Ceiling Component Analogous Least Appears In Row Or Column Distribution Method To Evaluate Enriched Network Design

: In this research article, suggested methodology namely Ceiling Component Analogous Least Appears in Row Or Column Distribution Method is warranted to decide the feasible solution with respect to minimize the cost from the necessary reasonable elucidation set for the shipping tribulations. The recommended methodology is a unique way to achieve the practicable (or) may be best possible elucidation without disturbing the degeneracy condition for the unbalanced networks


Introduction
The transportation problem is a special type of linear programming problem where the objective consists in minimizing transportation cost of a given commodity from a number of sources (e.g.factory, manufacturing facility) to a number of destinations (e.g.warehouse, store) [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 [1] [8], [9].Now a days transportation problem have been broadly studied in Electronics and Communication branches along with Operations Research methods.It is one of the essential problems of network flow problem which is usually use to reduce the transportation cost for communication outlets with number of sources and number of destination while satisfying the supply and demand constraints [5].
Early days onwards transportation models play an important role in shipping and delivery management for minimizing the cost and maturing the services in communication and control engineering.Some former processes have been formulated solution system for the transportation problem with precise supply and demand constraints [6], [7].Optimized methods have been established for solving the transportation problems and assignment problems when the costs for the supply and demand quantities are known accurately [2], [4].In real situations, the supply and demand quantities in the transportation problem are sometimes hardly specified exactly because of varying the present scenario of their economic position [10].

Ceiling Component Analogous Least Appears in Row Or Column Distribution Method (CeCALAiROCD)
Step 1 : Construct the (TT) Transportation Table for the given (POM) pay off matrix.
Step 2 : Choose the maximum component from given POM.
Step 3 : Supply the demand for the minimum component which lies in the corresponding row or column of the selected maximum component in the (CTT) Constructed TT.
Step 4 : Select the next maximum component in (NCTT) Newly CTT and do again the steps 2 & 3 until degeneracy condition satisfied.

Pivot element cell is shaded.
Example 1: Consider the following unbalanced POM, cost for the transportation to be minimized.

Table: 1
By using the proposed methodology, we get Step 1: Here the maximum cost is 22 in TT (4, 2) (is a Pivot element for the POM which is shaded in the following Table : 2) in POM, by applying the above said methodology, the minimum cost is 2 in TT (1, 2) which appears in the corresponding column of the selected maximum cost and allocate the maximum possible demand 300 units for TT (1, 2) and delete the same row S1.Remaining rows will be considered as NCTT.

Table: 2
Step 2: Here the maximum cost is 22 in TT (3, 2) (is a Pivot element for the POM which is shaded in the following Table : 3) in POM, by applying the above discussed methodology, the minimum cost 4 in TT (2, 2) which appears in the corresponding column of the selected maximum cost and allocate the maximum possible demand 100 units for TT (2, 2) and delete the same column D2.Remaining columns will be considered as NCTT.

Table: 3
Step 3: Here the maximum cost is 20 in TT (3, 2) (is a Pivot element for the POM which is shaded in the following Table : 4) in POM, by applying the above proposed methodology, the minimum cost is 8 in TT (3, 3) which appears in the corresponding row of the selected maximum cost and allocate the maximum possible demand 150 units for TT (3,3) and delete the same column D4.Remaining columns will be considered as NCTT.Step 4: Here the maximum cost is 20 in TT (3, 2) (is a Pivot element for the POM which is shaded in the following Table : 5) in POM, by applying the above discussed methodology, the minimum cost is 12 in TT (1, 2) which appears in the corresponding column of the selected maximum cost and allocate the maximum possible demand 250 units for TT (1, 2) and delete the same column D3.Remaining columns will be considered as NCTT.

Table: 5
Step 5: Here the maximum cost is 18 in TT (3, 2) (is a Pivot element for the POM which is shaded in the following Table : 6) in POM, by applying the above said methodology, the minimum cost is 10 in TT (2, 2) which appears in the corresponding column of the selected maximum cost and allocate the maximum possible demand 400 units for TT (2, 2) and delete the same column D5.Remaining columns will be considered as NCTT.

Table: 6
Step 6: Here the maximum cost is 14 in TT (3, 1) (is a Pivot element for the POM which is shaded in the following Table : 7) in POM, by applying the above proposed methodology, the minimum cost is 6 in TT (1, 1) which appears in the corresponding column of the selected maximum cost and allocate the maximum possible demand 250 units for TT (1, 1) and delete the same row S2.Remaining rows will be considered as NCTT.Step 7: Here the maximum cost is 14 in TT (2, 1) (is a Pivot element for the POM which is shaded in the following Table: 8) in POM, by applying the above discussed methodology, the minimum cost is 8 in TT (1, 1) which appears in the corresponding column of the selected maximum cost and allocate the maximum possible demand 100 units for TT (1, 1) and delete the same column D1.Remaining columns will be considered as NCTT.

Table: 8
Step 8: Supply the maximum possible demand 225 units in TT (1, 1) and TT (2, 1) which leads to the solution satisfying all the conditions.

Table: 9
Step 9: The resulting basic feasible solution is

Table : 10 Optimum Cost: Table: 11 Example 2:
Consider the following unbalanced POM, cost for the transportation to be minimized.

Table : 12
By using the proposed methodology, the resulting basic feasible solution is

Table : 13 Optimum Cost: Table: 14 Example 3:
Consider the following unbalanced POM, cost for the transportation to be minimized.