13-1 Facility Location Decisions Chapter 13 CR (2004) Prentice Hall, Inc.

13-1

Facility Location Decisions

Chapter 13CR (2004) Prentice Hall, Inc.

13-2CR (2004) Prentice Hall, Inc.

Facility Location in Location Strategy

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Transport Strategy• Transport fundamentals• Transport decisions

Customer service goals

• The product• Logistics service• Ord . proc. & info. sys.

Inventory Strategy• Forecasting• Inventory decisions• Purchasing and supply

scheduling decisions• Storage fundamentals• Storage decisions

Location Strategy• Location decisions• The network planning process

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Transport Strategy• Transport fundamentals• Transport decisions

Customer service goals

• The product• Logistics service• Ord . proc. & info. sys.

Inventory Strategy• Forecasting• Inventory decisions• Purchasing and supply

scheduling decisions• Storage fundamentals• Storage decisions

Location Strategy•Location decisions• The network planning process


Location OverviewWhat'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 Overview (Cont’d)

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


When to Analyze Location

Changing service requirements

Partnerships

Shifting locations (customer/supplier)

Changing corporate ownership

Cost pressure

Global markets


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.


Methods of Solution

Single warehouse location

– Graphic

– Grid, or center-of-gravity, approach

Multiple warehouse location

– Simulation

– Optimization

– Heuristics

Location Overview (Cont’d)


-Finding solution can be challenging

-But with the advent of fast PCs, it is more widely used these days

-Model formulation

Optimization Method


Method appraisal 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


COG Method (Cont’d)

i ii

i iii

i ii

i iii

RV

YRVY,

RV

XRVX

where

Vi = volume flowing from (to) point I

Ri = transportation rate to ship Vi from (to) point i

Xi,Yi = coordinate points for point i

= coordinate points for facility to be locatedY,X


COG Method (Cont’d)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: Note rate is a

per mile costPointi

Prod-ucts Location

Annualvolume,

cwt.

Rate,$/cwt/

mi. Xi Yi1 S1 A Seattle 8,000 0.02 0.6 7.32 S2 B Atlanta 10,000 0.02 8.6 3.03 H1 A & B Los

Angeles5,000 0.05 2.0 3.0

4 H2 A & B Dallas 3,000 0.05 5.5 2.45 H3 A & B Chicago 4,000 0.05 7.9 5.56 H4 A & B New York 6,000 0.05 10.6 5.2


COG Method (Cont’d)Map scaling factor, K



Solve the COG equations in table form

i Xi Yi Vi Ri ViRi ViRiXi ViRiYi1 0.6 7.3 8,000 0.02 160 96 1,1682 8.6 3.0 10,000 0.02 200 1,720 6003 2.0 3.0 5,000 0.05 250 500 7504 5.5 2.4 3,000 0.05 150 825 3605 7.9 5.5 4,000 0.05 200 1,580 1,1006 10.6 5.2 6,000 0.05 300 3,180 1,560

1,260 7,901 5,538

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COG Method (Cont’d)Now,

X = 7,901/1,260 = 6.27

Y = 5,538/1,260 = 4.40

This is approximately Columbia, MO.

The total cost for this location is found by:

where K is the map scaling factor to convertcoordinates into miles.

i iiii YYXXKRVTC 22 )()(

CR (2004) Prentice Hall, Inc.


COGCOG Method (Cont’d)



2,360,882Total

660,4920.056,0005.210.66

196,6440.054,0005.57.95

160,7330.053,0002.45.54

561,7060.055,0003.02.03

271,8250.0210,0003.08.62

509,4820.028,0007.30.61

TCRiViYiXiiCalculate total cost at COG

221

4.40)(7.36.27)(0.6)(500)8,000(0.02TC


Note The center-of-gravity method does not necessarilygive optimal answers, but will give good answers if there area large numbers of points in the problem (>30) and thevolume for any one point is not a high proportion of the totalvolume. However, optimal locations can be found by theexact center of gravity method.

i iii

i iiiin

i iii

i iiiin

/dRV

/dYRVY,

/dRV

/dXRVX

where

22 )Y(Y)X(Xdn

i

n

ii

and n is the iteration number.



Solution procedure for exact COG


1) Solve for COG2) Using find di

3) Re-solve for using exact formulation4) Use revised to find revised di

5) Repeat steps 3 through 5 until there is no change in

6) Calculate total costs using final coordinates

Y,XY,X

Y,X

Y,X


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 problemthat:

Search for the best combination of facilities to minimizecosts

Do so within a reasonable computational time Do not require enormous amounts of data for the analysis

Multiple Location Methods

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Multiple COGFormulated as basic COG modelCan 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 procedureRank demand points from highest to lowest volumeUse the M largest as initial facility locations and assign

remaining demand centers to these locationsCompute the COG of the M locationsReassign all demand centers to the M COGs on the basis

of proximityRecompute the COGs and repeat the demand center

assignments, stopping this iterative process when there is no further change in the assignments or COGs



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

Examples of Practical COG Model Use


A method used commercially- Has good problem scope- Can be implemented on a PC- Running times may be long and memory requirements substantial

- Handles fixed costs well- Nonlinear inventory costs are not well

handled

A linear programming-like solution procedure can be used (MIPROG in LOGWARE)

Mixed Integer Programming

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Location by Simulation


•Can include more variables than typical algorithmic methods

•Cost representations can be precise so problem can be more accurately described than with most

algorithmic methods

•Mathematical optimization usually is not guaranteed, although heuristics can be included to guide solution process toward satisfactory solutions

•Data requirements can be extensive

•Has limited use in practice

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Commercial Models for Location

Features

•Includes most relevant location costs

•Constrains to specified capacity and customer service levels

•Replicates the cost of specified designs

•Handles multiple locations over multiple echelons

•Handles multiple product categories

•Searches for the best network design



Commercial Models (Cont’d)

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Retail Location

Methods

Contrasts with plant and warehouse location.- Revenue rather than cost driven- Factors other than costs such as parking, nearness to competitive

outlets, and nearness to customers are dominant

Weighted checklist - Good where many subjective factors are involved - Quantifies the comparison among alternate locations


A Hypothetical Weighted Factor Checklist for a Retail Location Example

a Weights approaching 10 indicate great importance.b Scores approaching 10 refer to a favored location status.

(1)FactorWeight

(1 to 10)a Location Factors

(2)

Factor Score(1 to 10)b

(3)=(1)(2)

WeightedScore

8 Proximity to competing stores 5 405 Space rent/lease

considerations 3 15

8 Parking space 10 807 Proximity to complementary

stores 8 56

6 Modernity of store space 9 549 Customer accessibility 8 723 Local taxes 2 63 Community service 4 128 Proximity to major

transportation arteries 7 56 Total index 391

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Retail Location (Cont’d) Huff's gravity model - A take-off on Newton's law of gravity. - "Mass" or retail "variety" attracts customers, and the distance from

customers repels them. - The basic model is:

E P C

S T

S TCij ij i

j ija

j ija

j

i= = /

/

where

Eij = expected demand from population center i that will be attracted to

retail location j Pij = probability of customers from point i traveling 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 competing locations j a = an empirically estimated parameter


Retail Location (Cont’d)Example of Huff's method

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 Bhas 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 salespotential of each shopping center?

Solution matrix

Custo- mer i

Time from Customer i

to Location j Tij

2

S Tj ij/ 2

PS T

S Tij

j ij

j ijj

=

/

/

2

2

E P Cij ij i=

A B A B A B A B A B C1 30.0 56.6 900 3200 555 313 0.64 0.36 $6.4 $3.6 C2 44.7 30.0 2000 900 250 1111 0.18 0.82 0.9 4.1 C3 36.0 28.3 1300 800 385 1250 0.24 0.76 1.7 5.3

Total shopping center sales ($ million) $9.0 $13.0

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0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

80Y

XTime (minutes)

Tim

e (m

inut

es)

C2

C1

C3

RB

RA

Retail Location (Cont’d)


Retail Location (Cont’d)

Location-Allocation Model

Mixed-Integer Programming Example – p.592

13-1 Facility Location Decisions Chapter 13 CR (2004) Prentice Hall, Inc.

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