Solving the Bi-Objective Integer Programming: A DEA methodology

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 t...

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Bibliographic Details
Published in:2014 International Conference on Control, Decision and Information Technologies (CoDIT) pp. 060 - 064
Main Authors: Keshavarz, Esmaiel, Toloo, Mehdi
Format: Conference Proceeding
Language:English
Published: IEEE 01.11.2014
Subjects:
Algorithm design and analysis
Artificial intelligence
Bi-Objective Integer Linear Programming
Computational modeling
Data envelopment analysis
Decision making
Efficient solution
Non-dominated point
Supported efficient solution
Vectors
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Summary: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.
DOI:10.1109/CoDIT.2014.6996868