Logistics Management

Location Strategy
Özgür Kabak, Ph.D.
Location Strategy
 What's located?
 Sourcing points
 Plants
 Vendors
 Ports
 Intermediate points
 Warehouses
 Terminals
 Public facilities (fire, police, and ambulance stations)
 Service centers
 Sink points
 Retail outlets
 Customers/Users
Location Strategy
 Key Questions
 How many facilities should there be?
 Where should they be located?
 What size should they be?

 Why Location is Important?

 Gives structure to the network
 Significantly affects inventory and transportation costs
 Impacts on the level of customer service to be achieved
Location Decisions
 Single Facility Location
 Multiple Facility Location
 Retail/service Location
Nature of Location Analysis
 Manufacturing (plants & warehouses)
 Decisions are driven by economics. Relevant costs such
as transportation, inventory carrying, labor, and taxes are
traded off against each other to find good locations.
 Retail
 Decisions are driven by revenue. Traffic flow and resulting
revenue are primary location factors, cost is considered
after revenue.
 Service
 Decisions are driven by service factors. Response time,
accessibility, and availability are key dimensions for
locating in the service industry.
Single Facility Location
 Locating a single plant, terminal, warehouse, or retail or
service point.

 Center-of-Gravity (COG) method

 A continuous location method
 Locates on the basis of transportation costs alone

 The COG method involves

 Determining the volumes by source and destination point
 Determining the transportation costs based on $/unit/mi.
 Overlaying a grid to determine the coordinates of source and/or
destination points
 Finding the weighted center of gravity for the graph
COG Method
 𝑀𝑖𝑛 𝑇𝐶 = 𝑖 𝑉𝑖 𝑅𝑖 𝑑𝑖

 TC = total transportation cost

 Vi = volume at point i
 Ri = transportation rate to point i
 di = distance to point i from the facility to be located

 The facility Location:

𝑖 𝑉𝑖 𝑅𝑖 𝑋𝑖 𝑖 𝑉𝑖 𝑅𝑖 𝑌𝑖
 𝑋= ,𝑌= ,
𝑖 𝑉𝑖 𝑅𝑖 𝑖 𝑉𝑖 𝑅𝑖

 Xi, Yi = coordinate points for point i

 𝑋 , 𝑌 = coordinate points for facility to be located
 COG Method
Example
 Suppose a regional medical warehouse is to be
established to serve several Veterans Administration
hospitals throughout the country. The supplies
originate at S1 and S2 and are destined for hospitals
at H1 through H4. The relative locations are shown
on the map grid. Other data are:
Point i Products Location Annual Rate Xi Yi
Volume, cwt. $/cwt/mi.
1 S1 A Seattle 8,000 0.02 0.6 7.3
2 S2 B Atlanta 10,000 0.02 8.6 3.0
3 H1 A&B Los Angeles 5,000 0.05 2.0 3.0
4 H2 A&B Dallas 3,000 0.05 5.5 2.4
5 H3 A&B Chigago 4,000 0.05 7.9 5.5
6 H4 A&B New York 6,000 0.05 10.6 5.2
COG Method
Example
Map scaling factor, K
COG Method
Example

i Xi Yi Vi Ri ViRi ViRiXi ViRiYi

1 0.6 7.3 8000 0.02 160 96 1168
2 8.6 3 10000 0.02 200 1720 600
3 2 3 5000 0.05 250 500 750
4 5.5 2.4 3000 0.05 150 825 360
5 7.9 5.5 4000 0.05 200 1580 1100
6 10.6 5.2 6000 0.05 300 3180 1560
1260 7901 5538

𝑋= 7,901/1,260 = 6.27
𝑌= 5,538/1,260 = 4.40
COG Method
Example
COG
 COG Method
Example
 The total cost for this location is found by:
𝑇𝐶 = 𝑉𝑖 𝑅𝑖 𝐾 (𝑋𝑖 − 𝑋)2 +(𝑌𝑖 − 𝑌)2
𝑖
 K is the map scaling factor to convert coordinates into
miles.
i Xi Yi Vi Ri TC
1 0.6 7.3 8000 0.02 509,706
2 8.6 3 10000 0.02 271,526
3 2 3 5000 0.05 561,597
4 5.5 2.4 3000 0.05 160,417
5 7.9 5.5 4000 0.05 196,859
6 10.6 5.2 6000 0.05 660,529
2,360,633
Multiple Location Methods
 A more complex problem that most firms have.
 It involves trading off the following costs:
 Transportation inbound to and outbound from the facilities
 Storage and handling costs
 Inventory carrying costs
 Production/purchase costs
 Facility fixed costs
 Subject to:
 Customer service constraints
 Facility capacity restrictions
 Mathematical methods are popular for this type of problem
that
 Search for the best combination of facilities to minimize costs
 Do so within a reasonable computational time
 Do not require enormous amounts of data for the analysis
Location Cost Trade-Offs

Total cost
Cost

Warehouse
fixed

Inventory carrying
and warehousing

Production/purchase
and order processing

Inbound and
outbound
transportation
0
0
Number of warehouses
Examples of Practical COG Model Use
 Location of truck maintenance terminals

 Location of public facilities such as offices, and police

and fire stations

 Location of medical facilities

 Location of most any facility where transportation cost

(rather than inventory carrying cost and facility fixed cost)
is the driving factor in location

 As a suggestor of sites for further evaluation

Multiple COG
 Formulated as basic COG model
 Can search for the best locations for a selected number of
sites.
 Fixed costs and inventory consolidation effects are handled
outside of the model.

 A multiple COG procedure

 Rank demand points from highest to lowest volume
 Use the M largest as initial facility locations and assign remaining
demand centers to these locations
 Compute the COG of the M locations
 Reassign all demand centers to the M COGs on the basis of
proximity
 Recompute the COGs and repeat the demand center
assignments, stopping this iterative process when there is no
further change in the assignments or COGs
 Multiple COG
Example
 Warehouse Cost = 800,000 𝑁
 For N = 1
 Total cost = Transportation cost + Warehouse Cost
 2,360,633 + 800,000 = 3,160,633

i Xi Yi Vi Ri TC
1 0.6 7.3 8000 0.02 509,706
2 8.6 3 10000 0.02 271,526
3 2 3 5000 0.05 561,597
4 5.5 2.4 3000 0.05 160,417
5 7.9 5.5 4000 0.05 196,859
6 10.6 5.2 6000 0.05 660,529
2,360,633
Multiple COG
Example
i Xi Yi Vi
 For N = 2 1 0.6 7.3 8000
2 8.6 3 10000
 Determine initial locations 3 2 3 5000
4 5.5 2.4 3000
 w1(8.6, 3) -- w2(0.6, 7.3) 5 7.9 5.5 4000
6 10.6 5.2 6000

 Compute the distance of each point from initial

locations
 Determine the cluster of each point
i Xi Yi d1 d2 Cluster #
1 0.6 7.3 9.08 0.00 2
2 8.6 3 0.00 9.08 1
3 2 3 6.60 4.52 2
4 5.5 2.4 3.16 6.93 1
5 7.9 5.5 2.60 7.52 1
6 10.6 5.2 2.97 10.22 1
Multiple COG
Example
 COG for the first Cluster

i Xi Yi Vi Ri ViRi ViXi ViYi

2 8.6 3 10000 0.02 200 1720 600
4 5.5 2.4 3000 0.05 150 825 360 w1=
5 7.9 5.5 4000 0.05 200 1580 1100 (7305/850;
6 10.6 5.2 6000 0.05 300 3180 1560 3520/850)=
(8.59,4.26)
850 7305 3520

 COG for the second Cluster

i Xi Yi Vi Ri ViRi ViXi ViYi w2=

1 0.6 7.3 8000 0.02 160 96 1168 (596/410;
3 2 3 5000 0.05 250 500 750 1918/410)=
(1.45, 4.68)
410 596 1918
Multiple COG
Example
 For w1(8.59,4.26) – w2(1.45, 4.68)
 Compute the distance of each point from locations
 Determine new clusters of each point
i Xi Yi d1 d2 Cluster #
1 0.6 7.3 8.55 2.76 2
2 8.6 3 1.26 7.34 1
3 2 3 6.71 1.76 2
4 5.5 2.4 3.61 4.64 1
5 7.9 5.5 1.42 6.50 1
6 10.6 5.2 2.22 9.16 1

 Clusters do not change, stop procedure!

 Multiple COG
Example
 Calculate Transportation cost for N =2

Transportation
i Xi Yi Vi Rj wx wy Distance Cost
1 0.6 7.3 8000 0.02 1.45 4.68 2.76 220,594
2 8.6 3 10000 0.02 8.59 4.26 1.26 125,884
3 2 3 5000 0.05 1.45 4.68 1.76 220,594
4 5.5 2.4 3000 0.05 8.59 4.26 3.61 270,716
5 7.9 5.5 4000 0.05 8.59 4.26 1.42 142,208
6 10.6 5.2 6000 0.05 8.59 4.26 2.22 332,357
1,312,351

 Total Cost (N=2) = 1,312,351 + 800.000 2= 2,443,722

 Total Cost (N=1) = 2,360,633 + 800,000 = 3,160,633
 Multiple COG
Example
 Minimum cost at N = 3;
Transportat
i Xi Yi Vi Rj wx wy Cluster # Distance ion Cost
1 0.6 7.3 8000 0.02 1.45 4.68 2 2.76 220,594
2 8.6 3 10000 0.02 7.50 3.75 1 1.33 132,880
3 2 3 5000 0.05 1.45 4.68 2 1.76 220,594
4 5.5 2.4 3000 0.05 7.50 3.75 1 2.41 180,783
5 7.9 5.5 4000 0.05 7.50 3.75 1 1.80 179,956
6 10.6 5.2 6000 0.05 10.60 5.20 3 0.00 0
934,807

Total Cost (N=3) = 934,807 + 800.000 3 = 2,320,447

Total Cost (N=2) = 1,312,351 + 800.000 2= 2,443,722
Total Cost (N=1) = 2,360,633 + 800,000 = 3,160,633
Multifacility Location Models
Places are Already Known
 Conventional Network
Multifacility Location Models
Places are Already Known
 Consider the following distribution system:
 Single product
 Two plants p1, p2
 Plant p2 has an annual capacity of 60,000 units
 The two plants have the same production costs
 Two existing warehouses, referred to as warehouse w1
and warehouse w2 have identical warehouse handling
costs
 Three markets, c1, c2, c3 with demands of 50,000,
100,000 and 50,000 respectively

Facility
Warehouse p1 p2 c1 c2 c3
 Distribution
w 0
Costs
4
per Unit:
3 4 5
1

w2 5 2 2 1 2
Multifacility Location Models
Places are Already Known

Handling = $2/cwt.
Capacity = 60,000 cwt.
Fixed = $100,000
/ c wt Customer C1
$ 4
$0/cwt.

.
50,000 cwt.

cwt
$2/
$5

Warehouse W1 $3
Plant P1 /cw
/cw

Production = $4/cwt. t.
t.

Capacity = wt.
/c
60,000 cwt. $1 Customer C2
t.

100,000 cwt.
cw
$4/

$5/
$2
/c

cwt
t. Warehouse W2 w
c w t
/

.
$2
Handling = $1/cwt.
Capacity =
Plant P2
Unrestricted
Production
Capacity = $4/cwt.
= 60,000 cwt. Customer C3
Fixed = $400,000
Capacity = 50,000 cwt.
Unrestricted Inventory carrying cost =
100(Throughput)0.7
Multifacility Location Models
Heuristics
 Heuristic 1
 For each market we choose the cheapest
warehouse to source demand.
 c1, c2, c3 would be supplied by w2.
 For this warehouse choose the cheapest plant;
 60,000 units from p2
 the remaining 140,000 from p1.
 Total cost = 2*50,000 + 1*100,000 + 2*50,000 + 2*60,000
+ 5*140,000 = 1,120,000
Multifacility Location Models
Heuristics
 Heuristic 2
 For each market area, choose the warehouse where the
total delivery costs to and from the warehouse are the
lowest; that is, consider inbound and outbound
distribution costs.
 Thus for market area c1, consider the paths
 p1-w1-c1, p1-w2-c1, p2-w1-c1, p2-w2-c1.
 The cheapest is p1-w1-c1, so choose w1 for c1.
 using a similar analysis, we choose w2 for c2 and w2 for c3.
 This implies that warehouse w1 delivers a total of 50,000 units
while warehouse w2 delivers a total of 150,000 units.
 The best inbound flow pattern is to supply 50,000 from plant p1
to warehouse w1, supply 60,000 units from plant p2 to
warehouse w2, and supply 90,000 from plant p1 to warehouse
w2.
 The total cost for this strategy is 920,000.
Multifacility Location Models
Optimization Model
 Places are already known
 Minimize total transportation cost
 0X(p1,w1)+5X(p1,w2)+4X(p2,w1)+2X(p2,w2)
 +3X(w1,c1)+4X(w1,c2)+5X(w1,c3)+2X(w2,c1)+1X(w2,c2)+2X(w2,c3)
 s.t.
 X(p2,w1)+X(p2,w2)≤60,000 Plant 2 capacity
 X(p1,w1)+X(p2,w1)=X(w1,c1)+X(w1,c2)+X(w1,c3) Whs.1 input/output
 X(p1,w2)+X(p2,w2)=X(w2,c1)+X(w2,c2)+X(w2,c3) Whs.2 input/output
 X(w1,c1)+X(w2,c1)=50,000 Customer 1 demand
 X(w1,c2)+X(w2,c2)=100,000 Customer 2 demand
 X(w1,c3)+X(w2,c3)=50,000 Customer 3 demand
Multifacility Location Models
Optimization Model
 EXCEL Solver
Multifacility Location Models
Optimization Model
 Result
 Total Cost: $ 740,000

w1 w2 c1 c2 c3

p1 140000 0 w1 50000 40000 50000

p2 0 60000 w2 0 60000 0
Retail Location
 Contrasts with plant and warehouse location.
 Factors other than costs such as parking, nearness to competitive
outlets, and nearness to customers are dominant

 Methods
 Weighted checklist
 Often many of the factors that are important to retail location are not
easily or inexpensively quantified
 Judgment is an integral part of the decision
 Good where many subjective factors are involved
 Quantifies the comparison among alternate locations
 Spatial-Interaction Model
 The gravity model to determining the drawing power, or overall
desirability, of a site
 The basic idea is that two competing cities attract trade from an
intervening town in direct propotion to each city’s population but inverse
proportion to square distance between cities and town.
A Hypothetical Weighted Factor Checklist
for a Retail Location Example
Factor Factor
Weight Score
(1 to 10) Location Factors (1 to 10) Weighted Score
8 Proximity to competing stores 5 40
5 Space rent/lease considerations 3 15
8 Parking space 10 80
7 Proximity to complementary stores 8 56
6 Modernity of store space 9 54
9 Customer accessibility 8 72
3 Local taxes 2 6
3 Community service 4 12
Proximity to major transportation
8 7 56
arteries
Total Index 391

Factor weights approaching 10 indicate great importance.

Factor scores approaching 10 refer to a favored location status.
Spatial-Interaction Model
Huff's Gravity Model
 A take-off on Newton's law of gravity.
 "Mass" or retail "variety" attracts customers, and the distance
from customer repels them.
 The basic model
𝑎
𝑆𝑗 /𝑇𝑖𝑗
 𝐸𝑖𝑗 = 𝑃𝑖𝑗 𝐶𝑖 = 𝑎 𝐶𝑖
𝑆 /𝑇
𝑗 𝑗 𝑖𝑗
 Eij = expected demand from population center i that will be
attracted to retail location j.
 Pij = probability of customers from i travelling to retail location j.
 Ci = customer demand at point i
 Sj = size of retail location j
 Tij = travel time between customer location i and retail location j
 n = number of retail locations j
 a = empirically estimated parameter
 Huff's Gravity Model
Example
 Two shopping centers (RA and RB ) are to attract
customers from C1, C2, and C3. Shopping center A
has 500,000 square feet of selling area whereas
center B has 1,000,000. The customer clusters have
a buying potential of $10, $5, and $7 million,
respectively. The parameter a is estimated to be 2.
What is the sales potential of each shopping center?
Time from 𝐸𝑖𝑗
Custo Customer i to
mer Location j 𝑇𝑖𝑗𝟐 𝑆𝑗 /𝑇𝑖𝑗𝟐 𝑃𝑖𝑗 Potential = 𝑃𝑖𝑗 𝐶𝑖𝑗
A B A B A B A B A B

C1 30 56,6 900 3204 556 312 0,640 0,360 10 6,403 3,597

C2 44,7 30 1998 900 250 1111 0,184 0,816 5 0,919 4,081

C3 36 28,3 1296 801 386 1249 0,236 0,764 7 1,652 5,348

Huff's Gravity Model
Example

Y 80

70
C2 RB
60
Time (minutes)

50
C3
40

30
C1 RA
20

10

0
0 10 20 30 40 50 60 70 80
Time (minutes) X
Other Methods for Retail Location
 Regression Analysis (to forecast the revenues that a
specific site can expect
 Covering models (particularly useful for locating
emergency services such as police and fire stations)
 Game Theory (suggested when competition is a key
factor)
 Location-Allocation models such as goal
programming and integer programming (see
example at the blackboard)
Next Class
 Final Exam

 June 20, 2012

 The exam will be in room D301 at 19:30.

 All course topics are included in the exam.

 It is strictly forbidden to use mobile phones for

calculations or other purposes.
 Please provide calculator for calculations.

 No class on June 13!