Staffing a call center with uncertain non-stationary arrival rate and flexibility

We consider a multi-period staffing problem in a single-shift call center. The call center handles inbound calls, as well as some alternative back-office jobs. The call arrival process is assumed to follow a doubly non-stationary stochastic process with a random mean arrival rate. The inbound calls have to be handled as quickly as possible, while the back-office jobs, such as answering emails, may be delayed to some extent. The staffing problem is modeled as a generalized newsboy-type model under an expected cost criterion. Two different solution approaches are considered. First, by discretization of the underlying probability distribution, we explicitly formulate the expected cost newsboy-type formulation as a stochastic program. Second, we develop a robust programming formulation. The characteristics of the two methods and the associated optimal solutions are illustrated through a numerical study based on real-life data. In particular we focus on the numerical tractability of each formulation. We also show that the alternative workload of back-office jobs offers an interesting flexibility allowing to decrease the total operating cost of the call center.

[1]  Avishai Mandelbaum,et al.  Statistical Analysis of a Telephone Call Center , 2005 .

[2]  Pierre L'Ecuyer,et al.  Modeling Daily Arrivals to a Telephone Call Center , 2003, Manag. Sci..

[3]  Ward Whitt,et al.  Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System , 2007 .

[4]  Zeynep Akşin,et al.  The Modern Call Center: A Multi‐Disciplinary Perspective on Operations Management Research , 2007 .

[5]  Stefan Helber,et al.  Profit-oriented shift scheduling of inbound contact centers with skills-based routing, impatient customers, and retrials , 2010, OR Spectr..

[6]  Terry P. Harrison,et al.  A stochastic programming model for scheduling call centers with global Service Level Agreements , 2010, Eur. J. Oper. Res..

[7]  Xuan Vinh Doan,et al.  Robust and data-driven approaches to call centers , 2010, Eur. J. Oper. Res..

[8]  Gary M. Thompson.  Accounting for the Multi-Period Impact of Service When Determining Employee Requirements for Labor Scheduling , 1993 .

[9]  Atul Bhandari,et al.  An Exact and Efficient Algorithm for the Constrained Dynamic Operator Staffing Problem for Call Centers , 2008, Manag. Sci..

[10]  Shane G. Henderson,et al.  Service system planning in the presence of a random arrival rate , 2004 .

[11]  Ward Whitt,et al.  Staffing of Time-Varying Queues to Achieve Time-Stable Performance , 2008, Manag. Sci..

[12]  Thomas R. Robbins,et al.  Managing service capacity under uncertainty , 2007 .

[13]  Linda V. Green,et al.  AN IMPROVED HEURISTIC FOR STAFFING TELEPHONE CALL CENTERS WITH LIMITED OPERATING HOURS , 2003 .

[14]  Terry P. Harrison,et al.  Partial cross training in call centers with uncertain arrivals and global service level agreements , 2007, 2007 Winter Simulation Conference.

[15]  Ger Koole,et al.  Managing uncertainty in call centres using Poisson mixtures , 2001 .

[16]  Dimitris Bertsimas,et al.  Constructing Uncertainty Sets for Robust Linear Optimization , 2009, Oper. Res..

[17]  Ward Whitt,et al.  Staffing a Call Center with Uncertain Arrival Rate and Absenteeism , 2006 .

[18]  Raik Stolletz,et al.  Approximation of the non-stationary M(t)/M(t)/c(t)-queue using stationary queueing models: The stationary backlog-carryover approach , 2008, Eur. J. Oper. Res..

[19]  Carl M. Harris,et al.  Fundamentals of queueing theory , 1975 .

[20]  Kurt M. Bretthauer,et al.  Real-Time Work Schedule Adjustment Decisions: An Investigation and Evaluation , 2009 .

[21]  Haipeng Shen,et al.  Interday Forecasting and Intraday Updating of Call Center Arrivals , 2008, Manuf. Serv. Oper. Manag..

[22]  Itay Gurvich,et al.  Staffing Call Centers with Uncertain Demand Forecasts: A Chance-Constrained Optimization Approach , 2010, Manag. Sci..

[23]  Ward Whitt,et al.  Dynamic staffing in a telephone call center aiming to immediately answer all calls , 1999, Oper. Res. Lett..

[24]  Jean-Philippe Vial,et al.  Automatic Formulation of Stochastic Programs Via an Algebraic Modeling Language , 2007, Comput. Manag. Sci..

[25]  P. Kolesar,et al.  The Pointwise Stationary Approximation for Queues with Nonstationary Arrivals , 1991 .

[26]  Wlodzimierz Ogryczak,et al.  Dual Stochastic Dominance and Related Mean-Risk Models , 2002, SIAM J. Optim..

[27]  J. Michael Harrison,et al.  A Method for Staffing Large Call Centers Based on Stochastic Fluid Models , 2005, Manuf. Serv. Oper. Manag..

[28]  Jean-Philippe Vial,et al.  A practical implementation of stochastic programming: an application to the evaluation of option contracts in supply chains , 2004, Autom..

[29]  Xudong Wu,et al.  A Survey and Experimental Comparison of Service-Level-Approximation Methods for Nonstationary M(t)/M/s(t) Queueing Systems with Exhaustive Discipline , 2007, INFORMS J. Comput..

[30]  Melvyn Sim,et al.  Constructing Risk Measures from Uncertainty Sets , 2009, Oper. Res..

[31]  Haipeng Shen,et al.  Multifactor Poisson and Gamma-Poisson Models for Call Center Arrival Times , 2004 .

[32]  Allen L. Soyster,et al.  Technical Note - Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming , 1973, Oper. Res..

[33]  Avishai Mandelbaum,et al.  Workload forecasting for a call center: Methodology and a case study , 2009, 1009.5741.

[34]  Melvyn Sim,et al.  The Price of Robustness , 2004, Oper. Res..

[35]  Jonathan Weinberg,et al.  Bayesian Forecasting of an Inhomogeneous Poisson Process With Applications to Call Center Data , 2007 .

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

[37]  Stanislav Uryasev,et al.  Conditional Value-at-Risk for General Loss Distributions , 2002 .