Location and Distribution
Henry C. Co
Technology and Operations Management,
California Polytechnic and State University
Contents
Location
I.


Importance of Location
Systematic Decision Process

Factor Rating




Distribution
II.


iii.
Cost-volume Analysis
Locational Breakeven Analysis
Single Facility Location
Multi-Facility Location
The Transportation Problem
The Transportation Problem with Lost Sales
It is not about time!
Location and Distribution (Henry C. Co)
2
Importance of Location
“Location, Location, Location!”

Location decisions for residential
homes are important because …



They affect travel time to work, to school,
to recreational centers, and to shopping
malls.
A home in a good school district is
particularly important for most parents
with school-age children.
A home in a “bad” neighborhood means
the residents are exposed to higher risk of
crimes and drugs, while a home is a “good”
neighborhood is a source of pride and
status.
Location and Distribution (Henry C. Co)
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
Location decisions are important to business
organizations because …


They affect the cost of doing business, and the
flow of goods and services.
 The faster the flow of goods and service in one
direction, the lower the inventory, and the quicker
funds ($$$) flow back in the reverse direction.
They commit the organization to long lasting
financial, employment, and distribution patterns.
 For retail outlets, location affects the demand for
their products/services.
 For labor-intensive operations, labor costs may
force an organization to relocate its operations to
locations where wages are lower.
Location and Distribution (Henry C. Co)
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

Location decisions are either demandpulled, supply-pushed, or more
frequently, both demand-pulled and
supply pushed.
Demand-pulled

Market-related factors such as the location
of customers, the location of the
competition, the need for room for
expansion, and the community’s attitude
towards the organization.
Location and Distribution (Henry C. Co)
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
Supply-pushed location factors

Based on the cost of doing business. The cost of
doing business may be tangible or intangible.
 Tangible costs include the cost of site and
construction, the availability and costs of labor,
transportation cost (proximity to suppliers and
markets), utilities (availability and costs), taxes,
and real estate (site acquisition, preparation and
construction) costs.
 Intangible costs include:

Zoning and legal regulations, community attitudes,
proximity to parent company’s facilities, expansion
potential, labor climate, training and employment
services, and the quality of life (schools and churches,
recreation and cultural attractions, amount and type
of housing available) are examples of important
location factors that are difficult to quantify.
Location and Distribution (Henry C. Co)
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Technology-Based Firms

Tend to cluster around these organizations.

Eventually developed into regional networks of
expertise.




Stanford University, which spawned Silicon Valley
MIT which spawned Route 128 in Boston
In the United Kingdom, Imperial College and
Cambridge which spawned Science Parks.
Large well-established firm also serve as incubators.



Xerox PARC and Bell Laboratories spawned Fairchild
Semiconductor which in turn led to numerous spin-offs
including Intel, Advanced Memory Systems, Teledyne, and
Advanced Micro-Devices.
Engineering Research Associates (ERA) led to more than 40
new firms, including Cray, Control Data Systems, Sperry and
Univac.
Technology-based firms cluster around their
‘incubator’ organizations to gain financial and
technical support.
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International Locations

Trade quotas, language, culture,
government stability and cooperation,
monetary system, infrastructure, etc.
can sometimes force a multinational
corporation to divest its interest in a
country.
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Systematic Decision Process
Quantitative Approaches
Qualitative Approaches
Integrating Qualitative & Quantitative Data
1.
2.
Define the location objectives and associated
constraints.
Identify the relevant decision criteria.


3.
4.
5.
Quantitative (e.g., cost of doing business)
Qualitative (i.e., less tangible).
Relate the objectives to the criteria using
appropriate models (e.g., economic cost models,
BEP analysis, LP, factor rating system).
Do field research to generate relevant data and use
the models to evaluate the alternative locations.
Select the location that best satisfies the criteria.
Monks, J. G., Operations Management –Theory and Problems, 3rd Edition,
McGraw-Hill Book Company, ISBN 0-07-042727-5, p. 106.
Location and Distribution (Henry C. Co)
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

Qualitative Approaches
Quantitative Approaches





Conventional approaches... cost-volume
analysis, net-present value
Decision trees
Transportation (Linear Programming)
Computer Simulation.
Integrating Qualitative & Quantitative


Rating scale approach
Relative-aggregate-scores approach.
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Qualitative Approach –
Factor Rating Method
1.
2.
3.
4.
5.
Develop a checklist of relevant factors
Assign weight to each factor to indicate its
relative importance (total = 100%)
Assign a common scale to each factor (e.g.,
1-5, 5=best), and designate any minimum
Score each potential location according to
the designated scale, and multiply the
scores by the weights
Total the points for each location, and
choose the location with the maximum
points
Location and Distribution (Henry C. Co)
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Factor Rating Template (Illustration)
Location Factors
1.
2.
3.
4.
5.
6.
Weight
Total patient miles per month
Facility utilization
Average time per emergency trip
Expressway accessibility
Land and construction costs
Employee preferences
Rating
Weighted Score
25
20
20
15
10
10
Total location
score =
Location and Distribution (Henry C. Co)
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Which of these locations is better?
Location Factors
1.
2.
3.
4.
5.
6.
Total patient miles per month
Facility utilization
Average time per emergency trip
Expressway accessibility
Land and construction costs
Employee preferences
Location Factors
1.
2.
3.
4.
5.
6.
Total patient miles per month
Facility utilization
Average time per emergency trip
Expressway accessibility
Land and construction costs
Employee preferences
Weight
25
20
20
15
10
10
Weight
25
20
20
15
10
10
Location and Distribution (Henry C. Co)
Rating
Weighted Score
4
3
3
4
1
5
Total location
score =
100
60
60
60
10
50
Rating
Weighted Score
4
5
4
3
1
3
Total location
score =
100
100
80
45
10
30
340
365
16
Locational Breakeven Analysis
To identify the ranges of demand volume where each
location is preferable.




Determine fixed and
variable costs.
Plot total costs.
Determine lowest total
costs.
Example:
$(000)
800
700
600
500
400
300
200
100
0
0
D
B
C
A
A Superior
C Superior
B Superior
2
4
6
8
10
12
14
16
Annual Output (000)
Cell D3 =B3+C3*$B$1. To determine the total costs for the other three
locations, we copy the formula for D3 and paste onto cells D4:D6.
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$(000)
800
700
600
500
400
300
200
100
0
0
D
B
C
A
A Superior
C Superior
B Superior
2
4
6
8
10
12
14
16
Annual Output (000)



Between of 0 and 5,000 units, the line segment
associated with location B is the lowest.
Between annual outputs of 5,000 and approximately
11,000 units, location C is superior.
Beyond approximately 11,000 units, location A is
superior.
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Using Goal Seek to find the breakeven volume

Between A and C




D11=B11+$B$13*C11
and D12
=B12+$B$13*C12
Set Cell: D13 (the cost
difference)
To value: 0 (the two costs
must be equal)
By changing cell: B13
(the volume)
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
Between B and C





D17=B17+$B$19*C17
D18=B18+$B$19*C18
Set Cell: D19 (the cost
difference)
To value: 0 (the two costs
must be equal)
By changing cell: B19
(the volume)
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$(000)
800
700
600
500
400
300
200
100
0
0
D
B
C
A
A Superior
C Superior
B Superior
2
4
6
8
10
12
14
16
Annual Output (000)




Below 5,000 units, B is the best alternative.
Beyond 11,111 units, B is the best alternative.
Between 5,000 and 11,111 units, C is the best alternative.
Alternative D is never a good choice.
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Single Facility Location
Assumptions





Demand volumes are frequently
assumed to be concentrated at one
point (demand cluster)
The basis of variable costs
Total transportation costs usually are
assumed to increase proportionately
with distance
Straight-line routes are commonly
assumed b/w the facility and other
network points
Not dynamic
Location and Distribution (Henry C. Co)
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Center of Gravity Approach

Center-of-gravity approach, the grid method,
centroid method, p-median method


Transportation cost is the only locational factor,
static continuous location model
Illustration
Location and Distribution (Henry C. Co)
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



E2=B2*D2; copy an paste onto E3:E8
F2=C2*D2; copy an paste onto F3:F8
D9=SUM(D2:D8); copy an paste onto E9:F9
D12=E9/D9; D13=F9/D9.
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How good is the center of gravity?





First, consider Euclidean distances.
Geometrically, the straight line connecting the center
of gravity and demand center A is the hypotenuse of
a right triangle.
The lengths of the two legs of the right triangle
correspond to the x- and y- coordinate distances
between the center of gravity and demand center A,
i.e., (6.669 – 2.5) along the x-axis, and (4.5 –
3.022) along the y-axis.
From the Pythagorean Theorem, the square of the
length of the hypotenuse equals the sum of square of
the length of the two legs = (6.669 – 2.5) 2 + (4.5 –
3.022)2 = 19.566.
The Euclidean distance therefore is 4.423. The
corresponding Excel formula is F6 = SQRT((B6$C$2)^2+(C6-$C$3)^2).
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Euclidean Distances
Copy and paste the formula for F6 onto F7:F12.
The total weighted sum of the distances is the sumproduct
of the forecasted demand and the Euclidean distances =
141,166.
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Use Solver to optimize the location
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Total weighted sum of the distances is reduced to 136,204.
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Rectilinear Distance

Parallel to the x- and y- axes (east-west,
north-south, and making 90 turns only.
F6=ABS(B6-$C$2)+ABS(C6-$C$3); copy an paste onto F7:F12
G6=D6*F6; copy an paste onto G7:G12
G13=SUM(G6:G12)
Location and Distribution (Henry C. Co)
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
Use Solver to optimize the location
Location and Distribution (Henry C. Co)
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Solver was able to reduce the total weighted sum of the
distances based on rectilinear distance from 180,147 to
161,000 or by about 10.6%!
Location and Distribution (Henry C. Co)
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Multiple Facility Location



In many distribution/logistics problems, we
are concerned with finding the minimum
cost way to get products from a variety of
plants/suppliers to their final markets.
Typically, different suppliers have different
costs and capacities; transportation costs
are specific to a supplier / market pair; and
different markets have different
requirements and possibly profitability.
Realistic problems of this type can involve
large numbers of suppliers, products, and
markets and can be difficult to figure out by
intuition or gut feel.
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Solution Methods


There are many approaches to the distribution
system planning problem.
The usual approach is to develop a first cut solution
either by making simplifying assumptions or using
heuristics, and then fine-tuning the solution with
more advanced methodologies such as mathematical
programming techniques and computer simulation.


The center of gravity method is an example of a first
cut solution. The solution was derived by taking
weighted average of the x- and y- coordinates of the
demand clusters.
Solver improved the solution by than 10%.

What we just solved is actually a complex non-linear
optimization problem. The availability of inexpensive
high-speed computer has made such a complex
problem appear so trivial!
Location and Distribution (Henry C. Co)
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Basic Planning Question

Warehouses



Customers



How many warehouses should there be in the
logistics network?
How large should they be, and where should they
be located?
Which customers should be assigned to which
warehouses?
Which warehouses should be assigned to which
plants, vendors, and ports?
Distribution


Which products should be stocked in which
warehouses?
Which products should be shipped directly from
plants/vendors/ports to customers?
Location and Distribution (Henry C. Co)
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Distribution
The Transportation Problem


How to satisfy demands at a given
number of destinations with supplies
from given set of origins.
Structure of the system is known




Location and characteristics of facilities
Location and profile/demand of customers
Transportation means and costs
Distribution strategy to satisfy
demand at least cost.
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Illustration

The Hottest Mexican Restaurant has restaurants in 5
Midwestern cities. They order their tortillas from the
Laredo Tortilla Factory, which has warehouses in 6
cities. The shipping costs (in dollars per dozen
tortillas) are given below:
Location and Distribution (Henry C. Co)
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
The demand for each restaurant and the
tortillas available at each warehouse are:
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Excel Spreadsheet

Step 1: Set up the EXCEL spreadsheet as shown below:
Location and Distribution (Henry C. Co)
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


Notice that there are two sections. The first section
shows the unit shipping costs. The cells have been
formatted as currency with 2 decimal places (Select
by highlighting the cells, then click on ‘Format’- ‘Cell’‘Currency’ ).
The second section shows the allocation and shipping
costs. The optimal allocations have been assigned to
cells B20:F25. (at this time, these cells are all
blanks). These are the decision variables.
The demand and supply have been entered in cells
B27:F27 and cells H20:H25, respectively. Also, row
28 has been formatted as “currency” with 2 decimal
places, and all other cells formatted as number with
2 decimal places.
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Sums of Cells

Step 2: Enter the formulae for the sum of demand (cells
B26:F26) and the sum of supply (cells G20:G25),
respectively.



For example, B26=SUM(B20:B25) ;copy and paste the
formula from C26:F26 .
G20=SUM(B20:F20) ;copy and paste the formula from
G21:G25 .
To find out if supply is sufficient, enter the formulae of
the total system demand and the total system supply.



Total system supply H26=SUM(H20:H25)
Total system demand G27=SUM(B27:F27)
The sum of supply is H26=423. Similarly, compute the
sum of demand. The sum is G27=370. In this case, there
will be excess supply.
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Shipments from ... Shipments to …


Step 3: Enter the formula for cell G20=SUM(B20:F20), the total
shipment from Tulsa, as shown. Note that cells B20:F20 = the
allocations from Tulsa to Minneapolis, Salina, Kansas, Lincoln, and
Wichita, respectively. Copy this formula and paste it onto cells
G21:G25.
Step 4: Likewise, enter the formula for cell B26=SUM(B20:B25),
the shipments to Minneapolis; copy and paste the formula onto cells
C26:F26.
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Shipping Costs


Step 5: Enter the formula for cell
B28=SUMPRODUCT(B3:B8,B20:B25),
the total shipping cost to Minneapolis. Copy
and paste the formula onto cells C28:F28.
Step 6: Enter the formula for cell
G28=SUM(B28:F28), the total system
cost.
Location and Distribution (Henry C. Co)
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Location and Distribution (Henry C. Co)
47

What we have just modeled is a linear
programming problem.



The objective function is the total
transportation cost (to be minimized),
subject to the demand-supply constraints.
We are now ready to solve the
problem using an Excel tool called
Solver.
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The “Northwest Corner” Solution

Starting from cell B20 (the “northwest corner”), let us find
out how many units we can allocate from Tulsa to
Minneapolis.




Tulsa has 77 units available and Minneapolis needs 52 units.
Suppose we allocated 52 from Tulsa, to satisfy the demand of
Minneapolis.
The leaves Tulsa with a remaining capacity of 77-52=25 units.
Allocate the remaining 25 units from Tulsa to Salina (cell
C20).
Salina has a demand of 99 units. With 25 units from Tulsa,
Salina still needs 74 units. Allocate 45 units from the next
origin Oklahoma. This will exhaust the supply of Oklahoma.
The remaining 29 units will come from Denver.
Etc., etc.
Location and Distribution (Henry C. Co)
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Solver


Step 7 Click on “Tool”, and
choose “Solver” in the pulldown menu. You should see
this:


Step 8: In the Tool-Solver
menu, enter the following
(the “Set Target Cell” is
$G$28, the grand total cost):
By changing cells B20:F25
(the cells highlighted in light
green is our allocation table).
Select the Min button to
minimize the grand total cost.
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Adding Constraints



Step 9: Add the following constraints (one at a time):
Since total capacity exceeds demand, the shipment from each
source should be less than or equal to its capacity: G20:G25 
H20:H25, i.e.
Since total demand is less than total capacity, the total shipment
to each destination should be equal to its demand, B26:F26 =
B27:F27
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Options: Linear, Non-negative, Auto-Scale

Step 10:After entering all constraints, set
the option as shown:
Location and Distribution (Henry C. Co)
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
Step 11: Click the ‘Solve’ button!
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The Transportation Problem
with Lost Sales


Suppose, the warehouse in Omaha becomes
unavailable.
Originally, the sum of supply was 423.




With Omaha gone, the total supply is now 351
units.
Since total demand is 370 units, 19 (=370-351)
units of demand will not be satisfied.
Replace Omaha by “Lost Sales,” with
capacity equal to the demand not satisfied,
i.e., 19 units.
Suppose the unit cost of unsatisfied demand
is $30 for the restaurants in Salina and
Kansas, and $20 for the other locations.
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The Northwest Corner Solution


Row 8 has been changed to Lost Sales.
Cell H25 and cell B16 equals the demand not satisfied = 19 units.
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

Solver reduced total cost by 40% (from $2,277 down to $1,369).
Lincoln & Wichita will have shortages (4 & 15 units, respectively).
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It is not about time!
Based in part from:
http://www.business.auburn.edu/~gibsobj/SCM%20-%200129%20-%20Location%20Location.doc.
Journal of Commerce Inc. Feb 26, 2001
How many warehouses?

About every five years, large
companies undertake a network
design project to determine if their
warehouses are properly positioned.



Many companies hire consultants for this
and use software to perform the analysis.
They address the positioning of
warehouses but not all the elements of
the supply chain.
Most important of these elements is how
warehouse design affect customer service.
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59
Customer's Lead-time

Lead-time is based on two components - inventory
availability and product acquisition time.



Acquisition time is only relevant when the inventory is
unavailable.
When inventory is available, the time to get product
from the warehouse to the customer is almost always
fixed. It consists of the time to process the order plus
the time it takes to transport it to the customer. These
times don't vary much. Moreover, customers generally
are aware of and accustomed to them.
When inventory is unavailable. Acquisition time
becomes important.

Customer's lead time includes the added time to get
the product back in stock or the time to process and
ship the product from some other location such as
another warehouse, a manufacturing plant or a supplier.
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Example

Suppose a warehouse processes all
the orders for which it has inventory in
one day and that the average transit
time is an additional day.



If inventory is available, customer's lead
time = 2 days.
Suppose the product is available 90% of
the time and the average time to acquire
out-of-stock product is 10 days.
The expected customer's lead time = 2
days + (100%-90%)*10 days = 3 days.
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Components of Customer Lead-time

Components of Customer Lead-time





Transit time (one day, on average, in our
example)
Order processing time (also one day)
Probability that inventory is available (90
percent)
The acquisition time (10 days).
Which of these is dependent on the
location of the warehouses?
Location and Distribution (Henry C. Co)
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
The location impacts only one of these
elements: the transit time from the
warehouse to the customer.



This transit time generally depends on the
distance from the warehouse to the customer.
In most supply chains the average distance
decreases as warehouses are added to the
network.
In our example, the location only impacts
one day of the three-day average customer
lead time. That's only a third of the total!
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Adding more warehouses …

Think about the capability of the network to
decrease transit times by adding more
warehouses. In most markets, customers
are distributed approximately like the U.S.
population and adding more warehouses
impacts the average distance only slightly.



In a 4-warehouse network, for example, the most
the transit time can be reduced by adding a 5th
warehouse is 15.9%.
Moreover the transit time is only part of the
customer's lead time - a third in this case.
The added warehouse reduces overall
customer lead time by 1/3*15.9%  5%!
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64
Conclusion

Importance of warehouse location is
overrated.



Warehouse network may have some effect on
these components. However, that effect is small.
May have contrary effect. As the number of
warehouses increases, inventory availability goes
down, causing lead times and costs to increase.
More effective levers include



Order processing times
Inventory availability
Acquisition time
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65
Warehouse network designers must consider more than
just where warehouses are located. They should account
for all the elements of the customer's lead time.