Question

You work for Best Buy, which is looking for a new warehousing location given their push for a consolidation of their warehouses given their recent purchase of whole foods. The warehouse is for the west coast, and is meant to be a distribution center that services other distribution centers in the region. Given the following cities and volumes, please answer the questions below.

City	Volume
Las Vegas	5,000 units
Salt Lake City	4,000 units
San Francisco	8,000 units
San Diego	4,000 units
Los Angeles	9,000 units
Seattle	7,000 units

1. Using the information above, how would you go about placing these locations on a coordinate grid?
2. Using the center of gravity method, what is the closest town or city to the location the method tells you to pick?
3. Amazon predicts that growing populations in Las Vegas, Salt Lake City, and San Diego will bolster demand in the future. Assuming demand for each of these cities increases by 5,000 units over current demand, where would the new center of gravity be?

Answer 1

a.

The best approach will be to collect the latitudes and longitude values and use them as x and y axis values for each of the locations. Once we have these values we can easily place them on a coordinate grid. Next we could use methods such as center of gravity or Euclidean distance to determine the ideal location for the warehouse.

b.

The calculated center of gravity method solution is shown below.

City	Volume	X	Y		X*Volume	Y*Volume
Las Vegas	5000	36.16	115.13		180800	575650
Sal Lake City	4000	40.76	111.89		163040	447560
San Francisco	8000	37.77	122.41		302160	979280
San Diego	4000	32.71	117.16		130840	468640
Los Angeles	9000	34.05	118.24		306450	1064160
Seattle	7000	47.6	122.33		333200	856310
Sum	37000				1416490	4391600
Ideal location		38.28351	118.6919

The closest town or city is Los Angeles. This is due to the volume of business offered by the city.

c.

If the demand in these three cities increase by 5000 then the modified COG result will be as shown below

City	Volume	X	Y		X*Volume	Y*Volume
Las Vegas	10000	36.16	115.13		361600	1151300
Sal Lake City	9000	40.76	111.89		366840	1007010
San Francisco	8000	37.77	122.41		302160	979280
San Diego	9000	32.71	117.16		294390	1054440
Los Angeles	9000	34.05	118.24		306450	1064160
Seattle	7000	47.6	122.33		333200	856310
Sum	52000				1964640	6112500
Ideal location		37.78154	117.5481