Facility Location
Inventory Management
Dr. Ron Tibben-Lembke
Location Decisions
Long-term decisions
 Difficult to reverse
 Affect fixed & variable costs

 Transportation
costs (25% of price)
 Other costs: taxes, wages, rent

Objective: maximize benefit of location to
firm
What factors should we consider?
Skilled workforce
 Environmental laws / cost of compliance
 Cost of utilities, labor, taxes
 Suppliers close by – fast & cheap access
 Customers close by
 Competitors close by? Skilled labor pool
 International - control issues?

Service Facilities – Traffic focus

Revenue changes a huge amount, depending
on the location.
 Old
Navy in Stead because of cheap land?
 Location, location, location: you need traffic
 Make it convenient!
 vitamins: need enough, but it has to be the right kind
 people who would want to buy your products when
they are there.

Cost probably doesn’t change nearly as much,
by location
 All
malls have high rent
Wal-Mart
Office
Max
WinCo
Toys
Party
“I-80 & McCarran” sounds great.
Kmart Sins:
Can’t see from anywhere
- see where we’re going
Very circuitous entry
- feels inconvenient, no matter
how long it actually takes
Cost Focus

Revenue does not vary much, depending
on the location.
 Customers
don’t care if your warehouse is in
Sparks or Sacramento

Location is a major cost driver
 Impacts
shipping, labor, production costs
 Varies greatly by location
Cost Minimization
Identify the costs that will vary most with the
location you choose.
 Transportation,
taxes, labor,
 Facility construction cost, utilities
Other considerations
 Proximity
of services, suppliers
 Quality of life
 Government incentives
Cost Focus Process Overview
1.
Identify general region to locate in

2.
Identify a list of candidate cities


3.
Usually based on mostly on transp. costs
Choose cities with good transp. Access
Estimate labor cost & availability, facilities costs
Select metro area, identify candidate
properties.

Find cost of building or leasing individual properties
Case Study:
Importing from China to E. Coast
Customer Location
More detail on East
Coast possibilities
Interstate
Detail
China to U.S. Container Rates
NY / NJ $3,600
36 days
Wilmington DE $3,950
36 days (door)
Norfolk $3,600
34 days
Charleston $3,600
35 days
New Orleans $3,200
36 days
Atlanta
$3,200
37 days (door)
Allentown
Drayage
Rates
North
Elizabeth, NJ
Harrisburg
Philadelphia
Wilmington
Baltimore
Roanoke
Norfolk
China to Long Beach
Landbridge Data
Columbus $3000, 21days
Cincinnati $2925, 21d
Louisville $3050, 20d
Murray $3350, 22d
Memphis $2900, 18.5d
Nashville
$3300, 22d
Atlanta $3300, 23d
Interstate Access
Distribution Center Location
Minimize demand-weighted distance:
distance to each customer times the
volume of shipments to the customer
 How many to build?
 Where to build?

Case Study: Retailer
Location of a 5th returns processing facility
 Addresses of 2125 Continental U.S. stores
 Location of 4 Return Goods Processing
Centers
 List of all return shipments from each
store, including pounds and # pallets
 Calculated actual highway distances from
every store to its DC

Local Streets
Transportation Cost Approx.
Current Pallets:
205,254
 Current Pallet Miles:
77.9m
 Cost / pallet-mile
11.68 cents
 Pallet-Mile = 1 pallet traveling 1 mile
 Minimize average distance traveled

Solution Software


Some locations must have a facility
Considers adding a facility at every existing
store
 We




won’t really build next to a store, but that’s ok
Finds one best facility to add
Finds second best facility to add
Reconsider first added facility, then second, etc.
Improvement heuristics, optimal methods
Current RCs
Dallas Realignment
Close 1 existing RDC
Location Methods

Minimize demand-weighted distance
of Gravity – minimizing demand-weighted
distances of one facility
 Ardalan – minimize transportation of multiple facilities,
but must locate by customers
 (P-Median Problem, Maximum Covering)
 Center


Factor Weighting – consider qualitative factors
Break-even – Consider fixed & variable costs
Center of Gravity





Compute X and Y
coordinates separately
dix is the X coordinate of
location i.
diy is the Y coordinate of i.
Wi is the X demand at i.
CX and CY are the
coordinates of the DC.
d W

W
ix
CX
i
i
i
i
d W

W
iy
CY
i
i
i
i
Center of Gravity Example 1
You need to decide where to build a new
DC for Motorola.
 It needs to serve wholesalers in Reno,
Dallas, and Chicago.
 Locate these cities on an unscientific,
rectangular grid.
 Grid must maintain relative distances, but
X and Y grids could be different.

100
80
60
40
20
0
0
20
40
60
80
100
120
140
160
Center of Gravity Method
City
Demand
 Reno is at 17, 55
100
 Fort Worth is at 78, 20
90
 Chicago is at 110, 65.
120

Demand is TL/month
Center of Gravity
d W

W
ix
CX
i
i
i
17 *100 78* 90  110*120

100 90  120
i
1,700 7,020 13,200 21,920
CX 

 70.7
310
310
i diyWi 55*100 20* 90  65*120
CY 

100 90  120
Wi
i
5,500 1,800 7,800 15,100
CY 

 48.7
310
310
100
80
60
40
20
0
0
20
40
60
80
100
120
140
160
North
Platte
Sharon
Springs
Salina KS
Compromise Solution

Closest town is Sharon Springs, KN
 Population
872
 30 miles from I-70.
 Probably not a good choice
Salina, KN puts us at I-70 and I-35
 North Platte NE is at I-80 and 83.

 Access
to Dallas less convenient
100
80
60
40
20
0
0
20
40
60
80
100
120
140
160
Finalizing City

Go where other warehouses are
 More
choice in pre-built buildings
 Cheaper, easier to build a new one
 More trucks to and from town, means more carriers
there, means cheaper rates.
 Backhaul situation

Get estimates of inbound, outbound trucking
costs.
 Provide
lists of # loads per year to each destination,
from each source
Center of Gravity Example 2
You need to decide where to locate a DC
in South Dakota
X
Y
Demand
 Pierre
78 47
50
 Watertown
150 65
8
 Sioux Falls
160 25
90
 Rapid
12 42
60

100
80
60
40
20
0
0
20
40
60
80
100
120
140
160
Center of Gravity
d W

W
ix
CX
i
i
i

78* 50  150* 8  160* 90  12* 60
50  8  90  60
i
3,900 1,200 14,400 720 20,220
CX 

 97.2
208
208
d W

W
iy
CY
i
i
i
47 * 50  65* 8  25* 90  42* 60

50  8  90  60
i
2,350 520 2,250 2,520 7,640
CY 

 36.7
208
310
100
80
60
40
20
0
0
20
40
60
80
100
120
140
160
Ardalan Heuristic





Need a matrix of distances or costs from each
customer location to every other location
Demand at each location
Weight – give higher weight to more important
customers – their pain of traveling a longer
distance is worth more.
Only consider locating where customers are
Identify the one best place to locate at, then the
second one to add, then the third, etc.
Ardalan Heuristic
Minimize weighted distance traveled
To
From A B C D Dem. Weight
A
0 11 8 12 10
1.1
B 11 0 10 7
8
1.4
C
8 10 0
9
20
0.7
D 9.5 7
9
0
12
1.0

Ardalan Method
Expected demand at each location.
 Weight represents importance of serving
location (bigger = more important)
 Step 1: Multiply distances * weights *
demand
 A to B: 11 * 1.1 * 10 = 121

Ardalan Method
Step 2. Add up values in columns
From
A
B
C
D
A
0
121 88 132
B 123.2 0 112 78.4
C
112 140 0
126
D
114 84 108
0
349.2 345 308 336.4
Ardalan Method
Choose smallest value as first site.
From
A
B
C
D
A
0
121 88 132
B 123.2 0 112 78.4
C
112 140 0
126
D
114 84 108
0
349.2 345 308 336.4
Ardalan Method
3. If larger, set each cost equal to cost in same row
in the chosen column
From
A
B
C
D
A
0
112
0
108
B
C
88 88
0 112
0
0
84 108
D
88
78.4
0
0
220
172 308
166.4
Ardalan Method
Get rid of previously chosen column.
Sum, choose smallest sum.
From
A
B
D
A
0
88
88
B
112
0
78.4
C
0
0
0
D
108
84
0
220 172 166.4
Ardalan Method
Repeat 3 & 4 until enough sites chosen.
From
A
B
D
A
0
88
88
B
78.4
0
78.4
C
0
0
0
D
0
0
0
78.4 88 166.4
Ardalan Method
Repeat 3 & 4 until enough sites chosen.
From
A
B
A
0
88
B
78.4
0
C
0
0
D
0
0
78.4
88
Ardalan Summary
What we decided is that if we only want to
build one location, it should be in C.
 If we want to build two, they should be in C
and D. If we add a third one, it should be
in A.

Ardalan Summary




Assumes that we have to locate in the same city as one
of our customers, which is not always the case.
However, it can be used to find more than one location.
Center of Gravity does not try to locate in the same city
as one of the customers, but can only set one site.
If we choose the same sites as customers A and X, we
obviously don’t really have to put the warehouses in
those exact cities.
P-Median Problem
Minimize average weighted distance to
customers, when locating P facilities,
where P>=1.
 Can consider 100s of locations.
 Complex to solve – there is software for
this.

Maximum Covering Problem
A facility can “cover” a customer if the
customer is within X miles of the facility.
 Try to find the best location, and minimum
number of facilities to cover all demands.
 Cover a table with plates.
 Math also very hard.

Comparison of Results
(Using Distances of 150, 200, 250,250)
Demand Covered
100.00%
99.00%
98.00%
97.00%
96.00%
Lower Bound
95.00%
Greedy Solution
94.00%
Upper Bound
93.00%
92.00%
91.00%
90.00%
15
16
17
18
19
20
21
22
23
24
25
26
Number of
Facilities
Solving large problems
Incremental or clean-slate apprach
Take into account existing facilities
 What is the best location to add, given the
existing facilities?
 What is the best to add, if we were to
close down one of the current facilities?
 Unfortunately, only P-Median or Maximum
Covering can deal with these.

Factor Rating Method








Most widely used method?
Useful for service or industrial facilities: can
include intangible, qualitative factors
List relevant factors, assign a weight
Develop a scale for each factor
Score each factor using the scale
Multiply scores by weights, add up
Choose location with highest total score
Kind of like “Miss America”
Factor Rating Example


We need to decide where to build a new coffee
roasting plant. There are two possible locations:
Dallas, and Denver.
We consider the following factors
 Transp:
annual trucking costs in $k
 Lease: annual costs in $k
 Labor availability: scale 1-10, unemployment, related
industries
 Quality of life: scale 1-10: outdoor activities, cultural,
sports, education
Factor Rating Example
Using a scoring system we developed, we
have the following.
Factor
Weight
TX
CO
Transportation
0.5
900 1,023
Plant Lease Cost 0.3
45
39
Labor availability
0.2
10
8
Quality of Life
0.1
7
9.5

Normalizing Scores
All factors must be scored on the same
scale, like 1-10, or 0-1.0, etc.
 Costs need to be re-scaled

 Lowest
cost site gets a 10.
 More expensive site gets 39/45 * 10 or
900/1,023 * 10
Factor Rating Example
TX
Factor Wt Raw Wtd
Tr
0.4 10
4.00
Plant
0.3
8.7 2.61
Labor
0.2 10
2.00
Q Life
0.1
7
0.70
TOTAL
9.31
TX is best
CO
Raw Wtd
8.80 3.52
10
3.00
8
1.60
9.5
0.95
9.07
Possible Approach
Use Ardalan to find out which general
regions to locate in (state / county).
 Use factor weighting to choose city.
 Ardalan has disadvantage of choosing
weights -- difficult to set levels.

Break-Even Analysis



Determine fixed and variable costs for each
location
Fixed cost: how much it would cost to open a
facility there
Variable cost: how much total costs would
increase as production increases:
 Transportation
 Labor costs
 Taxes
 Increased
costs
construction costs
Locating Service Facilities
Using Linear Regression
 Collect data about your current facilities
 Use regression to determine which
variables have a significant impact on
profits
 Choose new facilities which have these
characteristics
Method Comparison
Center of gravity minimizes average
distance for one facility only.
 Ardalan Minimizes weighted distances for
more than one facility.
 Breakeven: fixed & variable costs.
 Factor weighting considers many other
important aspects of location, but does not
minimize distance.

Transportation Method
You have 3 DCs, and need to deliver
product to 4 customers.
D2
A 10
E4
B 10
F 12
C 10
G 11
Find cheapest way to satisfy all demand
Solving Transportation Problems



Trial and Error
Linear Programming
– ooh, what’s that?!
Tell me more!
D
E
F
G
A
10
9
8
7
B
10
11
4
5
C
8
7
4
8