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An integer‐valued data envelopment analysis model with bounded outputs
Author(s) -
Kazemi Matin Reza,
Emrouznejad Ali
Publication year - 2011
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/j.1475-3995.2011.00828.x
Subject(s) - data envelopment analysis , axiom , bounded function , integer programming , mathematical optimization , integer (computer science) , returns to scale , mathematics , variable (mathematics) , linear programming , set (abstract data type) , computer science , production (economics) , economics , geometry , macroeconomics , mathematical analysis , programming language
Integer‐valued data envelopment analysis ( DEA ) with alternative returns to scale technology has been introduced and developed recently by Kuosmanen and Kazemi Matin. The proportionality assumption of their introduced “natural augmentability” axiom in constant and nondecreasing returns to scale technologies makes it possible to achieve feasible decision‐making units ( DMU s) of arbitrary large size. In many real world applications it is not possible to achieve such production plans since some of the input and output variables are bounded above. In this paper, we extend the axiomatic foundation of integer‐valued DEA models for including bounded output variables. Some model variants are achieved by introducing a new axiom of “boundedness” over the selected output variables. A mixed integer linear programming ( MILP ) formulation is also introduced for computing efficiency scores in the associated production set.