• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1195-1210
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• 2024

This research aims to determine an optimal (best) solution for transporting the logistics at a minimum cost from various sources to various destinations. We proposed a new algorithm for the initial basic feasible solution (IBFS). Developing a new IBFS is the first step towards finding the optimal solution. A new approach for the initial basic feasible solution that reduces iterations and produces the best answer in the initial process of the transportation issue. Different IBFS approaches have been generated in the literature review. Some statistical fundamentals, such as normal distribution and the root mean square technique, are employed to find new IBFS. A TP is transformed into a normal distribution, and penalties are determined using the root mean square method. Excel Solver is used to calculate normal distribution values. The second step involves using a stepping-stone approach to compute the optimum solution. The results of our study were calculated using numerical examples and contrasted with a few other methodologies, such as Vogel's approximation, the Continuous Allocation Method (CAM), the Supply Demand Repair Method (SDRM), and the Karagul-Sahin Approximation Method (KSAM). The conclusion of our proposed method gives more accurate results than the existing approach.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.647-661
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• 2024

This study aims to determine the optimal solution to transportation problems. We proposed a novel approach for tackling the initial basic feasible solution. This is a critical step toward achieving an optimal or near-optimal solution. The transportation issue is an issue of distributing goods from several sources to several destinations. The literature demonstrates many ways to improve IBFS. In this work, to solve the IBFS, we suggested a new method based on the statistical formula called cumulative distribution function (CDF) in exponential distribution, and inverse contra-harmonic mean (ICHM). The spreadsheet converts transportation cost values into exponential cost cell values. The stepping-stone method is used to identify an optimum solution. The results are compared with other existing methodologies, the suggested method incorporates balanced, and unbalanced, maximizing the profits, random values, and case studies which produce more effective outcomes.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.311-320
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• 2023

In this article, a new penalty and different ranking algorithms are used to find the lowest transportation costs for the fuzzy transportation problem. This approach utilises different ranking techniques when dealing with triangular fuzzy numbers. Also, we find that the fuzzy transportation solution of the proposed method is the same as the Fuzzy Modified Distribution Method (FMODI) solution. Finally, examples are used to show how a problem is solved.

• Journal of applied mathematics & informatics
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• v.42 no.5
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• pp.1077-1090
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• 2024

In this study, a dual hesitant uncertain setting is employed to study the transportation issue. The dual hesitant fuzzy set handles ambiguous, unreliable, or inaccurate data as well as conditions in real-world practical research queries that are impossible or difficult to solve according to current fuzzy uncertainties. The dual hesitant fuzzy set (DHFS) is composed of a membership hesitant function as well as a non-membership hesitant function. In this investigation, we developed a new scoring formula for converting dual hesitant fuzzy numbers (DHFNs) to crisp values and suggested a novel algorithm called contraharmonic mean for addressing the dual hesitant fuzzy problem of transportation. Excel solver is utilized to find the contraharmonic mean. Additionally, we employed the modified distribution (MODI) method to achieve the best possible result. The recommended approach is then explained using a mathematical instance, and its efficacy can be demonstrated by comparing it to previously used techniques.