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Paradox in The d-Dimensional Fixed Charge Transportation Problem and Algorithm for Finding The Paradox

Author(s)
Bib Paruhum Silalahi Department of Mathematics, IPB University,Bogor 16680,Indonesia
Eko Sulistyono Department of Mathematics, Batam Institute of Technology,Batam 29424,Indonesia
Fahren Bukhari Department of Mathematics, IPB University,Bogor 16680,Indonesia
Abstract
The d-dimensional fixed charge transportation problem is a generalization of fixed charge transportation. This problem has d-type of constraints so that it can be applied to more complex problem. In the transportation problem, sometimes there are some cases when increasing the product in shipping, the number of costs incurred is less than before increasing the product. This problem is called the transportation paradox. In this research, it will be explained about the model of d-dimensional fixed charge transportation problem and sufficient condition for the occurrence of the paradox. Furthermore an algorithm is given in finding the paradox in the d-dimensional fixed charge transportation problem with an example to support the theory presented.
Publication Details
Page(s) 329-336
DOI 10.18187/pjsor.v18i2.2807
Published Journal: Pakistan Journal of Statistics and Operation Research, Volume: 18, Issue: 2, Year: 2022

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Keywords
Transportation Problem., Fixed Charge, Linear programming, d-Dimensional, Transportation Paradox
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