TY - JOUR
T1 - Finding efficient assignments
T2 - An innovative DEA approach
AU - Keshavarz, Esmaiel
AU - Toloo, Mehdi
N1 - Funding Information:
The research was supported by the Czech Science Foundation (GACR project 14-31593S ) and through European Social Fund within the project CZ.1.07/2.3.00/20.0296 .
Publisher Copyright:
©2014 Elsevier Ltd. All rights reserved.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - Finding and classifying all efficient assignments for a Multi-Criteria Assignment Problem (MCAP) is one of the controversial issues in Multi-Criteria Decision Making (MCDM) problems. The main aim of this study is to utilize Data Envelopment Analysis (DEA) methodology to tackle this issue. Toward this end, we first state and prove some theorems to clarify the relationships between DEA and MCAP and then design a new two-phase approach to find and classify a set of efficient assignments. In Phase I, we formulate a new Mixed Integer Linear Programming (MILP) model, based on the Additive Free Disposal Hull (FDH) model, to gain an efficient assignment and then extend it to determine a Minimal Complete Set (MCS) of efficient assignments. In Phase II, we use the BCC model to classify all efficient solutions obtained from Phase I as supported and non-supported. A 4 × 4 assignment problem, containing two cost-type and single profit-type of objective functions, is solved using the presented approach.
AB - Finding and classifying all efficient assignments for a Multi-Criteria Assignment Problem (MCAP) is one of the controversial issues in Multi-Criteria Decision Making (MCDM) problems. The main aim of this study is to utilize Data Envelopment Analysis (DEA) methodology to tackle this issue. Toward this end, we first state and prove some theorems to clarify the relationships between DEA and MCAP and then design a new two-phase approach to find and classify a set of efficient assignments. In Phase I, we formulate a new Mixed Integer Linear Programming (MILP) model, based on the Additive Free Disposal Hull (FDH) model, to gain an efficient assignment and then extend it to determine a Minimal Complete Set (MCS) of efficient assignments. In Phase II, we use the BCC model to classify all efficient solutions obtained from Phase I as supported and non-supported. A 4 × 4 assignment problem, containing two cost-type and single profit-type of objective functions, is solved using the presented approach.
KW - Additive FDH model
KW - Data Envelopment Analysis (DEA)
KW - Multi-Criteria Assignment Problem (MCAP)
KW - Multi-Criteria Decision Making (MCDM)
KW - Non-dominated point
KW - Supported efficient assignment
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U2 - 10.1016/j.measurement.2014.09.014
DO - 10.1016/j.measurement.2014.09.014
M3 - Article
AN - SCOPUS:84907842518
SN - 0263-2241
VL - 58
SP - 448
EP - 458
JO - Measurement: Journal of the International Measurement Confederation
JF - Measurement: Journal of the International Measurement Confederation
ER -