A novel approach for solving decision-making problems with stochastic linear-fractional models

Authors

DOI:

https://doi.org/10.15587/1729-4061.2021.241916

Keywords:

Stochastic Models, Fractional Programming Problems, Goal Programming, Joint Probability Distribution

Abstract

Stochastic chance-constrained optimization has a wide range of real-world applications. In some real-world applications, the decision-maker has to formulate the problem as a fractional model where some or all of the coefficients are random variables with joint probability distribution. Therefore, these types of problems can deal with bi-objective problems and reflect system efficiency. In this paper, we present a novel approach to formulate and solve stochastic chance-constrained linear fractional programming models. This approach is an extension of the deterministic fractional model. The proposed approach, for solving these types of stochastic decision-making problems with the fractional objective function, is constructed using the following two-step procedure. In the first stage, we transform the stochastic linear fractional model into two stochastic linear models using the goal programming approach, where the first goal represents the numerator and the second goal represents the denominator for the stochastic fractional model. The resulting stochastic goal programming problem is formulated. The second stage implies solving stochastic goal programming problem, by replacing the stochastic parameters of the model with their expectations. The resulting deterministic goal programming problem is built and solved using Win QSB solver. Then, using the optimal value for the first and second goals, the optimal solution for the fractional model is obtained. An example is presented to illustrate our approach, where we assume the stochastic parameters have a uniform distribution. Hence, the proposed approach for solving the stochastic linear fractional model is efficient and easy to implement. The advantage of the proposed approach is the ability to use it for formulating and solving any decision-making problems with the stochastic linear fractional model based on transforming the stochastic linear model to a deterministic linear model, by replacing the stochastic parameters with their corresponding expectations and transforming the deterministic linear fractional model to a deterministic linear model using the goal programming approach

Author Biographies

Watheq Laith, University of Sumer

Industrial Engineering, Professor

Department of Businesses Administration

Rasheed Al-Salih, Missouri University of Science and Technology; University of Sumer

PhD, Professor

Department of Mathematics and Statistics

Department of Statistics

Ali Habeeb, University of Sumer

Applied Statistics, Professor

Department of Statistics

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Published

2021-10-29

How to Cite

Laith, W., Al-Salih, R., & Habeeb, A. (2021). A novel approach for solving decision-making problems with stochastic linear-fractional models. Eastern-European Journal of Enterprise Technologies, 5(4 (113), 73–78. https://doi.org/10.15587/1729-4061.2021.241916

Issue

Vol. 5 No. 4 (113) (2021): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2021 Watheq Laith, Rasheed Al-Salih, Ali Habeeb

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