Maximum Element Corresponding Minimum Appears In Row Or Column Allotment Method To Appraise Enhanced Groom Pattern

: In this article, proposed methodology namely Maximum Element Corresponding Minimum Appears in Row or Column Allotment Method is justified to finalize the feasible solution with respect to minimize the cost from the basic feasible solution set for the transportation problems. The proposed methodology is a distinctive way to gain the feasible (or) may be optimal solution without interrupt the degeneracy condition


Introduction
In logistics and supply chain management sectors using transportation techniques to minimize the cost [1] [2].Each source has a limited supply (i.e.maximum number of products that can be sent from it) while each destination has a demand to be satisfied (i.e.minimum number of products that need to be shipped to it) [3].The cost of shipping from a source to a destination is directly proportional to the number of units shipped [8], [9].
In Electronics and Communication branches along with Operations Research methods so many different techniques used to minimize the cost [5], [6], [7].Some preceding processes have been devised solution system for the transportation problem with precise supply and demand constraintsOptimized methods have been developed for solving the transportation problems and assignment problems when the cost coefficients for the supply and demand quantities are known exactly [4].In real world applications, the supply and demand quantities in the transportation problem are sometimes hardly specified precisely because of changing the current scenario of their economic status [10].

Maximum Element Corresponding Minimum Appears In Row Or Column Allotment Method (MxECMiROCA)
Step 1 : Construct the Transportation Table (TT) for the given pay off matrix (POM).
Step 2 : Choose the maximum element from given POM.
Step 3 : Supply the demand for the minimum element which lies in the corresponding row or column of the selected maximum element in the Constructed TT (CTT).
Step 4 : Select the next maximum element in Newly CTT (NCTT) and repeat the step 2 & 3 until degeneracy condition fulfilled.

Pivot element cell is highlighted.
Example 1: Consider the following balanced POM, cost for the transportation to be minimized.Step 1: Here the maximum cost is 4in TT (2, 1) (is a Pivot element for the POM highlighted in the following Table : 2)in POM, by applying the above said methodology, the minimum cost is 0in TT (2, 4) and TT (3, 1) which appears in the corresponding rowand corresponding column of the selected maximum cost, we got the tie up with minimum cost, so we have considered the minimum 0 along with the maximum demand 6 and allot the maximum possible demand 6 units for TT (2,4) and delete the same column D4.Remaining columns will be considered as NCTT.

Table: 2
Step 2: Here the maximum cost is 4in TT (2, 1) (is a Pivot element for the POM highlighted in the following Table : 3)in POM, by applying the above discussed methodology, the minimum cost 0 which appears in the corresponding column of the selected maximum cost and allot the maximum possible demand 4 units for TT(3, 1) and delete the same column D1.Remaining columns will be considered as NCTT.

Table: 3
Step 3: Here the maximum cost is 3in TT (1, 2) and TT (2, 1), we got the tie up with maximum cost, so we have considered the maximum cost 3in TT (1, 2) along with the maximum demand 8 (is a Pivot element for the POM highlighted in the following Table: 4)in POM, by applying the above proposed methodology, the minimum cost is 2in TT( 1, 1), TT (2, 2) and TT (3, 2) which appears in the corresponding row and corresponding column of the selected maximum cost, we got the tie up with minimum cost, so we have considered the minimum cost 2 along with the maximum demand 8and maximum supply 6, and allot the maximum possible demand 6 units for TT (3,2) and delete the same row S3.Remaining rows will be considered as NCTT.Step 4: Here the maximum cost is 3in TT (1, 2) and TT (2, 1), we got the tie up with maximum cost, so we have considered the maximum cost 3in TT (2, 1) along with the maximum demand 6 (is a Pivot element for the POM highlighted in the following Table: 5)in POM, by applying the above said methodology, the minimum cost is 2in TT (1, 1) and (2, 2), we got the tie up with minimum cost, so we have considered the minimum cost 2 along with the maximum demand 6 which appears in the corresponding column of the selected maximum cost and allot the maximum possible demand 6 units for TT(1, 1) and delete the same row S2and column D2.Remaining rows and columns will be considered as NCTT.

Table: 5
Step 5: Supply the maximum possible demand 2 units in TT (1, 1) which leads to the solution satisfying all the conditions.

Table: 6
Step 6: The resulting basic feasible solution is

Table : 1
By using the proposed methodology, we get

Table : 7 Optimum Cost: Table: 8 Example 2:
Consider the following balanced POM, cost for the transportation to be minimized.

Table : 9
By using the proposed methodology, the resulting basic feasible solution is

Table : 10 Optimum Cost: Table: 11 Example 3:
Consider the following balanced POM, cost for the transportation to be minimized.