TY - JOUR
T1 - Efficiency status of a feasible solution in the Multi-Objective Integer Linear Programming problems
T2 - A DEA methodology
AU - Keshavarz, Esmail
AU - Toloo, Mehdi
N1 - Publisher Copyright:
© 2014 Elsevier Inc.
PY - 2015/6/15
Y1 - 2015/6/15
N2 - Efficient solutions in Multi-Objective Integer Linear Programming (MOILP) problems are categorized into two distinct types, supported and non-supported. Many researchers try to gain some conditions to determine whether a feasible solution is efficient, nevertheless there is no attempt to identify the efficiency status of a given efficient solution, i.e. supported and non-supported. In this paper, we first verify the relationships between Data Envelopment Analysis (DEA) and MOILP and then design two distinct practical procedures: the first one specifies whether or not an arbitrary feasible solution is efficient, meanwhile the second one, as the main aim of this study, determines the efficiency status of an efficient solution. Finally, as a contribution of the suggested approach, we illustrate the drawback of Chen and Lu's methodology (Chen and Lu, 2007) which is developed for solving an extended assignment problem.
AB - Efficient solutions in Multi-Objective Integer Linear Programming (MOILP) problems are categorized into two distinct types, supported and non-supported. Many researchers try to gain some conditions to determine whether a feasible solution is efficient, nevertheless there is no attempt to identify the efficiency status of a given efficient solution, i.e. supported and non-supported. In this paper, we first verify the relationships between Data Envelopment Analysis (DEA) and MOILP and then design two distinct practical procedures: the first one specifies whether or not an arbitrary feasible solution is efficient, meanwhile the second one, as the main aim of this study, determines the efficiency status of an efficient solution. Finally, as a contribution of the suggested approach, we illustrate the drawback of Chen and Lu's methodology (Chen and Lu, 2007) which is developed for solving an extended assignment problem.
KW - Data Envelopment Analysis (DEA)
KW - Efficient solution
KW - Multi-Criteria Optimization (MCO) problem
KW - Multi-Objective Integer Linear Programming (MOILP)
KW - Supported/non-supported efficient solution
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U2 - 10.1016/j.apm.2014.11.032
DO - 10.1016/j.apm.2014.11.032
M3 - Article
AN - SCOPUS:84929289655
SN - 0307-904X
VL - 39
SP - 3236
EP - 3247
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
IS - 12
ER -