Title: Fuzzy goal programming approach for solving stochastic transportation problem with additional budgetary constraints

Authors: A. Akilbasha; Hamiden Abd El-Wahed Khalifa; Z.A.M.S. Juman; Ibrahim Mekawy

Addresses: School of Mathematics and Statistics, Dr. Vishwanath Karad MIT World Peace University, Pune-411 038, Maharashtra, India ' Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia; Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt ' Department of Mathematics, FOS, University of Peradeniya, Peradeniya 20400, Sri Lanka ' Department of Mathematics, College of Science and Arts, Qassim University, ArRass, 51951, Saudi Arabia

Abstract: This paper attempts to study a transportation problem with costs represented by octagonal fuzzy numbers (Oct-FN) and demands randomly distributed. Here, we use the normal distribution. A fuzzy goal programming (FGP) approach is applied for obtaining the optimal compromise solution. The advantage of FGP for the decision maker is easy to explain and implement in real-life transportation. The stability set of the first kind corresponding to the optimal solution is determined. A numerical example is given to highlight the solution approach. Furthermore, the proposed method is extended to fuzzy transportation problems (FTP). This will help the forthcoming researchers to enlarge this problem into the other problems with parameters like fuzzy interval integers, rough interval integers, and so on.

Keywords: stochastic transportation problem; octagonal fuzzy numbers; Oct-FN; normal distribution; ranking method; fuzzy goal programming; FGP; optimisation problems; stochastic process; decision making.

DOI: 10.1504/IJSTL.2024.137586

International Journal of Shipping and Transport Logistics, 2024 Vol.18 No.1, pp.30 - 45

Received: 14 Apr 2022
Accepted: 18 Jul 2022
Published online: 27 Mar 2024 *

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