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Characteristics and structures of weak efficient surfaces of production possibility sets. (English) Zbl 1253.90124
Summary: This paper studies the characteristics and structure of the weak surface of the production possibility set. We apply techniques and methods of transferring a polyhedral cone from its intersection form to its sum form, identify an intersection representation of the production possibility set. We give the structure theorem of weak surface of the production possibility set, which includes three complementary slackness conditions. We define the input weak efficiency and output weak efficiency for different DEA models according to the representation of the intersection form. It investigates the characteristics of the weak surfaces, and proves the structure theorems of input weak DEA efficiency and output weak DEA efficiency. The structure theorems establish weighted combination of inputs and outputs that are weak DEA efficient. Numerical examples are provided for illustration.

MSC:
90B50 Management decision making, including multiple objectives
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
90C29 Multi-objective and goal programming
Software:
Algorithm 457
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