This paper is aimed at studying the Time Minimizing Transportation Problem with Fractional Bottleneck Objective Function (TMTP-FBOF). TMTP-FBOF is related to a Lexicographic Fractional Time Minimizing Transportation Problem (LFTMTP), which will be solved by a lexicographic primal code. An algorithm is also developed to determine an initial efficient basic solution to this TMTP-FBOF. The developed TMTPFBOF Algorithm is supported by a real life example of Military Transportation Problem of Indian Army.