Transshipment DMM
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Transcript of Transshipment DMM
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TRANSSHIPMENT
PROBLEM 1Rinsi Daniel : 211111
Jithesh J : 211062
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Using the information given below, determinethe optimal solution:
ManufacturingPlants
P1 P2
Capacity 240 units 160 units
Warehouses W1 W2 W3
Requirements 80 units 120 units 200 units
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Transportation Costs : Exactly proportionalto the distances
(given in miles in the following figure)
P1 P2
W321
80
100 110140
120 9060
60 30
80
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(a) that inter-plant and inter-warehousetransfers are not allowed:
P1 P2 W1 W2 W3 Supply
P1 0 100 90 60 640
P2 0 120 140 110 560
W1 100 120 0 400
W2 90 140 0 400
W3 60 110 0 400
Demand 400 400 480 520 600 2400
Since total supply = total demand, the problem is balanced.
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Applying Vogels Approximation Method: P1 P2 W1 W2 W3 Supply
P1 0 100 90 60 640
P2 0 120 140 110 560
W1 100 120 0 400
W2 90 140 0 400
W3 60 110 0 400
Demand 400 400 480 520 600
400
160
60)
110)
100)
90)
60)
60) 120) 100) 90) 60)
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Applying Vogels Approximation Method: P1 P2 W1 W2 W3 Supply
P1 0 100 90 60 640
P2 0 120 140 110 160
W1 100 120 0 400
W2 90 140 0 400
W3 60 110 0 400
Demand 400 400 480 520 600
400
60)
10)
100)
90)
60)
60) - 100) 90) 60)
400
80
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Applying Vogels Approximation Method: P1 P2 W1 W2 W3 Supply
P1 0 100 90 60 640
P2 0 120 140 110 510
W1 100 120 0 400
W2 90 140 0 400
W3 60 110 0 400
Demand 400 400 80 520 600
400
60)
10)
-
90)
60)
60) - 20) 90) 60)
400
400
120
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Applying Vogels Approximation Method: P1 P2 W1 W2 W3 Supply
P1 0 100 90 60 640
P2 0 120 140 110 160
W1 100 120 0 400
W2 90 140 0 400
W3 60 110 0 400
Demand 400 400 80 120 600
400
60)
10)
-
-
60)
60) - 20) 50) 60)
400
400
200
400
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Applying Vogels Approximation Method: P1 P2 W1 W2 W3 Supply
P1 0 100 90 60 640
P2 0 120 140 110 160
W1 100 120 0 400
W2 90 140 0 400
W3 60 110 0 400
Demand 400 400 80 120 200
400
60)
10)
-
-
-
- 20) 50) 50)
400
400
400
400
240
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Applying Vogels Approximation Method: P1 P2 W1 W2 W3 Supply
P1 0 100 90 60
P2 0 120 140 110 160
W1 100 120 0 400
W2 90 140 0 400
W3 60 110 0 400
Demand 400 400 80 120 200
400
4030)
10)
-
-
-
- - 20) 50) 50)
400
400
20000 240
400
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Applying Vogels Approximation Method: P1 P2 W1 W2 W3 Supply
P1 0 100 90 60 40
P2 0 120 140 110 160
W1 100 120 0 400
W2 90 140 0 400
W3 60 110 0 400
Demand 400 400 80 120 200
400
10)
20)
-
-
-
- - 20) 50) -
400
400
20000 40
80
400
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Applying Vogels Approximation Method: P1 P2 W1 W2 W3 Supply
P1 0 100 90 60 40
P2 0 120 140 110 160
W1 100 120 0 400
W2 90 140 0 400
W3 60 110 0 400
Demand 400 400 80 80 200
400
-
20)
-
-
-
- - 120) 140) -
400
400
20000 40
80 80
400
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Applying Vogels Approximation Method: P1 P2 W1 W2 W3 Supply
P1 0 100 90 60 40
P2 0 120 140 110 80
W1 100 120 0 400
W2 90 140 0 400
W3 60 110 0 400
Demand 400 400 80 80 200
400
-
20)
-
-
-
- - 120) - -
400
400
20000 40
800
400
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Initial Basic Feasible Solution:P1 P2 W1 W2 W3
P1 400 - - 40 200
P2 - 400 80 80 -
W1 - 400 - -
W2 - - - 400 -
W3 - - - - 400
Here, m + n -1 =9, hence solution is non- degenerate.
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Applying MODI method to check for Optimality
P1 P2 W1 W2 W3
P1 0 - - 90 60
P2 - 0 120 140 -
W1 - 0 - -
W2 - - - 0
W3 - - - - 0
Cost for Occupied Cell:
60
110
-10
-30
0
-60 -110 10 30 0
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Applying MODI method to check for Optimality
P1 P2 W1 W2 W3
P1 - 100 - -
P2 - - - 110
W1 100 120 -
W2 90 140 -
W3 60 110 -
Cost for Unoccupied Cell:
60
110
-10
-30
0
-60 -110 10 30 0
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(b) that the units may be transshipped:
P1 P2 W1 W2 W3 Supply
P1 0 80 100 90 60 640
P2 80 0 120 140 110 560
W1 100 120 0 60 80 400
W2 90 140 60 0 30 400
W3 60 110 80 30 0 400
Demand 400 400 480 520 600 2400
Since total supply = total demand, the problem is balanced.
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Applying Vogels Approximation Method
P1 P2 W1 W2 W3 Supply
P1 0 80 100 90 60 640
P2 80 0 120 140 110 560
W1 100 120 0 60 80 400
W2 90 140 60 0 30 400
W3 60 110 80 30 0 400
Demand 400 400 480 520 600 2400
(60)
(80)
(60)
(30)
(30)
60) 80) 60) 30) 30)
400160
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Applying Vogels Approximation Method
P1 P2 W1 W2 W3 Supply
P1 0 80 100 90 60 640
P2 80 0 120 140 110 160
W1 100 120 0 60 80 400
W2 90 140 60 0 30 400
W3 60 110 80 30 0 400
Demand 400 400 480 520 600 2400
(60)
(30)
(60)
(30)
(30)
60) - 60) 30) 30)
400
400
80
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Applying Vogels Approximation Method
P1 P2 W1 W2 W3 Supply
P1 0 80 100 90 60 640
P2 80 0 120 140 110 160
W1 100 120 0 60 80 400
W2 90 140 60 0 30 400
W3 60 110 80 30 0 400
Demand 400 400 80 520 600 2400
(60)
(30)
-
(30)
(30)
60) - 20) 30) 30)
400
400
400240
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Applying Vogels Approximation Method
P1 P2 W1 W2 W3 Supply
P1 0 80 100 90 60 240
P2 80 0 120 140 110 160
W1 100 120 0 60 80 400
W2 90 140 60 0 30 400
W3 60 110 80 30 0 400
Demand 400 400 80 520 600 2400
(30)
(10)
-
(30)
(30)
- - 20) 30) 30)
400
400
400
400
120
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Applying Vogels Approximation Method
P1 P2 W1 W2 W3 Supply
P1 0 80 100 90 60 240
P2 80 0 120 140 110 160
W1 100 120 0 60 80 400
W2 90 140 60 0 30 400
W3 60 110 80 30 0 400
Demand 400 400 80 120 600 2400
(30)
(10)
-
-
(30)
- - 20) 60) 60)
400
400
400
400
400
200
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Applying Vogels Approximation Method
P1 P2 W1 W2 W3 Supply
P1 0 80 100 90 60 240
P2 80 0 120 140 110 160
W1 100 120 0 60 80 400
W2 90 140 60 0 30 400
W3 60 110 80 30 0 400
Demand 400 400 80 120 200 2400
(30)
(10)
-
-
-
- - 20) 50) 50)
400
120400
400
400
120
400
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Applying Vogels Approximation Method
P1 P2 W1 W2 W3 Supply
P1 0 80 100 90 60 120
P2 80 0 120 140 110 160
W1 100 120 0 60 80 400
W2 90 140 60 0 30 400
W3 60 110 80 30 0 400
Demand 400 400 80 120 200 2400
(40)
(10)
-
-
-
- - 20) - 50)
400
120400
400
400
120
80
400
Applying Vogels Approximation Method
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Applying Vogel s Approximation Method
P1 P2 W1 W2 W3 Supply
P1 0 80 100 90 60 120
P2 80 0 120 140 110 160
W1 100 120 0 60 80 400
W2 90 140 60 0 30 400
W3 60 110 80 30 0 400
Demand 400 400 80 120 80 2400
-
(10)
-
-
- - 20) - 30)
400
120400
400
400
120
80 80
400
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Applying Vogels Approximation Method
P1 P2 W1 W2 W3 Supply
P1 0 80 100 90 60 120
P2 80 0 120 140 110 80
W1 100 120 0 60 80 400
W2 90 140 60 0 30 400
W3 60 110 80 30 0 400
Demand 400 400 80 120 80 2400
-
(10)
-
-
-
- - 20) - -
400
120400
400
400
120
8080
400
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