A Two-Phase Method for Solving Transportation Models with Prohibited Routes
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Date
2022
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Publisher
Pakistan Journal of Statistics and Operation Research
Abstract
The Transportation Problem (TP) is a mathematical optimization technique which regulates the flow of items along
routes by adopting an optimum guiding principle to the total shipping cost. However, instances including road hazards,
traffic regulations, road construction and unexpected floods sometimes arise in transportation to ban shipments via
certain routes. In formulating the TPs, potential prohibited routes are assigned a large penalty cost, M; to prevent
their presence in the model solution. The arbitrary usage of the big M as a remedy for this interdiction does not go
well with a good solution. In this paper, a two-phase method is proposed to solve a TP with prohibited routes. The
first phase is formulated as an All-Pairs Least Cost Problem (APLCP) which assigns respectively a non-discretionary
penalty costM? ij M to each of n prohibited routes present using the Floyd’s method. At phase two, the new penalty
values are substituted into the original problem respectively and the resulting model is solved using the transportation
algorithm. The results show that, setting this modified penalty cost (M?) logically presents a good solution. Therefore,
the discretionary usage of the M 1 is not a guarantee for good model solutions. The modified cost M? M so
attained in the sample model, is relatively less than the Big M( 1) and gives a good solution which makes the
method reliable.
Description
This article is published by Pakistan Journal of Statistics and Operation Research 2022 and is also available at http://dx.doi.org/10.18187/pjsor.v18i3.3911
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Citation
Pak.j.stat.oper.res. Vol.18 No.3 2022 pp 749-758