Quantitative Analysis -Transport Method 1
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Transcript of Quantitative Analysis -Transport Method 1
Transportation Methods
Developing Initial Solutions
• Northwest Method• Intuitive Method• Vogel Approximation Method
Evaluating Solutions
• Stepping Stone Method• MODI Method
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Warehouse F
act
ory
Supply
Demand
Example
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X1 X2 X3
X4 X5 X6
OBJ. FUNCTION : Minimize C = 5X1 + 9X2 + 3X3 + 4X4 + 2X5 + 6X6
Constraints :
X1 +X2 + X3 = 100
X4 +X5 + X6 = 100
X1 +X4 = 80
X2 + X5 = 90
X3 +X6 = 30
Conditions :
X1 , X2 , X3 , X4 , X5 , X6 = > 0
Northwest corner rule
• Allocate the available supply to the cells starting from the northwest corner (Upper left) and moving down vertically or horizontally, satisfying the demand.
• Observed that the number of cells used must be equal to the number of rows + the number of columns – one.
• Compute for the cost of transportation summing up the products of the cost of transport and amount to be transported to the destination.
• Proceed to check for areas of improvement using any of the methods stated in the next number.
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Northwest Method
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Northwest Method
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Northwest Method
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TC =80(5)+20(9) + 70(2) + 30(6) = 900Completed Cells = R + C - 1 = 2 + 3 - 1 = 4
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Northwest Method
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Factory
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+
1B 2C
2A
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1A -5 +4
+3____ ____
+ -
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-2
+7 -7
+ 6
Stepping Stone Method
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1B
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+2____ ____
+ -
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Stepping Stone Method
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TC =80(5)+20(3) + 90(2) + 10(6) = 700
Stepping Stone Method
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1C -3 +9
+6____ ____
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Stepping Stone Method
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Stepping Stone Method
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Stepping Stone Method
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Stepping Stone Method
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+ -
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+4____ ____
+ -
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-2
+13 -7
+ 6
2A
1B
Stepping Stone Method
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- +
+ -
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1C -3 +5
+6____ ____
+ -
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+11 -7
+ 4
2A
1A
Stepping Stone Method
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TC =70(5)+30(3) + 10(4) + 90(2) = 660 SOLUTION IS OPTIMAL
Stepping Stone Method
Least Cost Method (Intuitive Method)
• Start from the cell with the least cost. Then work your way to the other cells always considering the least transportation cost.
• Compute the cost of transport and improve using any of the two methods in no. 4.
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Intuitive Method
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Intuitive Method
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Intuitive Method
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Intuitive Method
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Intuitive Method
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Completed Cells = R + C - 1 = 2 + 3 - 1 = 4 TC =70(5)+30(3) + 10(4) + 90(2) = 660
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MODI Method
30 70
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Index
0
5 3
-1
3
Cell Cost - ( Row Index + Column Index )
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MODI Method
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Index
0
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-1
3
1B: 9 - ( 0 + 3 ) = + 6
2C: 6 - (-1 + 3 ) = + 4
SOLUTION IS OPTIMAL
VAM - Vogel Approximation Method
Based on the concept of minimizing opportunitycost.
The opportunity cost of a given row or column is the difference between the lowest cost and the second lowest cost alternative.
Procedure :
1. For each row an column, select the lowest and second lowest alternatives from those not already allocated and calculate the opportunity cost.
2. Scan the opportunity cost figures and identify the row or columns with the largest opportunity cost.
3. Allocate as many units as possible to this row or column in the square with the least cost.
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VAM - Vogel Approximation Method
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Row/Column 2nd Lowest Cost - Lowest Cost = Opportunity Cost
Row W 8 5 3Row X 6 4 2Row Y 7 6 1Column A 7 6 1Column B 8 6 2Column C 5 4 1
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VAM - Vogel Approximation Method
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Row/Column 2nd Lowest Cost - Lowest Cost = Opportunity Cost
Row X 6 4 2Row Y 7 6 1Column A 7 6 1Column B 8 6 2Column C 9 4 5 Largest
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VAM - Vogel Approximation Method
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Row/Column 2nd Lowest Cost - Lowest Cost = Opportunity Cost
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VAM - Vogel Approximation Method
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VAM - Vogel Approximation Method
Thank You!
TC =25 (5)+15(6) + 20(4) + 15(7) + 25(6) = 550
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WA: 9 - ( 0 + 7 ) = + 2
WB: 8 - ( 0 + 6 ) = + 2
XB: 8 - ( -1 + 6 ) = + 3
YC: 9 - ( 0 + 5 ) = + 4
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