Staffing a Multiskilled Workforce with Varying Levels of Productivity: An Analysis of Cross-training Policies*

Service operations that utilize cross-trained employees face complex workforce staffing decisions that have important implications for both cost and productivity. These decisions are further complicated when cross-trained employees have different productivity levels in multiple work activity categories. A method for policy analysis in such environments can be beneficial in determining low-cost staffing plans with appropriate cross-training configurations. In this paper, we present an integer linear programming model for evaluating cross-training configurations at the policy level. The objective of the model is to minimize workforce staffing costs subject to the satisfaction of minimum labor requirements across a planning horizon of a single work shift. The model was used to evaluate eight cross-training structures (consisting of 36 unique cross-training configurations) across 512 labor requirement patterns. These structures, as well as the labor requirement patterns, were established based on data collected from maintenance operations at a large paper mill in the United States. The results indicate that asymmetric cross-training structures that permit chaining of employee skill classes across work activity categories are particularly useful.     

How planning and capital budgeting improve SME performance

This paper focuses on the use of strategic planning among small and medium sized enterprises (SMEs) in the UK manufacturing sector. It analyses the relationship between the intensity of strategic planning, business objectives, perceived performance, changes in the business environment and the use of capital budgeting techniques. Capital budgeting is of particular interest as an area of investigation, and is one which has seldom featured in previous studies of strategic planning behaviour. These issues were investigated via a survey of UK manufacturing SMEs carried out in the winter of 1996/97.

The key results suggest that SMEs incorporate a range of objectives into their strategic planning process, with profit improvement perceived to be the most important objective, followed by sales growth. SMEs engaged in detailed strategic planning are more likely to use formal capital budgeting techniques, including the net present value method, which is consistent with maximising the companys' value. Perceived profitability and success in achieving organisational objectives were positively associated with planning detail, suggesting that strategic planning is a key component improving performance. Planning detail was also associated with a significantly higher level of perceived change in the business environment.     

Simplified Estimating Functions for Diffusion Models with a High-dimensional Parameter

We consider estimating functions for discretely observed diffusion processes of the following type: for one part of the parameter of interest we propose to use a simple and explicit estimating function of the type studied by Kessler (2000); for the remaining part of the parameter we use a martingale estimating function. Such an approach is particularly useful in practical applications when the parameter is high-dimensional. It is also often necessary to supplement a simple estimating function by another type of estimating function because only the part of the parameter on which the invariant measure depends can be estimated by a simple estimating function. Under regularity conditions the resulting estimators are consistent and asymptotically normal. Several examples are considered in order to demonstrate the idea of the estimating procedure. The method is applied to two data sets comprising wind velocities and stock prices. In one example we also propose a general method for constructing diffusion models with a prescribed marginal distribution which have a flexible dependence structure.     

Non-parametric Estimation of the Residual Distribution

Consider a heteroscedastic regression model Y = m ( X ) +σ( X )ε, where the functions m and σ are smooth, and ε is independent of X . An estimator of the distribution of ε based on non-parametric regression residuals is proposed and its weak convergence is obtained. Applications to prediction intervals and goodness-of-fit tests are discussed.     

Estimation of relaxation time distributions in magnetic resonance imaging

Magnetic resonance imaging techniques can be used to measure some biophysical properties of tissue. In this context, the T₂ relaxation time is an important parameter for soft‐tissue contrast. The authors develop a new technique to estimate the integral of the distribution of T₂ relaxation time without imposing any constraint other than the monotonicity of the underlying cumulative relaxation time distribution. They explore the properties of the estimation and its applications for the analysis of breast tissue data. As they show, an extension of linear discriminant analysis is found to distinguish well between two classes of breast tissue.     

z Test for the significance of the mean of a stable probability distribution with 1<α≤2

The analysis of data using a stable probability distribution with tail parameter α<2 (sometimes called a Pareto–Levy distribution) seems to have been avoided in the past in part because of the lack of a significance test for the mean, even though it appears to be the correct distribution to use for describing returns in the financial markets. A z test for the significance of the mean of a stable distribution with tail parameter 1<α≤2 is defined. Tables are calculated and displayed for the 5% and 1% significance levels for a range of tail and skew parameters α and β. Through the use of maximum likelihood estimates, the test becomes a practical tool even when α and β are not that accurately determined. As an example, the z test is applied to the daily closing prices for the Dow Jones Industrial average from 2 January 1940 to 19 March 2010.     

Consistency of maximum likelihood estimators in a large class of deconvolution models

We consider the maximum likelihood estimator $\hat{F}_n$ of a distribution function in a class of deconvolution models where the known density of the noise variable is of bounded variation. This class of noise densities contains in particular bounded, decreasing densities. The estimator $\hat{F}_n$ is defined, characterized in terms of Fenchel optimality conditions and computed. Under appropriate conditions, various consistency results for $\hat{F}_n$ are derived, including uniform strong consistency. The Canadian Journal of Statistics 41: 98–110; 2013 © 2012 Statistical Society of Canada     

A course in constructing effective displays of data for pharmaceutical research personnel

Interpreting data and communicating effectively through graphs and tables are requisite skills for statisticians and non‐statisticians in the pharmaceutical industry. However, the quality of visual displays of data in the medical and pharmaceutical literature and at scientific conferences is severely lacking. We describe an interactive, workshop‐driven, 2‐day short course that we constructed for pharmaceutical research personnel to learn these skills. The examples in the course and the workshop datasets source from our professional experiences, the scientific literature, and the mass media. During the course, the participants are exposed to and gain hands‐on experience with the principles of visual and graphical perception, design, and construction of both graphic and tabular displays of quantitative and qualitative information. After completing the course, with a critical eye, the participants are able to construct, revise, critique, and interpret graphic and tabular displays according to an extensive set of guidelines. Copyright © 2013 John Wiley & Sons, Ltd.     

Central Limit Theorem approximations for the number of runs in Markov-dependent binary sequences

We consider Markov-dependent binary sequences and study various types of success runs (overlapping, non-overlapping, exact, etc.) by examining additive functionals based on state visits and transitions in an appropriate Markov chain. We establish a multivariate Central Limit Theorem for the number of these types of runs and obtain its covariance matrix by means of the recurrent potential matrix of the Markov chain. Explicit expressions for the covariance matrix are given in the Bernoulli and a simple Markov-dependent case by expressing the recurrent potential matrix in terms of the stationary distribution and the mean transition times in the chain. We also obtain a multivariate Central Limit Theorem for the joint number of non-overlapping runs of various sizes and give its covariance matrix in explicit form for Markov dependent trials.     

Understanding increments in model performance metrics

The area under the receiver operating characteristic curve (AUC) is the most commonly reported measure of discrimination for prediction models with binary outcomes. However, recently it has been criticized for its inability to increase when important risk factors are added to a baseline model with good discrimination. This has led to the claim that the reliance on the AUC as a measure of discrimination may miss important improvements in clinical performance of risk prediction rules derived from a baseline model. In this paper we investigate this claim by relating the AUC to measures of clinical performance based on sensitivity and specificity under the assumption of multivariate normality. The behavior of the AUC is contrasted with that of discrimination slope. We show that unless rules with very good specificity are desired, the change in the AUC does an adequate job as a predictor of the change in measures of clinical performance. However, stronger or more numerous predictors are needed to achieve the same increment in the AUC for baseline models with good versus poor discrimination. When excellent specificity is desired, our results suggest that the discrimination slope might be a better measure of model improvement than AUC. The theoretical results are illustrated using a Framingham Heart Study example of a model for predicting the 10-year incidence of atrial fibrillation.