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this is part of my study. i solved the numerical related with location selection
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International American University
Kings College architecting future
Kathmandu, Nepal
Operations Management & Supply Chain: Assignment no.4
Submitted by: Bikram prajapati
Submitted to: Matthew Keogh
Dec 27, 2013
Chapter 8: Location Planning and Analysis
4.) Given, Current Facilities are insufficient so the company is considering three alternatives as:
Alternatives Fixed cost/ year Variable cost / boat
New location A $250,000 $500
Subcontract B $0 $ 2,500
Expand C $50,000 $1,000
We need to plot Total - cost lines in order to determine the lower cost.
Total cost is given by: Fixed cost + Output * Variable cost
At the different level of output the different output are shown in below table as:
New location Subcontract Expand
Output Total cost Total cost Total cost
0 250000 0 50000
100 300000 250000 150000
150 325000 375000 200000
200 350000 500000 250000
500 500000 1250000 550000
0 100 200 300 400 500 6000
200000
400000
600000
800000
1000000
1200000
1400000
Total cost line
New location ASubcontract B Expand existing C
Annual output
Tota
l Ann
ual c
ost
The approximately ranges for which the various alternatives will yield the lowest cost as shown
in the figure. The exact range can be determined by finding the output level at which lines B and
C cross and lines C and A cross.
For alternatives B and C
2500 Q = 50,000 + 1000*Q
Or, Q = 33.33 unit of Boat.
For alternatives A and C
250000 + 500 Q = 50000 + 1000 Q
Or, Q = 400 units of boat
Decision:
Subcontract has lowest total cost when Volume < 33.33 boats
Expand has the lowest total cost when 33.33 < Volume < 400 boats
New Location has the lowest total cost when Volume > 400 boats.
B.) Expand has the lowest total cost i.e. $200,000
C.) Quality, price, delivery time, flexibility volume, profit, risk and location etc. are some other
factor need to consider.
14) Given:
Destination x ,y coordinate Quantity
D1 1, 2 900
D2 2,4 300
D3 3,1 700
D4 4,2 600
D5 5,3 1200
Total quantity = 3700
While solving the problem with the center of gravity we need to find out central coordinate. That
is given by
X mean = ∑(x*Q) / ∑Q
= 1*900 + 2*300 + 3*700+4*600 + 5*1200 / 3700
=3.24
Y mean = ∑(y*Q)/ ∑Q
= (2*900) + (4*300) + (1*700) + (2*600) + (3*1200) / 3700
= 2.3
Hence the center of gravity has the coordinates x= 3.24 and y= 2.3
8 S: The Transportation Model
3.) Solution
For Toledo location
Input matrix
A B C Suppl
y1 10 14 10 2102 12 17 20 1403 11 11 12 150
Toledo 18 8 13 160
Demand 220 220 220
Supply = Demand = 660
Step using VAM
A B C Supply I II III IV1 10(*) 14 (*) 10
(210)210 0 0 0 0
2 12 (140) 17 (*) 20 (*) 140 5 ←5 − −
3 11 (80) 11 (60) 12 (10) 150 0 0 0 1
Toledo 18 (*) 8 (160) 13 (*) 160 ←5 − − −
Demand 220 220 220
Cost difference
I 1 3 2
II 1 3 2III 1 ↑3 2IV 1 − ↑2
Cost Difference
Total cost 10*210+12*140+11*80+11*60+12*10+8*160 = $ 6720
Solution matrix
A B C Supply1 * * 210 2102 140 * * 1403 80 60 10 150
Toledo * 160 * 160
Demand 220 220 220 Demand/Supply = 660
For Cincinnati location
Input matrix
A B C Suppl
y
1 10 14 10 210 2 12 17 20 140 3 11 11 12 150
Cincinnati
7 17 13 160
Demand 220 220 220
Supply = Demand = 660
Step using VAM
A B C Supply
I II III IV
1 10(*) 14 (*) 10 (210) 210 0 0 ←4
−
2 12 (60) 17 (80) 20 (*) 140 5 ←5 3 3
3 11 (*) 11 (140)
12 (10) 150 0 0 1 1
Toledo 7 (160) 17 (*) 13 (*) 160 ←6 − − −
Demand
220 220 220
Cost difference
I 3 3 2
II 3 3 2III − 3 2IV − 6 ↑8
Total cost: 10*210+12*60+17*80+12*10+11*140+7*160= $ 6960
Solution matrix
A B C Supply 1 * * 210 210 2 60 80 * 140 3 * 140 10 150 Toledo 160 * * 160 Demand 220 220 220
Demand/Supply = 660
Cost Difference
Decision: Toledo location would provide the lower transportation cost such that management should select Toledo location for manufacturing.
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