Multi-objective optimization to the transportation problem considering non-linear fuzzy membership functions

Md. Musa Miah; Ali AlArjani; Abdur Rashid; Aminur Rahman Khan; Md. Sharif Uddin; El-Awady Attia; Md. Musa Miah; Ali AlArjani; Abdur Rashid; Aminur Rahman Khan; Md. Sharif Uddin; El-Awady Attia

doi:10.3934/math.2023527

AIMS Mathematics

2023, Volume 8, Issue 5: 10397-10419. doi: 10.3934/math.2023527

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Multi-objective optimization to the transportation problem considering non-linear fuzzy membership functions

1.
Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh
2.
Department of Industrial Engineering, College of Engineering, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
3.
Department of Mathematics, Jahangirnagar University, Savar, Dhaka-1342, Bangladesh
4.
Mechanical Engineering Department, faculty of engineering (Shoubra), Benha University, Cairo, Egypt

Received: 15 September 2022 Revised: 08 February 2023 Accepted: 09 February 2023 Published: 01 March 2023
MSC : 03E72, 49Q22

Considering the uncertainty of transporting goods from numerous origins to diverse destinations is a critical task for the decision-maker (DM). The ultimate goal of the DM is to make the right decisions that optimize the profit or loss of the organization under the vagueness of the uncontrollable effects. In this paper, mathematical models are proposed using fuzzy non-linear membership functions for the transportation problem considering the parameters' uncertainty that can help the DM to optimize the multi-objective transportation problems (MOTP) and to achieve the desired goals by choosing a confidence level of the uncertain parameters. Based on DM's selection of the confidence level, a compromise solution of the uncertain multi-objective transportation (UMOTP) is obtained along with the satisfaction level in percent for the DM. Two non-linear fuzzy membership functions are considered: the exponential and the hyperbolic functions. Using both membership functions, the sensitivity analysis was implemented by considering different confidence levels. According to the experimental results, the hyperbolic membership function gives 100% DM's satisfaction in many instances. Moreover, it shows stability against the exponential and linear functions.
- transportation problem,
- fuzzy multi-objective optimization,
- linear programming problem,
- non-linear fuzzy-membership functions,
- compromise solution
Citation: Md. Musa Miah, Ali AlArjani, Abdur Rashid, Aminur Rahman Khan, Md. Sharif Uddin, El-Awady Attia. Multi-objective optimization to the transportation problem considering non-linear fuzzy membership functions[J]. AIMS Mathematics, 2023, 8(5): 10397-10419. doi: 10.3934/math.2023527

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Abstract

Considering the uncertainty of transporting goods from numerous origins to diverse destinations is a critical task for the decision-maker (DM). The ultimate goal of the DM is to make the right decisions that optimize the profit or loss of the organization under the vagueness of the uncontrollable effects. In this paper, mathematical models are proposed using fuzzy non-linear membership functions for the transportation problem considering the parameters' uncertainty that can help the DM to optimize the multi-objective transportation problems (MOTP) and to achieve the desired goals by choosing a confidence level of the uncertain parameters. Based on DM's selection of the confidence level, a compromise solution of the uncertain multi-objective transportation (UMOTP) is obtained along with the satisfaction level in percent for the DM. Two non-linear fuzzy membership functions are considered: the exponential and the hyperbolic functions. Using both membership functions, the sensitivity analysis was implemented by considering different confidence levels. According to the experimental results, the hyperbolic membership function gives 100% DM's satisfaction in many instances. Moreover, it shows stability against the exponential and linear functions.

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