Question

Problem B GRD will be producing the new product described in Problem A in three plants and has initial plans to sell the product in five major metropolitan markets. Information about the Plant and Market locations, transportation rates and volume to be produced /demanded is shown in the table below Grid Coordinates Plants Rate" Tons PI 1.00 5,000 Horiz Vert 900 100 P2 1.25 4,000 P3 1.20 3,000 250 800 450 1000 Markets MI 2.05 2,000 200 50 M2 2.50 3,000 M3 2.70 2,000 M4 3.00 3,000 MS 3.30 2,000 250 120 120 280 300 300 400 350 |* Rate in S/ton-mile Questions for Problem B 1. To the nearest whole number, what are the grid coordinates of the ton-mile center of mass? (10 pts) 2. If outbound transportation rates triple from P2, what are the new grid coordinates of the ton-mile center of mass? (10 pts)

Answer 1

1.

The Grid technique helps us to locate a facility based on least cost. Eg in this case we can find a warehouse location (between plant and market)

The inputs are the following:

• Markets
• Volume of goods shipped
• Shipping costs

The center of mass shows the location:

center of mass = (238,450)

The center of mass Er*s*d +ER*M*D Σr*s +ΣR M

C D G H 1 Grid co-ordinates Calculations 2. Horizontal Vertical Plants Rate Tons d1 d2 ds'd1 r's d2 4. P1 5000 100 5 900 D5*E5*F5 D5*E5 G5 -D5'ES 1 =D6 * E6 " G6 - D6 ' E6 P2 40С 6 1.25 250 800 =D6*E6" F6 p3 D7 E7 F7 - D7 E7 7 1.2 3С 450 1000 D7 E7 G7 - SUM ( E5 E7 ) SUM(U5J7) - SUM(K5 K7) 8 SUM(I5:17) markets R Dt D2 R*M*D1 R*M*D2 R*M 10 D11 E11 G11 M1 D11 E11 F11 D11 E11 11 50 2.05 2000 200 -D12 " E12 M2 D12 E12 G12 12 3000 120 D12 E12 F12 2.5 250 D13 E13 13 ма =D13 E13 F13 2000 280 D13 E13 G13 2.7 120 -014'E14 F14 14 M4 D14 E14 G14 - D14 " E14 3000 300 15 MS D15 E15 F15 D15 E15 G15 D15 E15 АОО 3 5 2000 350 - -SUM( 1 11 : 115) 16 - SUM (K11:K15 SUM ( E11 : E15 ) -SUMU11115) 17 18 Numerator EI8+116 EJ8+16 Ersd+ER*MD 19 20 - K8+K16 Denominator 21 -квнк16 Ets+ERM 22 Grid center =118/ J21 23 =118/121 ші ший

L C D F G H J K 1 Grid co-ordinates Calculations 2 Horizontal Plants Vertical Rate Tons 3 d1 d2 r*s*d1 r*s*d2 r*s S 500000 P1 5000 100 900 4500000 5000 5 P2 1.25 4000 250 800 1250000 4000000 5000 6 1620000 P3 1.2 3000 450 1000 3600000 3600 7 12000 3370000 12100000 13600 8 markets R*M*D1 R M*D2 R*M R M D1 D2 10 M1 2.05 2000 50 200 205000 820000 4100 11 M2 900000 7500 2,5 3000 120 250 1875000 12 M3 2.7 2000 280 120 1512000 648000 5400 13 2700000 2700000 M4 3000 300 300 9000 14 M5 3.3 2000 350 400 2310000 2640000 6600 15 7627000 12000 8683000 32600 16. 17 Numerator 10997000 20783000 18 Er*s*dER*M*D 19 20 46200 46200 Denominator 21 Σr*s +ΣR*M 22 Grid center 238.03 449.85 23 LON

2.

New outbound rate at P2= $ 3.75

New center of mass = (240,512)

Home Insert Page Layout Formulas Data Review View Developer Security Warning Automatic update of links has been disabled Options... fe L25 N P Q R S T U V W X 1 Grid co-ordinates Calculations 2 Plants Horizontal Vertical Rate Tons d1 d2 r*s*d1 r*s*d2 r*s 4 r S 4500000 P1 1 5000 100 900 500000 5000 5 P2 3.75 4000 250 800 3750000 12000000 15000 6 1620000 P3 1.2 3000 450 1000 3600000 3600 7 23600 12000 5870000 20100000 markets R*M D1 R*M*D2 R*M R M D1 D2 10 2000 M1 2.05 50 200 205000 820000 4100 11 M2 2,5 3000 120 250 900000 1875000 7500 12 2,7 M3 2000 280 120 1512000 648000 5400 13 M4 3000 300 300 2700000 2700000 9000 14 2640000 M5 3.3 2000 350 400 2310000 6600 15 12000 7627000 8683000 32600 16 17 Numerator 13497000 28783000 18 Er*s*d ER*M*D 19 20 Denominator 56200 56200 21 Σrs +ΣR*Μ 22 Grid center 240.16 512.15 23