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A heuristic for obtaining better initial feasible solution to the transportation problem

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Abstract

Vogel’s Approximation Method (VAM) is known as the best algorithm for generating an efficient initial feasible solution to the transportation problem. We demonstrate that VAM has some limitations and computational blunders. To overcome these limitations we develop an Improved Vogel’s Approximation Method (IVAM) by correcting these blunders. It is compared with VAM on obtained initial feasible solutions to a numerical example problem. Reduction in the total transportation cost over VAM by IVAM is found to be 2.27%. Besides, we have compared IVAM with each of twelve previously developed methods including VAM on solutions to numerical problems. IVAM leads to the minimal total cost solutions to seven, better solutions to four and the same better solution to the remaining one. Finally, a statistical analysis has been performed over the results of 1500 randomly generated transportation problems with fifteen distinct dimensions, where each of them has 100 problems instances. This analysis has demonstrated better performance of IVAM over VAM by reducing the total transportation cost in 71.8% of solved problems, especially for large size problems. Thus IVAM outperforms VAM by providing better initial feasible to the transportation problem.

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Authors and Affiliations

  1. Department of Quantitative Sciences (Mathematics), International University of Business Agriculture and Technology, Dhaka, Bangladesh

    Md. Ashraful Babu

  2. BRAC Business School, BRAC University, Dhaka, 1212, Bangladesh

    M. A. Hoque

  3. Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh

    Md. Sharif Uddin

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  1. Md. Ashraful Babu
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  2. M. A. Hoque
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  3. Md. Sharif Uddin
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Correspondence to M. A. Hoque.

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Babu, M.A., Hoque, M.A. & Uddin, M.S. A heuristic for obtaining better initial feasible solution to the transportation problem. OPSEARCH 57, 221–245 (2020). https://doi.org/10.1007/s12597-019-00429-5

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