Question

LaRosa Machine Shop (LMS) is studying where to locate its tool bin facility on the shop floor. The locations of the five production stations appear in figure shown below.

	Location
Station	X	Y	Demand
Fabrication	1.0	4.0	12
Paint	1.0	2.0	19
Subassembly 1	2.5	2.0	13
Subassembly 2	3.0	5.0	7
Assembly	4.0	4.0	12

In an attempt to be fair to the workers in each of the production stations, management has decided to try to find the position of the tool bin that would minimize the sum of the distances from the tool bin to the five production stations. We define the following decision variables:

X = horizontal location of the tool bin

Y = vertical location of the tool bin

We may measure the straight line distance from a station to the tool bin located at (X,Y) by using Euclidean (straight-line) distance. For example, the distance from fabrication located at the coordinates (1,4) to the tool bin located at the coordinates (X,Y) is given by .

(a)	Suppose we know the average number of daily trips made to the tool bin from each production station. The average number of trips per day are 12 for fabrication, 19 for Paint, 13 for Subassembly 1, 7 for Subassembly 2 and 12 for Assembly. It seems like we would want the tool bin closer to those stations with high average numbers of trips. Develop a new unconstrained model that minimizes the sum of the demand-weighted distance defined as the product of the demand (measured in number of trips) and the distance to the station.
	Min:
(b)	Solve the model you developed in part (a).
	If required, round your answer to six decimal places. Do not round intermediate calculation.
	X =
	Y =
(c)	The solution to the un-weighted model is X = 2.230 and Y = 3.349. Comment on the differences between the unweighted distance solution given and the demand-weighted solution found in part (b).
	The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

Solution:

a)

The distance between two points by eudidion distance formula is,

  

Demand	X	Y	Distance of each station
12	1	4
24	1	2
13	2.5	2
7	3	5
22	4	4

b)

X=2.09191706177165

Y=2.85182622020003

Using Excel Solver,

c)

Comparing the unweighted distance solution given and the demand-weighted solution we obtained we get, the horizontal location of the tool bin and vertical location of the tool bin for demand weight is less than the unweighted distance.