Finding efficient solutions in the interval multi-objective linear programming models

Abstract

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 the performance assessment.

Finding All Efficient Solutions of an Interval Multiple Objective Linear Programming Problem

“…Efficient extreme points of an IMOLP problem are dealt with in Inuiguchi and Kume [17]. If the coefficients of an IMOLP problem are satisfied probability distributions, then stochastic programming methods can be used to study this problem, see, for example, Batamiz and Allahdadi [4]. Theoretically, an IMOLP problem can be stated based on fuzzy numbers and can be solved by fuzzy programming methods.…”

“…ii ab is the i-th row of a matrix ( ) , Ab defined in(4). A formula to compute the efficient set of IMOLP problem (1)-(3) is shown in the following property:…”

Finding All Efficient Solutions of an Interval Multiple Objective Linear Programming Problem

“…the i-th row of a matrix ( ) , A b defined in(4).A formula to compute the efficient set of IMOLP problem (1)-(3) is shown in the following property:…”