Existing facilities are located as follows: P_1 = (4, 4), P_2 = (4, 10), P_3 = (

Question

Existing facilities are located as follows: P_1 = (4, 4), P_2 = (4, 10), P_3 = (6, 5), P_4 = (10, 5), P_5 = (10, 9), and P_6 = (12, 3). It is desired to locate one new machine with respect to the existing facilities. Travel between facilities is along a rectilinear aisle structure. The amount of item movement between the new facility and each existing facility is given as w_1 = 4, w_2 = 4, w_3 = 2, w_4 = 3, w_5 = 5, and w_6 = 6. Where should the new facility be located to minimize distance traveled? Plot contour lines and rank the following potential locations: A = (4, 6), B = (8, 8), C = (8, 5), D = (10, 3). Four hospitals located within a city are cooperating to establish a centralized blood-bank facility that will serve the hospitals. The new facility is to be located such that distance traveled is minimized. The hospitals are located as follows: P_1 = (5, 10), P_2 = (7, 6), P_3 = (4, 2) and P_4 = (16, 3). The number of deliveries to be made per year between the blood-bank facility and each hospital is estimated to be 450, 1200, 300, and 1500, respectively. Assuming rectilinear travel determine the optimum location. What assumption must be made concerning the deliveries of blood? Is it reasonable to expect delivery trips will always be to only one hospital when a delivery is made?

Explanation / Answer

4.2)

let the location is at O (x,y)

in excel x = A1 , y = B1

Minimize

Z = 4OP1 + 4OP2 + 2 OP3 + 3 OP4 + 5OP5 + 6 OP6

= (4*SQRT((A1 - 4)^2 + (B1- 4)^2)+4*SQRT((A1 - 4)^2 + (B1- 10)^2)+ 2 * SQRT((A1 - 6)^2 + (B1- 5)^2) +3 * SQRT((A1 - 10)^2 + (B1- 5)^2) + 5* SQRT((A1 - 10)^2 + (B1- 9)^2) +6* SQRT((A1 - 12)^2 + (B1-3)^2))

nearest is (8,5)

hence option C) is correct

4.3)

let the optimum location be (x,y)

minimize

Z = 450*sqrt((x-5)^2 + (y-10)^2) + 1200*sqrt((x-7)^2 + (y-6)^2) + 300*sqrt((x-4)^2 + (y-2)^2) + 1500*sqrt((x-16)^2 + (y-3)^2)

solving this in excel we get

x = 7 , y = 6

Please rate

8.85893 5.723413 Z 98.75678

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