4,126 research outputs found
Statistical and Economic Evaluation of Time Series Models for Forecasting Arrivals at Call Centers
Call centers' managers are interested in obtaining accurate point and
distributional forecasts of call arrivals in order to achieve an optimal
balance between service quality and operating costs. We present a strategy for
selecting forecast models of call arrivals which is based on three pillars: (i)
flexibility of the loss function; (ii) statistical evaluation of forecast
accuracy; (iii) economic evaluation of forecast performance using money
metrics. We implement fourteen time series models and seven forecast
combination schemes on three series of daily call arrivals. Although we focus
mainly on point forecasts, we also analyze density forecast evaluation. We show
that second moments modeling is important both for point and density
forecasting and that the simple Seasonal Random Walk model is always
outperformed by more general specifications. Our results suggest that call
center managers should invest in the use of forecast models which describe both
first and second moments of call arrivals
Statistical and Economic Evaluation of Time Series Models for Forecasting Arrivals at Call Centers
Call centers' managers are interested in obtaining accurate forecasts of call arrivals because these are a key input in staffing and scheduling decisions. Therefore their ability to achieve an optimal balance between service quality and operating costs ultimately hinges on forecast accuracy. We present a strategy to model selection in call centers which is based on three pillars: (i) a flexible loss function; (ii) statistical evaluation of forecast accuracy; (iii) economic evaluation of forecast performance using money metrics. We implement fourteen time series models and seven forecast combination schemes on three series of call arrivals. We show that second moment modeling is important when forecasting call arrivals. From the point of view of a call center manager, our results indicate that outsourcing the development of a forecasting model worth its cost, since the simple Seasonal Random Walk model is always outperformed by other, relatively more sophisticated, specifications
Forecasting Intraday Time Series with Multiple Seasonal Cycles Using Parsimonious Seasonal Exponential Smoothing
This paper concerns the forecasting of seasonal intraday time series. An extension of Holt-Winters exponential smoothing has been proposed that smoothes an intraday cycle and an intraweek cycle. A recently proposed exponential smoothing method involves smoothing a different intraday cycle for each distinct type of day of the week. Similar days are allocated identical intraday cycles. A limitation is that the method allows only whole days to be treated as identical. We introduce an exponential smoothing formulation that allows parts of different days of the week to be treated as identical. The result is a method that involves the smoothing and initialisation of fewer terms than the other two exponential smoothing methods. We evaluate forecasting up to a day ahead using two empirical studies. For electricity load data, the new method compares well with a range of alternatives. The second study involves a series of arrivals at a call centre that is open for a shorter duration at the weekends than on weekdays. By contrast with the previously proposed exponential smoothing methods, our new method can model in a straightforward way this situation, where the number of periods on each day of the week is not the same.Exponential smoothing; Intraday data; Electricity load; Call centre arrivals.
From Packet to Power Switching: Digital Direct Load Scheduling
At present, the power grid has tight control over its dispatchable generation
capacity but a very coarse control on the demand. Energy consumers are shielded
from making price-aware decisions, which degrades the efficiency of the market.
This state of affairs tends to favor fossil fuel generation over renewable
sources. Because of the technological difficulties of storing electric energy,
the quest for mechanisms that would make the demand for electricity
controllable on a day-to-day basis is gaining prominence. The goal of this
paper is to provide one such mechanisms, which we call Digital Direct Load
Scheduling (DDLS). DDLS is a direct load control mechanism in which we unbundle
individual requests for energy and digitize them so that they can be
automatically scheduled in a cellular architecture. Specifically, rather than
storing energy or interrupting the job of appliances, we choose to hold
requests for energy in queues and optimize the service time of individual
appliances belonging to a broad class which we refer to as "deferrable loads".
The function of each neighborhood scheduler is to optimize the time at which
these appliances start to function. This process is intended to shape the
aggregate load profile of the neighborhood so as to optimize an objective
function which incorporates the spot price of energy, and also allows
distributed energy resources to supply part of the generation dynamically.Comment: Accepted by the IEEE journal of Selected Areas in Communications
(JSAC): Smart Grid Communications series, to appea
A Spatio-Temporal Point Process Model for Ambulance Demand
Ambulance demand estimation at fine time and location scales is critical for
fleet management and dynamic deployment. We are motivated by the problem of
estimating the spatial distribution of ambulance demand in Toronto, Canada, as
it changes over discrete 2-hour intervals. This large-scale dataset is sparse
at the desired temporal resolutions and exhibits location-specific serial
dependence, daily and weekly seasonality. We address these challenges by
introducing a novel characterization of time-varying Gaussian mixture models.
We fix the mixture component distributions across all time periods to overcome
data sparsity and accurately describe Toronto's spatial structure, while
representing the complex spatio-temporal dynamics through time-varying mixture
weights. We constrain the mixture weights to capture weekly seasonality, and
apply a conditionally autoregressive prior on the mixture weights of each
component to represent location-specific short-term serial dependence and daily
seasonality. While estimation may be performed using a fixed number of mixture
components, we also extend to estimate the number of components using
birth-and-death Markov chain Monte Carlo. The proposed model is shown to give
higher statistical predictive accuracy and to reduce the error in predicting
EMS operational performance by as much as two-thirds compared to a typical
industry practice
Forecasting emergency medical service call arrival rates
We introduce a new method for forecasting emergency call arrival rates that
combines integer-valued time series models with a dynamic latent factor
structure. Covariate information is captured via simple constraints on the
factor loadings. We directly model the count-valued arrivals per hour, rather
than using an artificial assumption of normality. This is crucial for the
emergency medical service context, in which the volume of calls may be very
low. Smoothing splines are used in estimating the factor levels and loadings to
improve long-term forecasts. We impose time series structure at the hourly
level, rather than at the daily level, capturing the fine-scale dependence in
addition to the long-term structure. Our analysis considers all emergency
priority calls received by Toronto EMS between January 2007 and December 2008
for which an ambulance was dispatched. Empirical results demonstrate
significantly reduced error in forecasting call arrival volume. To quantify the
impact of reduced forecast errors, we design a queueing model simulation that
approximates the dynamics of an ambulance system. The results show better
performance as the forecasting method improves. This notion of quantifying the
operational impact of improved statistical procedures may be of independent
interest.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS442 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Impact of Special Days in Call Arrivals Forecasting:A Neural Network Approach to Modelling Special Days
A key challenge for call centres remains the forecasting of high frequency call arrivals collected in hourly or shorter time buckets. In addition to the complex intraday, intraweek and intrayear seasonal cycles, call arrival data typically contain a large number of anomalous days, driven by the occurrence of holidays, special events, promotional activities and system failures. This study evaluates the use of a variety of univariate time series forecasting methods for forecasting intraday call arrivals in the presence of such outliers. Apart from established, statistical methods, we consider artificial neural networks (ANNs). Based on the modelling flexibility of the latter, we introduce and evaluate different methods to encode the outlying periods. Using intraday arrival series from a call centre operated by one of Europe’s leading entertainment companies, we provide new insights on the impact of outliers on the performance of established forecasting methods. Results show that ANNs forecast call centre data accurately, and are capable of modelling complex outliers using relatively simple outlier modelling approaches. We argue that the relative complexity of ANNs over standard statistical models is offset by the simplicity of coding multiple and unknown effects during outlying periods.NOTICE: this is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, [264, 3, (2016)] DOI: 10.1016/j.ejor.2016.07.015© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0
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