Initial Basic Feasible Solution for Transportation Problem using TOCM with Zero Point Minimum Method
Keywords:
Initial Basic Feasible Solution; Optimal Solution; Total Opportunity Cost Matrix; Transportation Problem; Zero Point Minimum Method;Abstract
The effective distribution of commodities from several suppliers to numerous consumers while minimising transportation costs is the focus of the well-researched optimisation problem known as The Transportation Problem (TP) in operations research and logistics. A tactical tool for simulating the costs involved in moving commodities among sources and destinations is the Transportation Operation Cost Matrix (TOCM). In order to provide an initial basic feasible solution, the TOCM and the Zero Point Minimum Method (ZPMM) are employed in this study to present a novel technique to addressing the Transportation Problem. The ZPMM entails finding the least expensive cell in the TOCM that hasn't been allocated and giving it the greatest amount of stock. Iteratively repeating this approach until supply and demand restrictions are satisfied results in a fundamentally workable solution. The suggested approach tries to offer a quick and easy way to arrive at a preliminary answer to the Transportation Problem, which is a key first step for further optimisation methods like the Modified Distribution Method or the Vogel's Approximation Method. The Transportation Problem (TP) estimates minimum cost for the transportation of goods to different destinations from a number of different sources. This minimum cost is called the optimal solution of the transportation problem. Before finding optimal solution, one needs to find an Initial Basic Feasible Solution (IBFS). A new method Total Opportunity Cost Matrix-Zero Point Minimum Method for determining IBFS is developed in this paper. The results obtained in terms of transportation cost are compared with the Vogel`s Approximation Method (VAM) and the optimal solution. Several numerical tests are run on various transport scenarios to gauge the effectiveness of the suggested approach. The outcomes show that the developed initial basic feasible solutions are both feasible and optimal, opening the door for future improvement utilising cutting-edge optimisation methods.
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