Modeling and simulation of call centers.

In this review, we introduce key notions and describe the decision problems commonly encountered in call center management. Main themes are the central role of uncertainty throughout the decision hierarchy and the many operational complexities and relationships between decisions. We make connections to analytical models in the literature, emphasizing insights gained and model limitations.The high operational complexity and the prevalent uncertainty suggest that simulation modeling and simulation-based decision-making could have a central role in the management of call centers. We formulate some common decision problems and point to recently developed simulation-based solution techniques. We review recent work that supports modeling the primitive inputs to a call center and highlight call center modeling difficulties

Modeling and simulation of a telephone call center

We consider a system with two types of traffic and two types of agents. Outbound calls are served only by blend agents, whereas inbound calls can be served by either inbound-only or blend agents. Our objective is to allocate a number of agents such that some service requirement is satisfied. We have taken two approaches in analyzing this staffing problem: We developed a simulation model of the call center, which allows us to do a what-if analysis, as well as continuous-time Markov chain (CTMC) queueing models, which provide approximations of system performance measures. We describe the simulation model in this paper

Simulation-based optimization of agent scheduling in multiskill call centers.

We examine and compare simulation-based algorithms for solvingthe agent scheduling problem in a multiskill call center.This problem consists in minimizing the total costs of agents underconstraints on the expected service level per call type,per period, and aggregated.We propose a solution approach that combines simulation withinteger or linear programming, with cut generation.In our numerical experiments with realistic problem instances,this approach performs better than all other methods proposedpreviously for this problem.We also show that the two-step approach, which is the standard methodfor solving this problem, sometimes yield solutions that arehighly suboptimal and inferior to those obtained by our proposed method.<br/

Convergence of the stochastic mesh estimator for pricing Bermudan options

Broadie and Glasserman (2004) proposed a Monte Carlo algorithm they named “stochastic mesh” for pricing high-dimensional Bermudan options. Based on simulated states of the assets underlying the option at each exercise opportunity, the method produces an estimator of the option value at each sampled state. We derive an asymptotic upper bound on the probability of error of the mesh estimator under the mild assumption of the finiteness of certain moments. Both the error size and the probability bound are functions that vanish with increasing sample size. Moreover, we report the mesh method’s empirical performance on test problems taken from the recent literature. We find that the mesh estimator has large positive bias that decays slowly with the sample size

Efficient Monte Carlo and quasi-Monte Carlo option pricing under the variance gamma model

We develop and study efficient Monte Carlo algorithms for pricing path-dependent options with the variance gamma model. The key ingredient is difference-of-gamma bridge sampling, based on the representation of a variance gamma process as the difference of two increasing gamma processes. For typical payoffs, we obtain a pair of estimators (named low and high) with expectations that (1) are monotone along any such bridge sampler, and (2) contain the continuous-time price. These estimators provide pathwise bounds on unbiased estimators that would be more expensive (infinitely expensive in some situations) to compute. By using these bounds with extrapolation techniques, we obtain significant efficiency improvements by work reduction. We then combine the gamma bridge sampling with randomized quasi–Monte Carlo to reduce the variance and thus further improve the efficiency. We illustrate the large efficiency improvements on numerical examples for Asian, lookback, and barrier options

The application of forecasting techniques to modeling emergency medical system calls in Calgary, Alberta.

We develop and evaluate time-series models of call volume to the emergency medical service of a major Canadian city. Our objective is to offer simple and effective models that could be used for realistic simulation of the system and for forecasting daily and hourly call volumes. Notable features of the analyzed time series are: a positive trend, daily, weekly, and yearly seasonal cycles, special-day effects, and positive autocorrelation. We estimate models of daily volumes via two approaches: (1) autoregressive models of data obtained after eliminating trend, seasonality, and special-day effects; and (2) doubly-seasonal ARIMA models with special-day effects. We compare the estimated models in terms of goodness-of-fit and forecasting accuracy. We also consider two possibilities for the hourly model: (3) a multinomial distribution for the vector of number of calls in each hour conditional on the total volume of calls during the day and (4) fitting a time series to the data at the hourly level. For our data, (1) and (3) are superior

Markov chain models of a telephone call center with call blending.

Motivated by a Bell Canada call center operating in blend mode, we consider a system with two types of traffic and two types of agents. Outbound calls are served only by blend agents, whereas inbound calls can be served by either inbound-only or blend agents. Inbound callers may balk or abandon. There are several performance measures of interest, including the rate of outbound calls and the proportion of inbound calls waiting more than some fixed number of seconds. We present a collection of continuous-time Markov chain (CTMC) models which capture many real-world characteristics while maintaining parsimony that results in fast computation. We discuss and explore the tradeoffs between model fidelity and efficacy and compare our different CTMC models with a realistic simulation model of a Bell Canada call center, used as a benchmark