Inefficiency identification for closed series production systems

Decomposing the system efficiency of a network production system into the component division efficiencies helps identify the divisions that affect the performance of the system the most, and making improvements in these increases the system efficiency more effectively. This paper proposes a slacks-based measure (SBM) model to decompose the system efficiency of a closed series system into the product of the division efficiencies divided by the linkage efficiencies, which are expressed as the product of the efficiencies of the intermediate product as the output of the preceding division and the input of the succeeding division. The model has two forms, non-cooperative and cooperative, where the latter always has perfect linkage efficiency. An example of twenty-four Taiwanese non-life insurance companies shows that the system efficiency can indeed be decomposed into division and linkage efficiencies. Since the non-cooperative model sets higher standards than the cooperative model to measure efficiencies, the resulting efficiencies are lower, which alerts the decision maker about the relatively worse performance of the divisions.