Abstract
One of the popular operation research problems is transportation problem. Its solution is basically divided into two parts. Initially Initial Basic Feasible Solution (IBFS) is obtained then the result is used to calculate the optimal solution. The popular methods to find IBFS of transportation problem are North West Corner Method (NWCM), Least Cost Method (LCM), and Vogel’s Approximation Method (VAM). In this paper, a novel approximation method is proposed to find out the IBFS of the transportation problem. There are five different examples used for which the IBFS are calculated using NWCR, LCM, VAM, and our proposed method. The results show that our proposed method provides the best result among them.
Highlights
There are many problems discussed in operations research and Transportation problem is one of the widely used problems discussed in linear programming problem of operation research which is directly used in our day to day logistics and supply chain activities
Initial Basic Feasible Solution (IBFS) affects the optimal solution of the transportation problem
The proposed novel method for finding IBFS provides the best solution among NWCR, Least Cost Method (LCM) and Vogel’s Approximation Method (VAM) in most of the cases
Summary
There are many problems discussed in operations research and Transportation problem is one of the widely used problems discussed in linear programming problem of operation research which is directly used in our day to day logistics and supply chain activities. It helps to solve problems related to distribution and transportation of resources from various sources to destinations so that the cost of transportation should be optimal for the commodity. The units of resources to be supplied from source to destination are the primary objective so that the cost of transportation should be minimal and profit should be maximum. Let xij be the quantity transported from the source i to the destination j. The problem is mathematically formulated as follows: Minimize Z=. Z : Objective function is minimize the total transportation cost. Cij: Transportation cost per unit from source i to destination j. Xij: Units of commodity sent from source i to destination j. Ai : Quantity supplied from source i. The total number of constraints for the transportation problem is m+n. The organization of the paper is as follows: section II deals with literature review; section III deals the proposed approximation method; section IV deals with results analysis and section V concludes the paper
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