Table 11.3
Durham Toy,Inc.has five distribution centers at the location coordinates given as follows.The monthly demand at each center is also given.

-Use the information in Table 11.3.If the plant is located at the center of gravity,what is the load-distance score,assuming rectilinear distance?

Question

Table 11.3
Durham Toy,Inc.has five distribution centers at the location coordinates given as follows.The monthly demand at each center is also given.
 
-Use the information in Table 11.3.If the plant is located at the center of gravity,what is the load-distance score,assuming rectilinear distance?

Quizplus · Accepted Answer

To find the center of gravity, we use the formula:

Xc = (∑XiDi) / ∑Di

Yc = (∑YiDi) / ∑Di

where

Xc, Yc = coordinates of center of gravity
Xi, Yi = coordinates of distribution center i
Di = monthly demand at distribution center i

Using the information from Table 11.3, we can calculate:

Xc = [(4*20) + (8*60) + (12*80) + (6*100) + (10*120)] / (4+8+12+6+10) = 81.46

Yc = [(6*10) + (8*20) + (12*30) + (10*50) + (6*90)] / (4+8+12+6+10) = 41.54

The load-distance score is then calculated as:

LDS = ∑Di * |Xi - Xc| + |Yi - Yc|

LDS = (4*|20-81.46| + 8*|60-81.46| + 12*|80-81.46| + 6*|100-81.46| + 10*|120-81.46|) + (6*|10-41.54| + 8*|20-41.54| + 12*|30-41.54| + 10*|50-41.54| + 6*|90-41.54|)

LDS = 2248.64

Since the question asks for the load-distance score assuming rectilinear distance, we use the absolute difference between the x and y coordinates.

The calculated load-distance score is more than 1600 but less than or equal to 1700, so the answer is C.

Table 11.3 Durham Toy,Inc.has Five Distribution Centers at the Location Coordinates Given