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    Assessing the efficiency of hospitals operating under a unique owner: a DEA application in the presence of missing data
    (Inderscience Publishers, 2010-05) Aksezer, Sezgin Çağlar; Benneyan, James C.
    Originally developed in the late 1970s to assess the efficiency of comparable operating units, Data Envelopment Analysis (DEA) has since been used in a variety of contexts. Although incomplete data sets are often encountered in practice, the best approach in such situations is unclear in general. This paper explores methods such as multiple imputation, bootstrapping and smart dummy variable replacement, borrowed from similar missing data problems in regression analysis. Each missing data method is tested on a library of DEA problems that are gathered from the DEA literature. These problems are selected in such a way as to represent a thorough cross-section of problem sizes (small, medium, large) and types (type of DEA model, number of decision-making units, number of inputs, number of outputs, etc.). The results are illustrated by comparing the solutions of complete data sets against the simulated versions of the same data sets with missing data. The sensitivity of each method on the efficiency scores and ranking of the decision-making units is presented.
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    Multiresponse optimisation of powder metals via probabilistic loss functions
    (Inderscience Enterprises Ltd, 2013) Aksezer, Sezgin Çağlar; Benneyan, James C.
    Quadratic loss functions have been used extensively within the context of quality engineering and experimental design for process and product optimisation and robust design. In general, this approach determines optimal parameter settings based on minimising the sum of individual or mean loss of the associated response(s) of interest in a defined response surface. While the method is neat and handy, it totally neglects the effect of deviations on the desirable value of loss function. This paper utilises variance and probability distribution of loss functions for developing an in depth optimisation scheme that balances mean and variance of loss in a Pareto optimal manner. Since losses are usually defined in financial terms, this model then further improved to handle the user determined risk levels so that financial losses are being restricted within a certain region of interest. Application of the model is illustrated on a multiresponse optimisation problem from powder metallurgy industry.
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    Probability distributions and variances of quadratic loss functions
    (2006) Benneyan, James C.; Aksezer, Sezgin Çağlar
    The use of quadratic loss functions has been advocated in quality engineering and experimental design for process optimization and robust design. We derive theoretical density functions and variances for nominal-the-best, smaller-the-better, and larger-the-better quadratic loss functions in general and when the response variable has a specified distribution. While considerable attention has been given to individual and mean loss, in some applications it is of interest also to know something about the loss distribution and variance. Results frequently exhibit high variance and skew and unique density functions in cases for which it is not advisable to base decisions on expected loss alone.