Innovative Applications of O.R.Modeling latent sources in call center arrival data
Section snippets
Introduction and overview
In this paper, we consider modeling call center arrival data that are typically linked to individual advertisements. As pointed out by Soyer and Tarimcilar (2008), analysis of such data requires models that allow for advertisement specific analysis of call arrivals and poses new modeling challenges. One of the challenging problems is to model and analyze such data when there is incomplete information about the sources of the call arrivals. Our aim is to develop a modeling strategy to address
Modulated poisson process model with latent variables
Following Soyer and Tarimcilar (2008) we define as the number of calls arrived during a time interval of length t as response to the ith advertisement and as a vector of covariates that describe the characteristics of the ith advertisement. Typically, the covariate vector will consist of media expense (in $’s), venue type (monthly magazine, daily newspaper etc.), ad format (full page, half page, color, etc.), offer type (free shipment, payment schedule etc.) and seasonal
Bayesian analysis of the latent variable model
In the modulated NHPP model with missing links we assume a Dirichlet prior on with parameters which is independent across the intervals. Thus, for the jth interval we assume a Dirichlet prior asIt follows from (3.1) thatWe can specify the prior parameters proportional toto reflect the fact that, for , larger number of calls during the early phases of the life of an ad will be followed by
Example using simulated data
We consider data simulated from a modulated nonhomogeneous Poisson process with cost of the advertising as the single covariate and with baseline cumulative intensity is a power law function. Thus, the cumulative intensity function for ad i is given bywhere is a scalar and is the cost of the ith advertisement. Data was generated for 10 different ads starting at the same time assuming and . The costs of the ads changed between 1 and 10 units and 20 time
Concluding remarks
In conclusion, our experience with the proposed Bayesian approach for modeling latent sources and the corresponding data augmentation algorithm within the Gibbs sampler have shown a lot of promise. The proposed approach provided very close posterior inference results for the model parameters and actual arrivals when it is compared with complete source model results. The inferences about ’s when compared to actual values were found to be sufficiently close.
Furthermore, we note that in our
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Cited by (11)
Forecasting: theory and practice
2022, International Journal of ForecastingCitation Excerpt :The works by Soyer and Tarimcilar (2008) and Weinberg, Brown, and Stroud (2007) model call volumes from a Bayesian point of view. Other Bayesian inspired approaches have been adopted mainly for estimating various model parameters, but also allowing for intraday updates of forecasts (Aktekin & Soyer, 2011; Landon, Ruggeri, Soyer, & Tarimcilar, 2010). A further class of approach addresses the dimensionality challenge related to high frequency call data using Singular Value Decomposition (SVD).
Decision making under uncertain and dependent system rates in service systems
2021, European Journal of Operational ResearchCitation Excerpt :Even though joint modeling of the system rates is not common practice in the literature, there is a stream of recent work that discusses the modeling of each individual rate. For instance, Aktekin and Soyer (2011); Landon, Ruggeri, Soyer, and Tarimcilar (2010); Weinberg, Brown, and Stroud (2007) focus on the modeling of the arrival rate, Aktekin (2014); Dimitriou (2018); Ibrahim, L’Ecuyer, Shen, and Thiongane (2016) on the service times distribution and its rate and Aktekin and Soyer (2014); Kuzu and Soyer (2018) on the abandonment times distribution and its rate. Optimal staffing problems have received a tremendous amount of attention in the service system literature, especially in call center applications.
Modeling and forecasting call center arrivals: A literature survey and a case study
2016, International Journal of ForecastingCitation Excerpt :Auxiliary information is often available in call centers, and can improve point or distributional forecasts considerably. For example, when a company sends notification letters to customers, or runs advertisements, this may trigger a large volume of calls; see Landon, Ruggeri, Soyer, and Tarimcilar (2010). Also, large sporting events or festivals can result in a significant increase in calls to emergency systems; see Channouf et al. (2007).
Call center service process analysis: Bayesian parametric and semi-parametric mixture modeling
2014, European Journal of Operational ResearchEstimating the population utility function: A parametric Bayesian approach
2012, European Journal of Operational ResearchCitation Excerpt :Thus, this paper presents an alternative approach for health state utility estimation by combining ideas from the MAUT and Bayesian statistics. Bayesian applications in OR are common in areas such as call center operations (Landon et al., 2010), queueing (Armero and Conesa, 2004), inventory (Berk et al. (2007)), and quality control (Chun and Sumichrast, 2007). But applications of Bayesian methods in health economics have been limited with the exceptions of Kharroubi et al. (2005, 2007).
Forecasting: theory and practice
2020, arXiv