Several Algorithms to Determine Multipliers for Use in Cone-Ratio Envelopment Approaches to Efficiency Evaluations in DEA

In this paper, we will discuss subjects related to virtual multipliers in the cone-ratio model in DEA. Usually, there exists ambiguity in the virtual multipliers in the polyhedral cone-ratio method when some exemplary efficient DMUs’ multipliers are employed as the admissible directions of the cone. We will propose three practical methods for resolving this ambiguity, along with an example. Then, we will discuss possible applications of vertex enumeration software, based on the Double Description Method.

[1]  D. B. Sun,et al.  Evaluation of managerial performance in large commercial banks by data envelopment analysis , 1988 .

[2]  P. S. Dharmapala,et al.  DEA ARs and CRs applied to worldwide major oil companies , 1994 .

[3]  S. Vajda,et al.  Contribution to the Theory of Games , 1951 .

[4]  Kaoru Tone,et al.  AN e-FREE DEA AND A NEW· MEASURE OF EFFICIENCY , 1993 .

[5]  Roy E. Marsten,et al.  The interior-point method for linear programming , 1992, IEEE Software.

[6]  A. Charnes,et al.  A structure for classifying and characterizing efficiency and inefficiency in Data Envelopment Analysis , 1991 .

[7]  Abraham Charnes,et al.  Cone ratio data envelopment analysis and multi-objective programming , 1989 .

[8]  H. Raiffa,et al.  3. The Double Description Method , 1953 .

[9]  M. Kojima,et al.  A primal-dual interior point algorithm for linear programming , 1988 .

[10]  B. Golany,et al.  Alternate methods of treating factor weights in DEA , 1993 .

[11]  Clyde L. Monma,et al.  An Implementation of a Primal-Dual Interior Point Method for Linear Programming , 1989, INFORMS J. Comput..

[12]  Barton A. Smith,et al.  Comparative Site Evaluations for Locating a High-Energy Physics Lab in Texas , 1986 .

[13]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[14]  Clyde L. Monma,et al.  Further Development of a Primal-Dual Interior Point Method , 1990, INFORMS J. Comput..

[15]  Russell G. Thompson,et al.  The role of multiplier bounds in efficiency analysis with application to Kansas farming , 1990 .

[16]  Hiroshi Yamashita A globally convergent primal-dual interior point method for constrained optimization , 1998 .

[17]  A. Charnes,et al.  Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks , 1990 .