I need detailed solution about this. (Operation research 1) 6. (20 points) A com
ID: 3340591 • Letter: I
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I need detailed solution about this. (Operation research 1)
6. (20 points) A company produces widgets at 2 factories. A and B. They have orders from 3 eustomers for May and June as in the table below. 1 lcompany 2 compa 100 May 200 June 450 310 520 350 The per unit shipping costs are: company 1 I $40 company 1 company 2 company 3 $28 $38 $32 $24 $36 The production capacity at each factory is 400 a month. The company has 200 widgets in inventory at factory A and 250 at facotry B. Widgets can be delivered early but not late. In case it cannot meet demand, it has a contract to buy widgets from another company at a cost of $700 per widget (cost includes delivery). Formulate a Balanced Transportation Problem to minimize the costs by giving the cost and requirement table.Explanation / Answer
May
Company 1
Company 2
Company 3
Supply + stored in inventory
A
40
28
32
600
B
36
38
24
650
demand
200
310
400
By Least Cost method, assign as much as possible to the cell with the smallest unit cost in the entire table. Cross out the row or column which has satisfied supply or demand. If a row and column are both satisfied then cross out only one of them.
This gives, X23 (Amount transferred to company 3 from B) = 400
This gives, X12 (Amount transferred to company 2 from A) = 310
This gives, X21 (Amount transferred to company 1 from B) = 200
Balance in inventory after May, A = 290, B= 50
June
Company 1
Company 2
Company 3
Supply + stored in inventory
A
40
28
32
690
B
36
38
24
450
demand
450
520
350
By Least Cost method, assign as much as possible to the cell with the smallest unit cost in the entire table. Cross out the row or column which has satisfied supply or demand. If a row and column are both satisfied then cross out only one of them.
This gives, X23 (Amount transferred to company 3 from B) = 250
This gives, X12 (Amount transferred to company 2 from A) = 520
This gives, X21 (Amount transferred to company 1 from B) = 100
This gives, X11 (Amount transferred to company 1 from A) = 170
Since this is balanced transportation model supply = demand.
Therefor number of widgets to buy from outside = 450 –(100+170)= 180
.
Company 1
Company 2
Company 3
Supply + stored in inventory
A
40
28
32
600
B
36
38
24
650
demand
200
310
400
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