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A Total Opportunity Cost Matrix Tiebreaker Vogel’s Approximation Method for Transportation Problems

Madamedon, S (2024) A Total Opportunity Cost Matrix Tiebreaker Vogel’s Approximation Method for Transportation Problems. Doctoral thesis, Liverpool John Moores University.

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The allocation of resources is one of the most significant challenges met by decision-makers because it affects any company's profitability. One sort of resource allocation problem is transportation problems; in this case, the decision-maker must choose the quantity of goods to be delivered from various sources to various destinations at the lowest possible cost. Therefore, in this research, we have explored the state-of-the-art method Total Opportunity Cost Matrix Vogel’s Approximation Method and noticed that it has a drawback as it arbitrarily makes allocations when there are ties in the decision-making process, and we have then developed a novel and effective algorithm after controlling for this limitation. The Total Opportunity Cost Matrix Tiebreaker Vogel’s Approximation Method, which is the proposed method, systematically breaks ties at several levels in the iteration process of decision-making and produces an improvement on the state-of-the-art method. Additionally, for continuous cost transportation problems, since it is difficult to have ties, an extension of the proposed method known as Total Opportunity Cost Matrix Tiebreaker Vogel's Approximation Method Threshold uses a percentage threshold to induce ties at the maximum penalty which provides the algorithm with alternative pathways to access more costs that can be considered as the minimum cost during the iteration process, resulting, on average, in a lower initial basic feasible solution. This study compared the performance of the state-of-the-art method with 20,000 simulated balanced transportation problems with real-valued costs and 35 benchmark balanced transportation problems with integer cost values from previously published literature. The results show that, on average, the state-of-the-art method can be improved by about 2% when we take a range of percentage thresholds as the maximum penalty. Although we are aware of the modest increase in computational complexity of this proposed method (which is not expensive to run), we point out that the quality of the initial basic feasible solution obtained can have a significant impact on business overheads as it is generally believed that the better the initial basic feasible solution obtained, the smaller is the number of iterations required to obtain the optimal solutions saving the company time and money overall. Additionally, apart from the fact that it is simple to understand, this proposed method's best quality is that it can be used with other existing optimisation methods by inducing ties to break ties and can also add another step to methods that break ties, for example using the maximum mean cost to break a tie in the minimum cost for transportation problems.

Item Type: Thesis (Doctoral)
Uncontrolled Keywords: Transportation Problems; Vogel's Approximation Method; TieBreaker Vogel's Approximation Method
Subjects: H Social Sciences > HE Transportation and Communications
Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Computer Science & Mathematics
SWORD Depositor: A Symplectic
Date Deposited: 18 Jan 2024 09:15
Last Modified: 18 Jan 2024 09:16
DOI or ID number: 10.24377/LJMU.t.00022250
Supervisors: Correa, E and Lisboa, P
URI: https://researchonline.ljmu.ac.uk/id/eprint/22250
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