S O L V E D P R O B L E M
Cool Air, a manufacturer of automotive air conditioners, currently
produces its XB-300 line at three
different locations: Plant A, Plant B, and Plant C. Recently
management decided to build all compressors,
a major product component, in a separate dedicated facility, Plant D.
Using the centroid method and the information displayed in Exhibits
TN11.8 and TN11.9, determine
the best location for Plant D. Assume a linear relationship between
volumes shipped and
shipping costs (no premium charges).
Solution
d1x = 150 d1y = 75 V1 = 6,000
d2x = 100 d2y = 300 V2 = 8,200
d3x = 275 d3y = 380 V3 = 7,000
Cx =
_di x Vi
_Vi =
(150 × 6,000) + (100 × 8,200) + (275 × 7,000)
6,000 + 8,200 + 7,000 = 172
La Quinta implemented the model on a spreadsheet and routinely uses
the spreadsheet to screen
potential real estate acquisitions. The founder and president of La
Quinta has accepted the model?s
validity and no longer feels obligated to personally select the sites.
This example shows that a specific model can be obtained from the
requirements of service organizations
and used to identify the most important features in site selection. ?

Plant Location Matrix
400
300
200
100
100 200 300 400
Plant B (100, 300)
Plant C (275, 380)
Plant A (150, 75)
exhibit TN11 . 9 Quantity of Compressors Required by Each Plant
COMPRESSORS REQUIRED
PLANT PER YEAR
A 6,000
B 8,200
C 7,000

Cy =
_di yVi
_Vi =
(75 × 6,000) + (300 × 8,200) + (380 × 7,000)
21,200 = 262.7
Plant D[Cx, Cy] = D[172, 263]

P R O B L E M S
1 Refer to the information given in the solved problem. Suppose
management decides to shift
2,000 units of production from Plant B to Plant A. Does this change
the proposed location of
Plant D, the compressor production facility? If so, where should Plant
D be located?

2 A small manufacturing facility is being planned that will feed parts
to three heavy manufacturing
facilities. The locations of the current plants with their coordinates
and volume requirements
are given in the following table:
PLANT LOCATION COORDINATES (x, y) VOLUME (PARTS PER YEAR)
Peoria 300, 320 4,000
Decatur 375, 470 6,000
Joliet 470, 180 3,000
Use the centroid method to determine the best location for this new facility.
462 section 3 SUPPLY CHAIN DESIGN
exhibit TN11 . 8 Plant Location Matrix
400
300
200
100
100 200 300 400
Plant B (100, 300)
Plant C (275, 380)
Plant A (150, 75)
exhibit TN11 . 9 Quantity of Compressors Required by Each Plant
COMPRESSORS REQUIRED
PLANT PER YEAR
A 6,000
B 8,200
C 7,000

4 Rent?R Cars is a multisite car rental company in the city. It is
trying out a new ?return the car
to the location most convenient for you? policy to improve customer
service. But this means
that the company has to constantly move cars around the city to
maintain required levels of
vehicle availability. The supply and demand for economy cars, and the
total cost of moving
these vehicles between sites, are shown below.
a. Find the solution that minimizes moving costs using Microsoft® Excel.
b. What would you have to do to the costs to assure that A always
sends a car to D as part of
the optimal solution?

S O L V E D P R O B L E M
Cool Air, a manufacturer of automotive air conditioners, currently
produces its XB-300 line at three
different locations: Plant A, Plant B, and Plant C. Recently
management decided to build all compressors,
a major product component, in a separate dedicated facility, Plant D.
Using the centroid method and the information displayed in Exhibits
TN11.8 and TN11.9, determine
the best location for Plant D. Assume a linear relationship between
volumes shipped and
shipping costs (no premium charges).
Solution
d1x = 150 d1y = 75 V1 = 6,000
d2x = 100 d2y = 300 V2 = 8,200
d3x = 275 d3y = 380 V3 = 7,000
Cx =
_di x Vi
_Vi =
(150 × 6,000) + (100 × 8,200) + (275 × 7,000)
6,000 + 8,200 + 7,000 = 172
La Quinta implemented the model on a spreadsheet and routinely uses
the spreadsheet to screen
potential real estate acquisitions. The founder and president of La
Quinta has accepted the model?s
validity and no longer feels obligated to personally select the sites.
This example shows that a specific model can be obtained from the
requirements of service organizations
and used to identify the most important features in site selection. ?

Plant Location Matrix
400
300
200
100
100 200 300 400
Plant B (100, 300)
Plant C (275, 380)
Plant A (150, 75)
exhibit TN11 . 9 Quantity of Compressors Required by Each Plant
COMPRESSORS REQUIRED
PLANT PER YEAR
A 6,000
B 8,200
C 7,000

Cy =
_di yVi
_Vi =
(75 × 6,000) + (300 × 8,200) + (380 × 7,000)
21,200 = 262.7
Plant D[Cx, Cy] = D[172, 263]

P R O B L E M S
1 Refer to the information given in the solved problem. Suppose
management decides to shift
2,000 units of production from Plant B to Plant A. Does this change
the proposed location of
Plant D, the compressor production facility? If so, where should Plant
D be located?

2 A small manufacturing facility is being planned that will feed parts
to three heavy manufacturing
facilities. The locations of the current plants with their coordinates
and volume requirements
are given in the following table:
PLANT LOCATION COORDINATES (x, y) VOLUME (PARTS PER YEAR)
Peoria 300, 320 4,000
Decatur 375, 470 6,000
Joliet 470, 180 3,000
Use the centroid method to determine the best location for this new facility.
462 section 3 SUPPLY CHAIN DESIGN
exhibit TN11 . 8 Plant Location Matrix
400
300
200
100
100 200 300 400
Plant B (100, 300)
Plant C (275, 380)
Plant A (150, 75)
exhibit TN11 . 9 Quantity of Compressors Required by Each Plant
COMPRESSORS REQUIRED
PLANT PER YEAR
A 6,000
B 8,200
C 7,000

4 Rent?R Cars is a multisite car rental company in the city. It is
trying out a new ?return the car
to the location most convenient for you? policy to improve customer
service. But this means
that the company has to constantly move cars around the city to
maintain required levels of
vehicle availability. The supply and demand for economy cars, and the
total cost of moving
these vehicles between sites, are shown below.
a. Find the solution that minimizes moving costs using Microsoft® Excel.
b. What would you have to do to the costs to assure that A always
sends a car to D as part of
the optimal solution?

From\To    D     E    F    G        Supply
  A        $9    $8   $6    $5       50
  B        9      8    8     0       40
  c        5      3    3     10      75
  Demand   50     60   25    30      165\165
   

P R O B L E M S
1 Demand for stereo headphones and CD players for joggers has caused
Nina Industries to grow
almost 50 percent over the past year. The number of joggers continues
to expand, so Nina
expects demand for headsets to also expand, because, as yet, no safety
laws have been passed to
prevent joggers from wearing them. Demand for the stereo units for
last year was as follows:
DEMAND DEMAND
MONTH (UNITS) MONTH (UNITS)
January 4,200 July 5,300
February 4,300 August 4,900
March 4,000 September 5,400
April 4,400 October 5,700
May 5,000 November 6,300
June 4,700 December 6,000
a. Using least squares regression analysis, what would you estimate
demand to be for each
month next year? Using a spreadsheet, follow the general format in
Exhibit 13.13. Compare
your results to those obtained by using the forecast spreadsheet function.
b. To be reasonably confident of meeting demand, Nina decides to use
three standard errors of
estimate for safety. How many additional units should be held to meet
this level of confidence?
FORECASTING chapter 13 549

3 The following tabulations are actual sales of units for six months
and a starting forecast in January.
a. Calculate forecasts for the remaining five months using simple
exponential smoothing with
? = 0.2.
b. Calculate MAD for the forecasts.
ACTUAL FORECAST
January 100 80
February 94
March 106
April 80
May 68
June 94






5 Sales data for two years are as follows. Data are aggregated with
two months of sales in each
?period.?
MONTHS SALES MONTHS SALES
January?February 109 January?February 115
March?April 104 March?April 112
May?June 150 May?June 159
July?August 170 July?August 182
September?October 120 September?October 126
November?December 100 November?December 106


20 Your manager is trying to determine what forecasting method to use.
Based upon the following
historical data, calculate the following forecast and specify what
procedure you would utilize.
ACTUAL ACTUAL
MONTH DEMAND MONTH DEMAND
1 62 7 76
2 65 8 78
3 67 9 78
4 68 10 80
5 71 11 84
6 73 12 85
a. Calculate the simple three-month moving average forecast for periods 4?12.
b. Calculate the weighted three-month moving average using weights of
0.50, 0.30, and 0.20
for periods 4?12.
c. Calculate the single exponential smoothing forecast for periods
2?12 using an initial forecast
(F1) of 61 and an ? of 0.30.
d. Calculate the exponential smoothing with trend component forecast
for periods 2?12 using
an initial trend forecast (T1) of 1.8, an initial exponential
smoothing forecast (F1) of 60, an
? of 0.30, and a ? of 0.30.
e. Calculate the mean absolute deviation (MAD) for the forecasts made
by each technique in
periods 4?12. Which forecasting method do you prefer?