Multicomponent Efficiency Measurement and Shared Inputs in Data Envelopment Analysis: An Application to Sales and Service Performance in Bank Branches

In most applications ofDEA presented in the literature, the models presented are designedto obtain a single measure of efficiency. In many instances however,the decision making units involved may perform several differentand clearly identifiable functions, or can be separated intodifferent components. In such situations, inputs, in particularresources, are often shared among those functions. This sharingphenomenon will commonly present the technical difficulty ofhow to disaggregate an overall measure into component parts.In the present paper, we extend the usual DEA structure to onethat determines a best resource split to optimize the aggregateefficiency score. The particular application area investigatedis that involving the sales and service functions within thebranches of a bank. An illustrative application of the methodologyto a sample of branches from a major Canadian bank is given.     

On the generalized Poisson distribution

We use Euler's difference lemma to prove that, for θ > 0 and 0 ≤λ < 1, the function P _n defined on the non-negative integers by
P _n (θ, λ) = [θ(θ + n λ) ^{n −1}/ n !]e^{− n λ−θ}
defines a probability distribution, known as the Generalized Poisson Distribution.