XYZ company manufactures toys in three different countries: S1, S2 and S3. It sells these toys in four countries: A, B, C and D. The following table shows the total requirement for each type of toy by country of manufacture:
|
|
A
|
B
|
C
|
D
|
|
S1
|
10
|
40
|
60
|
10
|
|
S2
|
4
|
15
|
21
|
36
|
|
S3
|
31
|
20
|
14
|
16
|
XYZ is looking at two potential options:
Option 1. Direct shipment. Each factory directly ships its toys to the destination country. In this case, transportation cost is $1.50 per lb-mile. Assume that each toy weighs 1 lb (one lb-mile indicates transportation effort to ship one pound weight over one mile distance).
Option 2. Via warehouse. In this case, a central warehouse is established. All shipments from S1, S2 and S3 go to the central warehouse. In the central warehouse, toys are repackaged by destination - that is, all toys needed for A are consolidated and shipped to A. Cost of transportation for in-bound units to the central warehouse is $0.85 per lb-mile, and outbound transportation cost is $1.30 per lb-mile.
The (x, y) coordinates for the factories and customers are given below:
|
|
A
|
B
|
C
|
D
|
S1
|
S2
|
S3
|
|
x- coordinate
|
7
|
8
|
13
|
20
|
5
|
10
|
1
|
|
y- coordinate
|
4
|
15
|
12
|
12
|
13
|
14
|
5
|
Answer the following questions:
What is the total cost if direct shipments are used?
Should XYZ establish a central warehouse? If so, where should it be located? Justify or support your analysis with adequate computational analysis.