Determine Penalty Cost for Better Feasible Solution of Transportation Problem

Determine Penalty Cost for Better Feasible Solution of Transportation Problem

Prof. Mohan Tulshiram Chede, Dr. Ajay Tekchandani

Amity Global Business

School, Mumbai.

Abstract

In Operation Research, obtaining significant result for Transportation Problems is very important now-a-days. Vogel’s Approximation Method (VAM) is the very. efficient algorithm to solve the transportation problem for feasible solution which is nearer to optimal solution. In this paper we identified a computational error in VAM and approached a logical development of VAM algorithm. The main concept of VAM is to determine penalty cost which obtains from the difference of smallest and next to smallest cost in each row or column and make maximum allocation in lowest cost cell of that row or column which have largest penalty. The difficulty arises when the smallest cost and next to smallest cost have same magnitude. In that case we find a very logical concept to resolve this and developed a new algorithm “Advanced Vogel's j Approximation Method (AVAM)” to find a feasible solution to transportation problem which is very close to optimal solution more than VAM.

Keyword: AVAM, VAM, Penalty Cost, Feasible Solution, Error Estimation, Transportation Problem (TP).