TY - GEN
T1 - Solving the bi-objective integer programming
T2 - 2014 International Conference on Control, Decision and Information Technologies, CoDIT 2014
AU - Keshavarz, Esmaiel
AU - Toloo, Mehdi
N1 - Publisher Copyright:
© 2014 IEEE.
PY - 2014/12/23
Y1 - 2014/12/23
N2 - Finding and classifying all efficient solutions for a Bi-Objective Integer Linear Programming (BOILP) problem is one of the controversial issues in Multi-Criteria Decision Making problems. The main aim of this study is to utilize the well-known Data Envelopment Analysis (DEA) methodology to tackle this issue. Toward this end, we first state some propositions to clarify the relationships between the efficient solutions of a BOILP and efficient Decision Making Units (DMUs) in DEA and next design a new two-stage approach to find and classify a set of efficient solutions. Stage I formulates a two-phase Mixed Integer Linear Programming (MILP) model, based on the Free Disposal Hull (FDH) model in DEA, to gain a Minimal Complete Set of efficient solutions. Stage II uses a variable returns to scale DEA model to classify the obtained efficient solutions from Stage I as supported and non-supported. A BOILP model containing 6 integer variables and 4 constraints is solved as an example to illustrate the applicability of the proposed approach.
AB - Finding and classifying all efficient solutions for a Bi-Objective Integer Linear Programming (BOILP) problem is one of the controversial issues in Multi-Criteria Decision Making problems. The main aim of this study is to utilize the well-known Data Envelopment Analysis (DEA) methodology to tackle this issue. Toward this end, we first state some propositions to clarify the relationships between the efficient solutions of a BOILP and efficient Decision Making Units (DMUs) in DEA and next design a new two-stage approach to find and classify a set of efficient solutions. Stage I formulates a two-phase Mixed Integer Linear Programming (MILP) model, based on the Free Disposal Hull (FDH) model in DEA, to gain a Minimal Complete Set of efficient solutions. Stage II uses a variable returns to scale DEA model to classify the obtained efficient solutions from Stage I as supported and non-supported. A BOILP model containing 6 integer variables and 4 constraints is solved as an example to illustrate the applicability of the proposed approach.
KW - Bi-objective integer linear programming
KW - Data envelopment analysis
KW - Efficient solution
KW - Non-dominated point
KW - Supported efficient solution
UR - http://www.scopus.com/inward/record.url?scp=84921341929&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84921341929&partnerID=8YFLogxK
U2 - 10.1109/CoDIT.2014.6996868
DO - 10.1109/CoDIT.2014.6996868
M3 - Conference contribution
AN - SCOPUS:84921341929
T3 - Proceedings - 2014 International Conference on Control, Decision and Information Technologies, CoDIT 2014
SP - 60
EP - 64
BT - Proceedings - 2014 International Conference on Control, Decision and Information Technologies, CoDIT 2014
A2 - Kacem, Imed
A2 - Laroche, Pierre
A2 - Roka, Zsuzsanna
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 3 November 2014 through 5 November 2014
ER -