# Least Cost Method and Vogel's Approximation method

May 11th, 2015
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The least-Cost Method is a method for computing a basic feasible solution of a transportation problem, where the basic variables are chosen according to the unit cost of transportation. This method is very useful because it reduces the computation and the time required to determine the optimal solution. The following steps summarize the approach. The Vogel Approximation (Unit penalty) method is an iterative procedure for computing a basic feasible solution of a transportation problem. This method is preferred over the two methods i.e. North West Corner Rule and Least cost Method, because the initial basic feasible solution obtained by this method is either optimal or very close to the optimal solution. The standard instructions are paraphrased below:

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Mathematical MethodsMATHEMATICAL METHODS1. Finding An Initial Basic Feasible Solution:An initial basic feasible solution to a transportation problem can be found by any one of the three following methods: I. North West Corner RuleII. The Least Cost MethodIII. Vogels Approximation Method1. North West Corner RuleThe North West corner rule is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North-West Corner (i.e. top left corner). The standard North West corner rule instructions are paraphrased below: Steps:Step 1.Select the north west (upper left hand) corner cell of the transportation table and allocate as many units as possible equal to the minimum between available supply and demand. Step 2.Adjust the supply and demand numbers in the respective rows and columns. Step 3.If the demand for the first cell is satisfied, then move horizontally to the next cell in the second row. Step 4.If the supply for the first row is exhausted, then move down to the first cell in the second row. Step 5.If for any cell, supply equals demand, then the next allocation can be made in either in the next row or

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