Three methods are used to obtain the initial feasible solution for the transportation problem: Least Cost Method, Vogel's Approximation Method, and North-West Corner Rule. The method that is NOT used to solve the transportation problem is the Minimum Space Method. The Least Cost Method involves selecting the cell with the minimum unit cost and allocating as much as possible, while Vogel's Approximation Method produces an optimal solution but does not guarantee it. The North-West Corner Rule allocates starting from the North-West corner cell and removes the row or column whose supply or demand is fulfilled until all allocations are over.