Obtaining a good primal solution to the uncapacitated transportation problem

Abstract Sharma and Sharma [European Journal of Operational Research 122 (3) (2000) 37] have given a new procedure to solve the dual of the well-known uncapacitated transportation problem. This is expected to enhance the performance of dual based optimizing algorithms for solving the transportation problems. In this paper we give a heuristic that obtains a very good starting solution (with a duality gap of less than 2%) for the primal transportation problem in O( n 3 ) time, and this is expected to enhance the performance of network simplex algorithm that obtains the optimal solution and runs in O( n 3 log( n )) time. Empirical investigation revealed that our heuristic gave significantly better solutions than the well-known Vogel's approximation method that runs in O( n 2 ) time.