Question

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Zone Technology is a toy manufacturer that makes innovative simple toys for fast food restaurants around the world. As 3-D printing technology has become much cost-effective, the company plans to set up a giant centralized 3-D printing factory to serve the market. The company buys printing materials and supplies from 2 suppliers and sends finished products to 4 warehouses around the world. The table below gives the location and shipping costs per unit information. Please use Gravity Location Model from our textbook to solve the best location for this centralized factory. Sources/Markets $/(unit Mile) unit Coordinates (Fn) Dn Sources Jefferson City 1.5 500 700 1200 Jacksonville 0.3 4720 250 600 yn 500 Markets Warehouse A Warehouse B Warehouse C Warehouse D 1500 450 175 600 1050 800 1200 300 975 1.5 925 Please copy paste the Y-coordinate of the new factory from the Excel worksheet.

Answer 1

Optimization model:

D BC Xn Yn E Fn F Dn Fn * dn * Dn A 1 2 Centralized factory 3 Jefferson City 4 Jacksonville 5 Warehouse A 6 Warehouse B 7 Warehouse C 8 Warehouse D 9 700 250 600 1050 800 925 1200 600 500 1200 300 975 =SQRT($B$2-B3)2+($C$2-C3) 2) 1.5 =SQRT($B$2-B4) 2+($C$2-C4) 2) 0.3 =SQRT(($B$2-B5) 2+($C$2-C5) 2) 1.5 =SQRT(($B$2-B6) 2+($C$2-C6) 2) 1.5 =SQRT(($B$2-B7) 2+($C$2-C7) 2) 1.5 =SQRT(($B$2-B8) 2+($C$2-C8) 2) 1.5 500 =D3*E3*F3 4720 =D4*64*F4 230 =D5*E5*F5 1500 =D6*E6*F6 450 =D7*E7*F7 175 =D8*E8*F8 Total cost =SUM(G3:58)

Solver inputs:

Set Objective: $G$9 To: O Max Min value of: By Changing Variable Cells: $B$2:$C$2 Subject to the Constraints: Add Change Delete Reset All Load/Save Make Unconstrained variables Non-Negative Select a Solving Method: GRG Nonlinear Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve close

Solution:

	Xn	Yn	dn	Fn	Dn	Fn * dn * Dn
Centralized factory	862.30	1038.76
Jefferson City	700	1200	228.78	1.5	500	171584.08
Jacksonville	250	600	753.27	0.3	4720	1066629.26
Warehouse A	600	500	599.21	1.5	230	206729.03
Warehouse B	1050	1200	247.45	1.5	1500	556764.68
Warehouse C	800	300	741.38	1.5	450	500430.44
Warehouse D	925	975	89.42	1.5	175	23473.69
					Total cost	2525611.19

So, the location of the centralized factory is X = 862.30 and Y = 1038.76