Context-dependent dea with an application to tokyo public libraries

TLDR: A context-dependent DEA is presented which measures the relative attractiveness of libraries on a specific performance level against libraries exhibiting poorer performance and provides finer DEA results with respect to the performance of all DMUs.

Abstract: Data envelopment analysis (DEA) identifies an empirical efficient frontier of a set of peer decision making units (DMUs) with multiple inputs and outputs. The efficient frontier is characterized by the DMUs with an unity efficiency score. The performance of inefficient DMUs is characterized with respect to the identified efficient frontier. If the performance of inefficient DMUs deteriorates or improves (up to the frontier), the efficient DMUs still have an unity efficiency score. However, the performance of DMUs may be influenced by the context — e.g. a product may appear attractive against a background of less attractive alternatives and unattractive when compared to more attractive alternatives. With an application to Tokyo public libraries, the current paper presents and demonstrates a context-dependent DEA which measures the relative attractiveness of libraries on a specific performance level against libraries exhibiting poorer performance. The set of libraries are grouped into different levels of efficient frontiers. Each efficient frontier (on a specific performance level) is then used as evaluation context for the relative attractiveness. The performance of the efficient libraries changes as the inefficient libraries change their performance. The context-dependent DEA can also be used to differentiate the performance of efficient DMUs. The context-dependent DEA provides finer DEA results with respect to the performance of all DMUs.