman,et al.  Multimodularity, Convexity, and Optimization Properties , 2000, Math. Oper. Res..

[7]  Robert A. Shumsky.  Approximation and Analysis of a Queueing System with Flexible and Specialized Servers , 1999 .

[8]  Ger Koole,et al.  Exponential Approximation of Multi-Skill Call Centers Architecture , 2000 .

[9]  M. Lothaire,et al.  Algebraic Combinatorics on Words: Index of Notation , 2002 .

[10]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[11]  George Ch. Pflug,et al.  Optimization of Stochastic Models , 1996 .

[12]  Ward Whitt,et al.  The Asymptotic Efficiency of Simulation Estimators , 1992, Oper. Res..

[13]  Ger Koole,et al.  Approximating multi-skill blocking systems by HyperExponential Decomposition , 2006, Perform. Evaluation.

[14]  Tolga Tezcan,et al.  Optimal control of parallel server systems with many servers in heavy traffic , 2008, Queueing Syst. Theory Appl..

[15]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[16]  Eugene A. Feinberg,et al.  Handbook of Markov Decision Processes , 2002 .

[17]  Eitan Altman,et al.  Discrete-Event Control of Stochastic Networks - Multimodularity and Regularity , 2004, Lecture notes in mathematics.

[18]  Avishai Mandelbaum,et al.  Queueing Models of Call Centers: An Introduction , 2002, Ann. Oper. Res..

[19]  Itay Gurvich,et al.  Service-Level Differentiation in Call Centers with Fully Flexible Servers , 2008, Manag. Sci..

[20]  G. A. Hedlund,et al.  Symbolic Dynamics II. Sturmian Trajectories , 1940 .

[21]  Arie Hordijk,et al.  Measure-Valued Differentiation for Stationary Markov Chains , 2006, Math. Oper. Res..

[22]  Ward Whitt,et al.  A Staffing Algorithm for Call Centers with Skill-Based Routing , 2005, Manuf. Serv. Oper. Manag..

[23]  Robert A. Shumsky.  Approximation and analysis of a call center with flexible and specialized servers , 2004, OR Spectr..

[24]  G. Hardy,et al.  An Introduction to the Theory of Numbers , 1938 .

[25]  F. Vázquez-Abad,et al.  Measure valued differentiation for random horizon problems , 2006 .

[26]  Constantinos Maglaras,et al.  On Customer Contact Centers with a Call-Back Option: Customer Decisions, Routing Rules, and System Design , 2004, Oper. Res..

[27]  M. Lothaire.  Algebraic Combinatorics on Words , 2002 .

[28]  Eitan Altman,et al.  Time-Sharing Policies for Controlled Markov Chains , 1993, Oper. Res..

[29]  Eitan Altman,et al.  Balanced sequences and optimal routing , 2000, JACM.

[30]  Naoto Miyoshi,et al.  m-Balanced words: A generalization of balanced words , 2004, Theor. Comput. Sci..

[31]  Sandjai Bhulai,et al.  A queueing model for call blending in call centers , 2003, IEEE Trans. Autom. Control..

[32]  Eitan Altman,et al.  Regular ordering and applications in control policies , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[33]  F. Vázquez-Abad,et al.  Measure-Valued Differentiation for Markov Chains , 2008 .

[34]  Xi-Ren Cao,et al.  Stochastic learning and optimization - A sensitivity-based approach , 2007, Annu. Rev. Control..

[35]  A. Hordijk,et al.  Taylor series expansions for stationary Markov chains , 2003, Advances in Applied Probability.

[36]  Eitan Altman,et al.  Optimal admission, routing and service assignment control: the case of single buffer queues , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).