2 business location

7/29/2019 2 Business Location

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Business Location Decisions

Dr. Everette S. Gardner, Jr.


2/19

Business Location 2

Complexity of the location problem

If there are N potential facility sites, there are (2^N) 1different geographical configurations.

Example: 4 potential sites (A,B,C,D)

(2^4) 1 = 15

Number of Number of

facilities used Alternatives Alternatives1 A,B,C,D 4

2 AB, AC, AD, BC, 6

BC, CD

3 BC, ABD, ACD, 4

BCD

4 ABCD 1

15


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Business Location 3

Complexity of the location problem(cont.)

Number of Number of alternative

potential sites geographical configurations

5 31

10 1,023

20 1,048,575

50 > 10^5

100 > 10^30


4/19

Business Location 4

100%

Customer service level (%)

Total distribution costs

Transportation costs

0 0Number of warehouses

Cost-service tradeoffsin logistics planning

Customerserviceaxis:

%o

fdeman

dfilledwithin

giventimeframe

Dollarcostaxis


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Business Location 5

Analog model for facility location

Center.xls


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Business Location 6

Dimensional analysis in locationdecisions

Location decisions are based on two typesof information:

Tangibles (objective or quantitative)

Intangibles (subjective) Dimensional analysis helps:

Measure and evaluate intangibles

Combine tangible and intangiblemeasurements into an overall value index foreach location


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Business Location 7

Building a dimensional analysis model

1. List the decision factors2. Score the decision factors:

Natural units for tangible factors (usually financial)

Subjective scores for intangibles, scale of 1 to 10

1 represents the ideal

10 represents a disaster

3. Weight each decision factor (scale of 1 to 5)

4. Compute weighted ratios

(Score for option A / Score for option B)^Weight

5. Compute preference number

Product of weighted ratios

Dimensional.xls


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Business Location 8

Basic calculations in dimensional

analysis: U.S. Air vs. Alaska airlines

On-Time Denied Mishandled Customer

Arrival % Boardings Baggage Complaints

US Airways 0.782 0.34 3.86 1.87

Alaska Airlines 0.690 1.36 3.00 1.27

Ratio (US Air/Alaska) 1.13 0.25 1.29 1.47

Weight 8.63 -8.03 -7.92 -7.17

RatioWeight 2.95 68,319.04 0.14 0.06

Preference number = 2.95 x 68,319.04 x 0.14 x 0.06 = 1,705.48


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Business Location 9

Break-even analysis

Break-even Total fixed costs

point = Unit Variable cost

in units price per unit

Example: FC = $25,000, P = $20, VC = $10

BE = $25,000 = 2,500 units

20 10


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Business Location 10

Break-even analysis (cont.)

$

Sales revenue

Profit

1000 2000 3000 4000 5000

Units of output

0

20000

40000

60000

80000

100000

Totalcosts

Variablecosts

FixedcostsLosses

Break-evenpoint


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Determining market areas

Laid down costs are the delivered costs of a

product.

LDC = P + RX

WhereP = Production cost/unit

R = Transportation rate

X = Distance


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Determining market areas (cont.)

Market boundaries are at points where lines ofequal LDC intersect:

A

$2

$4$6

$8

x

y

z$4

$2

$6

B

C

$2$4

$6$8

N


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LP models for location decisions

Simple transportation model

Sources Destinations


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LP models for location decisions(cont.)

Transshipment model

Sources Transshipment Destinationspoints

Both models can be used to plan shipments over multipletime periods


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Preliminary steps in locating serviceoutlets

1. Group population into geographic areas (usually usecensus blocks)

2. Use demographic data to determine probable facilityusage for each potential location

3. Choose objective function:

A. Maximize utilization

B. Minimize distance per capita

C. Minimize distance per visitD. Minimize average reduction in number of

visits made due to location decision

E. Weighted measures


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Figure 7. A hypothetical medical service area with 32 census blocks andthree cities. City populations are (approximately) A = 17,000, B = 9,000,and C = 13,000. Distances on x-y axes are in miles.

67

11

10

20

Y

X

-10

21

22

23

-10 10 2620

2

35 1

4

9

13

City A 108

15

12 18

14 2530

17

19

2029

32 3116 24

26 27

City C

City B


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TABLE 12Location coordinates in miles for three criteria

and different numbers of centers*

Criterion

Center number (1) Maximize (2) Minimize distance (4) Minimize distance

utilization per capita per encounter

x y x y x y

I With 1 center1 21.00 -3.00 0.64 1.20 -8.70 10.10

II With 2 centers

1 21.4 -3.7 17.6 -3.30 18.50 -3.30

2 -9.89 10.4 9.89 10.4 -9.90 10.40

III With 3 centers

1 22.40 -3.1 21.52 -2.78 22.30 -3.20

2 -10.16 10.40 -10.20 10.40 -10.20 10.40

3 3.63 -2.75 3.60 -2.80 3.60 -2.80

* See figures 7 and 8 for locations of coordinates.

** Determined only for the first criterion.


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TABLE 12Location coordinates in miles for three criteria

and different numbers of centers* (cont.)

Criterion

Center number (1) Maximize (2) Minimize distance (4) Minimize distance

utilization per capita per encounter

x y x y x y

IV With 4 centers

1 22.40 -3.14 22.00 -3.50 21.23 -3.082 -10.20 10.40 -10.10 10.30 -9.80 10.40

3 3.59 -2.78 2.69 -4.80 3.61 - 2.70

4 11.32 -2.25 3.76 3.04 -11.35 3.00

V With 5 centers**

1 22.40 -3.10

2 -9.72 10.61

3 3.24 -3.194 -11.62 3.24

5 11.04 -2.00

* See figures 7 and 8 for locations of coordinates.

** Determined only for the first criterion.


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CityA

Center

Criterion governingcenter locations

Figure 8. Location of one center based on three different criteria.

3

2

1

15

-5

-10 City B

City C

10

5

-15 -10 -5 5 10 15 20 25

2 business location

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