India, one of the economies with the fastest growth rates in the world, is expanding at a rate of 7% annually. The nation is striving hard to alter itself over the next few decades, with a population that is also expanding. The Indian government has public transit improvement high on its priority list. Even though private vehicle ownership in India is rising and producing significant traffic issues in big areas like Navi-Mumbai, there are numerous initiatives to upgrade and modernize transport systems. At least 1.42 billion people, or around 35.87% of the population of the country, are estimated to live in urban areas, according to the World Bank's collection of Development Indicators 2022. Even while the amount of urbanization may appear to be low in percentage terms, there are a huge number of people living in cities. India's urban population currently outnumbers the populations of Brazil and the United States combined. India's level of urbanization is predicted to rise even more, and by 2030, there should be around 600 million people living in cities. Sadly, there is a rising quantity of traffic on the streets of our cities nowadays, which is increasing the time it takes for goods to be transported as well. This traffic is also a big factor in problems like air and noise pollution, traffic accidents, and serious health hazards for locals. Technology will be crucial in identifying mobility gaps and altering current transport systems in order to create an inclusive, safer, and more sustainable city of the future. we are solving the transportation problem with the help of dual simplex and two-phase methods. Here we are solving this problem with the help of the Branch and Bound Method of Integer Programming Problem by using R software and we are comparing the obtained optimal solution with the Vogel Approximation Method.