Optimizing the Staffing and Routing of Small‐Size Hierarchical Call Centers

Multiple‐skill call centers propagate rapidly with the development of telecommunications. An abundance of literature has already been published on call centers. Here, we want to focus on centers that would typically occur in business‐to‐business environments; these are call centers that handle many types of calls but where the arrival rate for each type is low. To find an optimal configuration, the integrality of the decision variables is a much more important issue than for larger call centers. The present paper proposes an approach that uses elements of combinatorial optimization to find optimal configurations. We develop an approximation method for the evaluation of the service performance. Next, we search for the minimum‐cost configuration subject to service‐level constraints using a branch‐and‐bound algorithm. What is at stake is to find the right balance between gains resulting from the economies of scale of pooling and the higher cost or cross‐trained agents. The article shows that in most cases this method significantly decreases the staffing cost compared with configurations with only cross‐trained or dedicated operators.     

Alignments with non-overlapping moves,inversions and tandem duplications in <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis><Superscript>4</Superscript>) time

Sequence alignment is a central problem in bioinformatics. The classical dynamic programming algorithm aligns two sequences by optimizing over possible insertions, deletions and substitutions. However, other evolutionary events can be observed, such as inversions, tandem duplications or moves (transpositions). It has been established that the extension of the problem to move operations is NP-complete. Previous work has shown that an extension restricted to non-overlapping inversions can be solved in O(n ³) with a restricted scoring scheme. In this paper, we show that the alignment problem extended to non-overlapping moves can be solved in O(n ⁵) for general scoring schemes, O(n ⁴log n) for concave scoring schemes and O(n ⁴) for restricted scoring schemes. Furthermore, we show that the alignment problem extended to non-overlapping moves, inversions and tandem duplications can be solved with the same time complexities. Finally, an example of an alignment with non-overlapping moves is provided. A preliminary version of this paper appeared in the Proceedings of COCOON 2007, LNCS, vol. 4598, pp. 151–164.     

Nonparametric Wavelet Regression Based on Biased Data

The estimation of the regression function in the biased nonparametric regression model is investigated. We propose and develop a new wavelet-based methodology for this problem. In particular, an adaptive hard thresholding wavelet estimator is constructed. Under mild assumptions on the model, we prove that it enjoys powerful mean integrated squared error properties over Besov balls.     

Efficient MCMC sampling in dynamic mixture models

We show how to improve the efficiency of Markov Chain Monte Carlo (MCMC) simulations in dynamic mixture models by block-sampling the discrete latent variables. Two algorithms are proposed: the first is a multi-move extension of the single-move Gibbs sampler devised by Gerlach, Carter and Kohn (in J. Am. Stat. Assoc. 95, 819–828, 2000); the second is an adaptive Metropolis-Hastings scheme that performs well even when the number of discrete states is large. Three empirical examples illustrate the gain in efficiency achieved. We also show that visual inspection of sample partial autocorrelations of the discrete latent variables helps anticipating whether blocking can be effective.     

La tournée des facteurs Normes gestionnaires, régulation collective et stratégies d’activité

The work of mailmen is mainly defined by the delivery routes to which they are assigned. Since this special organization of work grants them broad autonomy, the processes for delimiting, defining, and conducting routes must be analyzed by taking into account observations from three levels. The first one focuses on the French Post Office’s managerial standards, which, though increasingly determined by objectives for making a profit, have little impact on mail deliverers’ activities. The second centers around this occupational group’s own regulations, which stem from a hierarchy based on seniority and control over mail delivery and routes. The third level of observation takes into view the strategies for delivering mail that postmen adopt on their routes. These strategies reflect different relations to managerial objectives and to customers; and they reveal contrasting conceptions of the job of delivering mail. Emphasis is laid on the fact that the situations for working at lower levels in the service sector cannot be separated from the factors defining and organizing these situations.     

Assessing switchability for biosimilar products: modelling approaches applied to children's growth

The present paper describes two statistical modelling approaches that have been developed to demonstrate switchability from the original recombinant human growth hormone (rhGH) formulation (Genotropin^®) to a biosimilar product (Omnitrope^®) in children suffering from growth hormone deficiency. Demonstrating switchability between rhGH products is challenging because the process of growth varies with the age of the child and across children. The first modelling approach aims at predicting individual height measured at several time‐points after switching to the biosimilar. The second modelling approach provides an estimate of the deviation from the overall growth rate after switching to the biosimilar, which can be regarded as an estimate of switchability. The results after applying these approaches to data from a randomized clinical trial are presented. The accuracy and precision of the predictions made using the first approach and the small deviation from switchability estimated with the second approach provide sufficient evidence to conclude that switching from Genotropin^® to Omnitrope^® has a very small effect on growth, which is neither statistically significant nor clinically relevant. Copyright © 2015 John Wiley & Sons, Ltd.     

A bivariate first-order signed integer-valued autoregressive process

Bivariate integer-valued time series occur in many areas, such as finance, epidemiology, business etc. In this article, we present bivariate autoregressive integer-valued time-series models, based on the signed thinning operator. Compared to classical bivariate INAR models, the new processes have the advantage to allow for negative values for both the time series and the autocorrelation functions. Strict stationarity and ergodicity of the processes are established. The moments and the autocovariance functions are determined. The conditional least squares estimator of the model parameters is considered and the asymptotic properties of the obtained estimators are derived. An analysis of a real dataset from finance and a simulation study are carried out to assess the performance of the model.     

Marginal distribution of Markov-switching VAR processes

We make available simple and accurate closed-form approximations to the marginal distribution of Markov-switching vector auto-regressive (MS VAR) processes. The approximation is built upon the property of MS VAR processes of being Gaussian conditionally on any semi-infinite sequence of the latent state. Truncating the semi-infinite sequence and averaging over all possible sequences of that finite length yields a mixture of normals that converges to the unknown marginal distribution as the sequence length increases. Numerical experiments confirm the viability of the approach which extends to the closely related class of MS state space models. Several applications are discussed.     

Adaptive wavelet estimation of a function in an indirect regression model

We consider a nonparametric regression model where m noise-perturbed functions f ₁,…,f _m are randomly observed. For a fixed ν∈{1,…,m}, we want to estimate f _ν from the observations. To reach this goal, we develop an adaptive wavelet estimator based on a hard thresholding rule. Adopting the mean integrated squared error over Besov balls, we prove that it attains a sharp rate of convergence. Simulation results are reported to support our theoretical findings.     

Adaptive wavelet estimation of a function from an m-dependent process with possibly unbounded m

The estimation of a multivariate function from a stationary m-dependent process is investigated, with a special focus on the case where m is large or unbounded. We develop an adaptive estimator based on wavelet methods. Under flexible assumptions on the nonparametric model, we prove the good performances of our estimator by determining sharp rates of convergence under two kinds of errors: the pointwise mean squared error and the mean integrated squared error. We illustrate our theoretical result by considering the multivariate density estimation problem, the derivatives density estimation problem, the density estimation problem in a GARCH-type model and the multivariate regression function estimation problem. The performance of proposed estimator has been shown by a numerical study for a simulated and real data sets.