The time required to reach the optimal solution for transportation problem (TP) is primarily dependent on the quality of the IBFS method. Therefore, many researchers are involved in developing a new IBFS method for TP. Another reason for proposing new IBFS methods is that most of the organizations are expecting better solution than the best solution in comparing with the type of expertise and technology required for obtaining best solution. Based on our detailed analysis of the literature, it is observed that there are 105 IBFS methods are presented in the literature. Though many IBFS methods are reported, to the best of our knowledge, there is no study systematically reviewed all the reported IBFS methods in the literature. So, this study addressed this gap. From the detailed analyses of the literature it is observed that (a) except a very few studies, all the reported studies in the literature did not follow the required research processes to claim that the proposed method(s) is(are) performing better/superior to the bench mark procedure(s) considered in their respective study, (b) almost all the researchers considered the VAM as bench mark procedure but  not the latest better performing IBFS method(a) reported in the literature; (c) a few sets of authors proposed different IBFS methods and published in different journals, but they never compared their own proposed methods together; and (d) though there are 143 tiny size transportation problems reported during 1965 to 2020 in the literature for performance analysis, all most all the research studies considered only a very small number of tiny TP instances out of these 143 instances, which are favoring their proposed method(s), for their performance analysis.