Supply Chain Management

1
Supply Chain Management

• Facility Location Techniques

2
Facilities

• Plants
• Warehouses
• Distribution centers
• Service centers
• Retail operations
• Public Service Facilities

3
Types Of Facilities

• Heavy manufacturing
• auto plants, steel mills, chemical plants
• Light industry
• small components manufacturing, assembly
• Warehouse distribution centers
• Retail service
• Public sector

4
Factors In Heavy Manufacturing Location

• Construction costs
• Land costs
• Raw material finished goods shipment modes
• Proximity to raw materials
• Utilities
• Labor availability

5
Factors In Light Industry Location

• Construction costs
• Land costs
• Easily accessible geographic region
• Education training capabilities

6
Factors In Warehouse Location

• Transportation costs
• Proximity to markets

7
Factors In Retail Location

• Proximity to customers
• Location is everything

8
Global Location Factors

• Government stability
• Government regulations
• Political economic systems
• Economic stability growth
• Exchange rates
• Culture
• Climate
• Export import regulations
• Duties tariffs
• Raw material availability

• Number and proximity of suppliers
• Transportation distribution system
• Labor cost education
• Available technology
• Commercial travel
• Technical expertise
• Cross-border trade regulations
• Group trade agreements

9
Regional Location Factors 1

• Labor (availability, education, cost unions)
• Proximity of customers
• Number of customers
• Construction/leasing costs
• Land costs
• Modes and quality of transportation
• Transportation costs

• Incentive packages
• Governmental regulations
• Environmental regulations
• Raw material availability
• Commercial travel
• Climate
• Infrastructure
• Quality of life

10
Regional Location Factors 2

• Community government
• Local business regulations
• Government services
• Business climate
• Community services
• Taxes

• Availability of sites
• Financial Services
• Community inducements
• Proximity of suppliers
• Education system

11
Site Location Factors

• Customer base
• Construction/leasing cost
• Land cost
• Site size
• Transportation
• Utilities

• Zoning restrictions
• Traffic
• Safety/security
• Competition
• Area business climate
• Income level

12
Location Incentives

• Tax credits
• Relaxed government regulation
• Job training
• Infrastructure improvement
• Money

13
Location Analysis Selected Techniques Models

• Location Rating Factor
• Median Location
• Center-of-Gravity
• Load-Distance
• Transportation Model
• p-Center Model

14
Location Rating Factor

• Identify important factors
• Weight factors (0.00 - 1.00)
• Subjectively score each factor (0 - 100)
• Sum weighted scores

15
Location Factor Example
Scores (0 to 100)
Location Factor
Weight
Site 1
Site 2
Site 3
Labor pool and climate Proximity to
suppliers Wage rates Community environment Proximi
ty to customers Shipping modes Air service
.30 .20 .15 .15 .10 .05 .05
80 100 60 75 65 85 50
65 91 95 80 90 92 65
90 75 72 80 95 65 90

16
Location Factor Example
Weighted Scores
Location Factor
Site 1
Site 2
Site 3
Labor pool and climate Proximity to
suppliers Wage rates Community environment Proximi
ty to customers Shipping modes Air service Total
Score
24.00 20.00 9.00 11.25 6.50 4.25 2.50 77.50
19.50 18.20 14.25 12.00 9.00 4.60 3.25 80.80
27.00 15.00 10.80 12.00 9.50 3.25 4.50 82.05

17
Single Facility Location (SFL)

• Let wi the interaction between the new facility
  and customer i
• Let di(x,y) the travel distance from customer
  location i to any location (x,y)
• The SFL Model

18
Distance Measures

• Using the Rectilinear Distance measure
• di(x,y) ai - x bi - y
• Using the Euclidean Distance measure
• di(x,y) (ai - x)2 (bi - y)21/2
• Using the Squared Euclidean Distance measure
  (Used in Center of Gravity!)
• di(x,y) (ai - x)2 (bi - y)21/22

19
SFL with Rectilinear Distance Median Problem

• Place Existing Facilities in a Non-Decreasing
  Order of the Coordinates (x and y, separately)
• Find the Cumulative Sum of the Weights and obtain
  the Median
• The Coordinate which corresponds to the
  Cumulative Sum of the Weights just Exceeding the
  Median point is the Median Location for the New
  Facility

20
Example

• Suppose four hospitals are located within a city
  at A(10,6), B(8,5), C(4,3), and D(15,6). Locate a
  centralized blood-bank facility at (x, y) that
  will serve the hospitals. The number of
  deliveries to be made per year between the
  blood-bank and each hospital is estimated to be
  350, 900, 420, and 1350, respectively.

21
Solution

• For x
• Hospital ai wi ?wi
• C 4 420 420
• B 8 900 1320
• A 10 350 1670
• D 15 1350 3020
• Median 3020/2 1510 x 10

22
Solution

• For y
• Hospital bi wi ?wi
• C 3 420 420
• B 5 900 1320
• A,D 6 3501350 3020
• Then, y 6

23
SFL with Squared Euclidean Distance
Center-of-Gravity Problem

• Locate facility at center of geographic area
• Based on weight distance traveled
• Establish grid-map of area
• Identify coordinates weights shipped for each
  location

24
Grid-Map And Coordinates
y
2 (x2, y2), W2
y2
1 (x1, y1), W1
y1
where, x, y coordinates of the new facility
at center of gravity xi, yi coordinates of
existing facility i Wi annual weight shipped
from facility i
3 (x3, y3), W3
y3
x1
x2
x3
x

25
Center-of-Gravity Example
A B C D X 200 100 250 500 Y 200 500 600 300 Wt 75
105 135 60
y

C
B
o
Center
D
A
0

26
Calculating Center-of-Gravity
238


444

27
Load-Distance Technique

• Compute (Load x Distance) for each site
• Choose site with lowest (Load x Distance)
• Distance can be actual or straight-line

28
Load-Distance Calculations
where,
LD the load-distance value
li the load expressed as a weight, number
of trips or units being shipped from the
proposed site and location i
di the distance between the proposed site
and location i
di (xi - x)2 (yi - y)2
where,
(x,y) coordinates of proposed site
(xi , yi) coordinates of existing facility

29
Load-Distance Example
Suppliers A B C D X 200 100 250 500 Y 200 500 6
00 300 Wt 75 105 135 60
Potential Sites Site X Y 1 360 180 2 420 450 3 250
400
Compute distance from each site to each supplier
161.2
dA (xA - x1)2 (yA - y1)2
Site 1
(200-360)2 (200-180)2
412.3
dB (xB - x1)2 (yB - y1)2
(100-360)2 (500-180)2
dC 434.2
dD 184.4

30
Compute load-distance
n
?
li di
LD
i 1
Site 1 (75)(161.2) (105)(412.3)
(135)(434.2) (60)(434.4) 125,063
Site 2 (75)(333) (105)(323.9) (135)(226.7)
(60)(170) 99,789
Site 3 (75)(206.2) (105)(180.3) (135)(200)
(60)(269.3) 77,555
Choose site 3

31
Transportation Model

• M different sources
• N different customers
• Si represents the capacity at source i
• Dj represents the demand of customer j
• cij is the cost per unit to produce the product
  at source i and send it to customer j

32
Transportation Model

• xij number of units to be shipped from source i
  to customer j
• The objective is to determine the minimum cost
  production and distribution plan for a given set
  of facilities

33
Mathematical Formulation of the Transportation
model
34
The Transportation Model

• Ship items at lowest cost
• Sources have fixed supplies
• Destinations have fixed demand

1

35
Transportation Problem
Grain Elevator Supply 1. Kansas City 150 2.
Omaha 175 3. Des Moines 275 600 tons
Mill Demand A. Chicago 200 B. St.
Louis 100 C. Cincinnati 300 600 tons
2

36
Shipping Cost Table

• Mill
• Grain Chicago St. Louis Cincinnati
• Elevator A B C
• Kansas City 6 8 10
• Omaha 7 11 11
• Des Moines 4 5 12

3

37
The Transportation Tableau
To
From
Chicago
St. Louis
Cincinnati
Supply
6
8
10
150
Kansas City
7
11
11
175
Omaha
4
5
12
275
Des Moines
Demand
200
100
300
600
4

38
Network Of Routes
4
Des Moines (275)
Chicago (200)
12
5
7
11
Omaha (175)
Cincinnati (300)
11
10
6
Kansas City (150)
St. Louis (100)
8
5

39
Solving Transportation Problems

• Manual methods
• Stepping-stone
• Modified distribution (MODI)
• Computer solution
• Excel
• POM for Windows

6

40
Solution For Grain Shipment

• Mill
• Elevator Chicago St. Louis Cincinnati Supply Ship
  ped
• Kansas City 25 0 125 150 150
• Omaha 0 0 175 175 175
• Des Moines 175 100 0 275 275
• Demand 200 100 300 600
• Shipped 200 100 300
• Cost 4525

7

41
A Solution

8

42
Unbalanced Problems
Location Capacity(tons) A. Charlotte 90 B.
Raleigh 50 C. Lexington 80 D. Danville 60 280
Location Demand (tons) 1. Richmond 120 2.
Winston-Salem 100 3. Durham 110 330
9

43
Shipping Costs
To From 1 2 3 A 70 100 50 B 120 90 40 C
70 30 110 D 90 50 70
10

44
Transportation Solution Tableau
To
Winston- Salem
Richmond
Durham
Supply
From
500
100
50
90
90
Charlotte
120
90
40
50
30
20
Raleigh
70
50
110
80
80
Lexington
90
70
50
Danville
60
40
20
120
100
110
Demand
Cost
15900
11

45
Public Service Facility Location Model p-Center
Model
Let yi 1, if a facility is opened at site j
0, otherwise xij 1, if people at
location j are assigned to the facility at site
i 0, otherwise w the maximum distance
between any customer and the serving
(closest) facility
46
p-Center Model

• for every customer j 1, , N
• for every site i 1, , M
• for every customer j 1, , N