Abstract
Most of the real-life decision-making problems have more than one conflicting and incommensurable objective functions. In this paper, we present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution. Randomness of the discrete intervals are considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are analyzed in two-stage stochastic programming. To solve the stated problem, first we remove the randomness of the problem and formulate an equivalent deterministic linear programming model with multiobjective interval coefficients. Then the deterministic multiobjective model is solved using weighting method, where we apply the solution procedure of interval linear programming technique. We obtain the upper and lower bound of the objective function as the best and the worst value, respectively. It highlights the possible risk involved in the decision-making tool. A numerical example is presented to demonstrate the proposed solution procedure.
Highlights
We present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution
The input parameters of the mathematical programming model are not exactly known because relevant data are inexistent or scarce, difficult to obtain or estimate, the system is subject to changes, and so forth, that is, input parameters are uncertain in nature
A multiobjective two-stage stochastic programming problem involving some interval discrete random variable has been presented in this paper
Summary
The input parameters of the mathematical programming model are not exactly known because relevant data are inexistent or scarce, difficult to obtain or estimate, the system is subject to changes, and so forth, that is, input parameters are uncertain in nature This type of situations are mainly occurs in real-life decision-making problems. These uncertainties in the input parameters of the model can characterized by random variables with known probability distribution. TSP can barely deal with independent uncertainties of the left-hand side coefficients in each constraint or the objective function It requires probabilistic specifications for uncertain parameters while in many pragmatic problems, the quality of information that can be obtained is usually not satisfactory enough to be presented as probability distributions. Interval random variables plays an important role in optimization theory
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