Geodesic
Finding Efficient Solutions in the Interval Multi-Objective Linear Programming Models
Yugoslav journal of operations research, Tome 31 (2021) no. 1, p. 95 .

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The aim of our paper is to obtain efficient solutions to the interval multi-objective linear programming (IMOLP) models. In this paper, we propose a new method to determine the efficient solutions in the IMOLP models by using the expected value and variance operators (EVV operators). First, we define concepts of the expected value, variance, and uncertainty distributions, and present some properties of the EVV operators. Then, we introduce the IMOLP model under these operators. An IMOLP model consist of separate ILPs, but using the EVV operators and the uncertainty distributions, it can be converted into the interval linear programming (ILP) models under the EVV operators (EVV-ILP model). We show that optimal solutions of the EEV-ILP model are the efficient solutions of IMOLP models with uncertainty variables. The proposed method, which is called EVV, is not hard to solve. Finally, Monte Carlo simulation is used to show its performance assessment.
Classification : 90B50, 90C29
Keywords: Uncertainty, Interval Multi-Objective Linear Programming, Efficient Solution, Expected Value, Variance, Monte Carlo Simulation 
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     author = {Aida Batamiz and Mehdi Allahdadi},
     title = {Finding {Efficient} {Solutions} in the {Interval} {Multi-Objective} {Linear} {Programming} {Models}},
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Aida Batamiz; Mehdi Allahdadi. Finding Efficient Solutions in the Interval Multi-Objective Linear Programming Models. Yugoslav journal of operations research, Tome 31 (2021) no. 1, p. 95 . http://geodesic.mathdoc.fr/item/YJOR_2021_31_1_a5/