The geometric programming problem is an important optimization technique that is often used to solve different nonlinear optimization problems and engineering problems. The geometric programming models that are commonly used are generally based on deterministic and accurate parameters. However, it is observed that in real-world geometric programming problems, the parameters are frequently inaccurate and ambiguous. In this paper, we consider chance-constrained geometric programming problems with uncertain coefficients and with geometric programming techniques in the uncertain-based framework. We show that the associated chance-constrained uncertain geometric programming problem can be converted into a crisp geometric programming problem by using triangular and trapezoidal uncertainty distributions for the uncertain variables. The main aim of this paper is to provide the solution procedures for geometric programming problems under triangular and trapezoidal uncertainty distributions. To show how well the procedures and algorithms work, two numerical examples and an application in the inventory model are given.
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DOI : 10.1051/ro/2022132
Keywords: Uncertainty theory, uncertain variable, chance-constrained geometric programming, triangular uncertainty distribution, trapezoidal uncertainty distribution
@article{RO_2022__56_4_2833_0,
author = {Mondal, Tapas and Ojha, Akshay Kumar and Pani, Sabyasachi},
title = {Solving geometric programming problems with triangular and trapezoidal uncertainty distributions},
journal = {RAIRO. Operations Research},
pages = {2833--2851},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {4},
doi = {10.1051/ro/2022132},
mrnumber = {4471379},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2022132/}
}
TY - JOUR AU - Mondal, Tapas AU - Ojha, Akshay Kumar AU - Pani, Sabyasachi TI - Solving geometric programming problems with triangular and trapezoidal uncertainty distributions JO - RAIRO. Operations Research PY - 2022 SP - 2833 EP - 2851 VL - 56 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2022132/ DO - 10.1051/ro/2022132 LA - en ID - RO_2022__56_4_2833_0 ER -
%0 Journal Article %A Mondal, Tapas %A Ojha, Akshay Kumar %A Pani, Sabyasachi %T Solving geometric programming problems with triangular and trapezoidal uncertainty distributions %J RAIRO. Operations Research %D 2022 %P 2833-2851 %V 56 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2022132/ %R 10.1051/ro/2022132 %G en %F RO_2022__56_4_2833_0
Mondal, Tapas; Ojha, Akshay Kumar; Pani, Sabyasachi. Solving geometric programming problems with triangular and trapezoidal uncertainty distributions. RAIRO. Operations Research, Tome 56 (2022) no. 4, pp. 2833-2851. doi: 10.1051/ro/2022132
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