The Hernandez Company has decided to open a single warehouse to meet the rising
ID: 379640 • Letter: T
Question
The Hernandez Company has decided to open a single warehouse to meet the rising market demands of its four markets which the company refers to as North, South, East, and West. The locations and demands of these four markets are provided in the table below. Distances are measured using rectilinear distance.
1. If the warehouse must be located at one of the four market locations, which of the four locations is most desirable? Use quantitative analysis to support your recommendation?
2. If the facility were to be located at a point that is central to the four markets as defined by the center of gravity of the four market locations and their corresponding demands, would that be a better location? Explain.
Market Coordinates Demand North (9,7) South (5,14) East (4,5) West (8,5) 10 10 15 14Explanation / Answer
1.
Let's calculate the distance of Markets w.r.t all markets one by one.
Using the formula for rectilinear Distance = (x2 - x1) + (y2 - y1)
Distance w.r.t. North Market :
South : 4 + 7 = 11
East : 5 + 2 = 7
West : 1+ 2 = 3
Total weighted distance = 11(10) + 7(15) + 3(14) = 257
Distance w.r.t. South Market :
North : 4 + 7 = 11
East : 1 + 9 = 10
West : 3 + 9 = 12
Total weighted distance = 11(10) + 10(15) + 12(14) = 428
Distance w.r.t. East Market :
North : 5 + 2 = 7
South : 1 + 9 = 10
West : 4 + 0 = 4
Total weighted distance = 7(10) + 10(10) + 4(14) = 226
Distance w.r.t. West Market :
North : 1+ 2 = 3
South : 3 + 9 = 12
East : 4 + 0 = 4
Total weighted distance = 3(10) + 12(10) + 4(15) = 210
Hence, the warehouse should be located at the West Market location.
2.
To calculate central position for warehouse :
Hence, to calculate the location of Warehouse :
X-Coordinate = XNDN + XSDS + XEDE + XWDW / DN + DS + DE + DW
= 9(10) + 5(10) + 4(15) + 8(14)/ (10 + 10 + 15 +14)
= 312/49 = 6.36
Y-Coordinate = YNDN + YSDS + YEDE + YWDW / DN + DS + DE + DW
= 7(10) + 14(10) + 5(15) + 5(14)/ (10 + 10 + 15 +14)
= 355/49 = 7.24
Hence, the warehouse should be placed at (6.36, 7.24)
Market X Coordinate Y Coordinate Demand North 9 7 10 South 5 14 10 East 4 5 15 West 8 5 14Related Questions
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