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.