The main aim of this paper is to develop an approach based on trapezoidal fuzzy numbers to optimize transportation problem in fuzzy environment. The present algorithm has representation of availability, demand and transportation cost as trapezoidal fuzzy numbers. This algorithm is found quicker in terms of runtime as comparison to fuzzy VAM discussed in [Kaur A., Kumar A., A new method for solving fuzzy transportation problem using ranking function, Appl. Math. Model. 35:5652–5661, 2011; Ismail Mohideen S., Senthil Kumar P., A comparative study on transportation problem in fuzzy environment, Int. J. Math. Res. 2:151–158, 2010]. On the other hand this technique gives much better results than some classical methods like north-west corner and least cost method. Another benefit of this algorithm is that for certain transportation problems it directly gives optimal solution. It is one of the simplest methods to apply and perceive. Practical usefulness of the new method over other existing methods is demonstrated with two numerical examples.
After a breakdown notified in Wuhan, China in December 2019, COVID-19 is declared as pandemic diseases. To the date more than 13 million confirmed cases and more than half a million are dead around the world. This virus also attached Malaysia in its immature stage where 8718 cases were confirmed and 122 were declared as death. Malaysia responsibly controlled the spread by enforcing MCO. Hence, it is required to visualize the pattern of Covid-19 spread. Also, it is necessary to estimate the impact of the enforced prevention measures. In this paper, an infectious disease dynamic modeling (SEIR) is used to estimate the epidemic spread in Malaysia. The main assumption is to update the reproduction number Rt with respect to the implemented prevention measures. For a time-frame of five month, the Rt was assumed to vary between 2.9 and 0.3. Moreover, the manuscript includes two possible scenarios: the first will be the extension of the stricter measures all over the country, and the second will be the gradual lift of the lock-down. After implementing several stages of lock-down we have found that the estimated values of the Rt with respect to the strictness degree varies between 0.2 to 1.1. A continuous strict lock-down may reduce the Rt to 0.2 and accordingly the estimated active cases will be reduced to 20 by the beginning of September 2020. In contrast, the second scenario considers a gradual lift of the enforced prevention measures by the end of June 2020, here we have considered three possible outcomes according to the MCO relaxation. Thus, the estimated values of Rt = 0.7, 0.9, 1.1, which shows a rapid increase in the number of active cases. The implemented SEIR model shows a close resemblance with the actual data recorded from 10, March till 7, July 2020.
The present paper wraps an innovative approach to optimize transportation problems through generalized trapezoidal numbers in a fuzzy environment. The main contribution here is to develop an innovative method to optimize the generalized fuzzy trapezoidal transportation problem and reduce the computational intricacy of the existing methods. Then again this method confers many improved results against classical North-West Corner and Least-Cost schemes in Fuzzy environment. An additional merit of the proposed scheme is that for several fuzzy transportation problems it furnishes the best possible way out directly. It is simple to understand and apply. The solution process is exemplified through two numerical examples and comparison with some standard existing methods.
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