1 utdallas.edu/~metin SC Design Facility Location Sections 4.1, 4.2 Chapter 5 and 6.

1utdallas.edu/~metin

SC Design

Facility Location Sections 4.1, 4.2 Chapter 5 and 6


Outline

Frequency decomposition of activities A strategic framework for facility location Multi-echelon networks Analytical methods for location


Frequency Decomposition

SCs are enormous It is hard to make all decisions at once Integration by smart decomposition Frequency decomposition yields several sets of

decisions such that each set is integrated within itself


Frequency Decomposition

Low frequency activity, ~ once a year, high fixed cost– R&D budget– Capacity expansion budget

Moderate frequency activity, ~ once a month– Cancellation of specific R&D projects depending on

experimental outcomes

– Specific machines to purchase High frequency activity, ~ once a day, low fixed cost

– What experiments to start / continue today

– What to produce


Facility Location: The Cost-Response Time FrontierAn inventory location based point of view

Local Finished Goods (FG) Inventory

Regional FG Inventory

Local WIP (work-in-process)

Central FG Inventory

Central WIP

Central Raw Material and Custom production

Custom production with raw material at suppliers

Cost

Response Time HiLow

Low

Hi7-Eleven

Sam’s Club

Regional

Central

Pull the inventory upstream


Service and Number of Facilities

Number of Facilities

ResponseTime


Customer

DC

Where inventory needs to be for a Where inventory needs to be for a one week one week order response timeorder response time - typical results --> 1 DC - typical results --> 1 DC


Customer

DC

5 day order response time5 day order response time - typical results -- - typical results --> 2 DCs> 2 DCs


Customer

DC

3 day order response time3 day order response time - typical results -- - typical results --> 5 DCs> 5 DCs


Customer

DC

Next day order response timeNext day order response time - typical - typical results --> 13 DCsresults --> 13 DCs


Customer

DC

Same day / next day order response timeSame day / next day order response time - - typical results --> 26 DCstypical results --> 26 DCs


Inbound and outbound shipping with more facilities

More inbound shipping and less outbound shipping with more facilities.Less (inbound + outbound) shipping costs with more facilities,

if economies of scale in transportation.

SupplierSupplier ManufacturerManufacturer CustomerCustomer

Add more facilities.

SupplierSupplier ManufacturerManufacturer DistributorDistributor RetailerRetailer CustomerCustomer

Inbound shipment Outbound shipment

Inbound shipment Outbound shipment


Costs and Number of Facilities

Costs

Number of facilities

Total SC Inventory

Transportation

Facility costs

No economies of scale in shipment size, SC covers a larger portion with each facility.

With economies of scale in inbound shipping to retailers.


Percent Service Percent Service Level Within Level Within

Promised TimePromised Time

TransportationTransportation

Cost Build-up as a function of facilities

Cos

t of

Op

erat

ion

sC

ost

of O

per

atio

ns

Number of FacilitiesNumber of Facilities

InventoryInventory

FacilitiesFacilities

Total CostsTotal Costs

LaborLabor


Network Design Decisions Facility function: Plant, DC, Warehouse: What facility performs what function

– Packaging at the manufacturer or warehouse– Should a rental computer return location run diagnostic tests on the returned

computers or should the testing be done at major warehouses? Question arising from CRU Computer Rental Case done in OPRE6302

Facility location– Starbucks opened up at UTD student apartments in 2005 but closed in 2006!– Recall Japanese 7-eleven and their blanketing strategy– SMU’s experimentation with Plano campus: http://www.smu.edu/legacy .

Capacity allocation– SOM car park took 80 cars in 2005 and expanded in 2006 to take about 110

cars. Supply and market allocation: Who serves whom

– By location: UT Austin serves central Texas students – By grade: UT Arlington serves undergraduate students


Strategic Factors Influencing Location Decisions

Strategic Facilities

Global Customers

Offshore<reduced tariffs>

<for exports>VW plants in Mexico Serving Latin America

Source<low-cost>

Nike plants in Korea

Regional Customers

Server<local-content>Suziki’s Indian venture

Maruti Udyog Contributor<customization>

<development skills>Maruti Udyog

Lead facility<advanced technology>Lockheed Martin’s JSF in Dallas

Outpost facility<Learn local skills>

Facilities in Japan; Toyota Prius


Factors Influencing Location Decisions Customer response time and local presence Operating costs Technological,

– Availability and economies of scale (fixed operational costs) » Semiconductor manufacturing takes place only in 5-6 countries worldwide

Infrastructure, electricity, phone lines, suppliers Macroeconomic,

– Tariffs, exchange rate volatility, economic volatility– Economic communities: Nafta, EU, Pacific Rim, Efta

Politic, stability

Logistics and facility costs Competitive

– Positive externalities» Nissan in India develops car suppliers which can also supply Suziki in India.» Toyota City » Shopping Malls» DFW Telecom corridor hosting Alcatel, Ericsson, Nortel, …

– Negative externalities, see the next slide


Negative externality:Market Splitting by Hotelling’s Model

0 a b 1

a b1-a-b

Suppose customers (preferences, e.g. sugar content in coke) are uniformly distributed over [0,1]

How much does firm at a get, how about firm at b?

If a locates first, where should b locate?

If a estimates how b will locate in response to a’s location,

where should a locate?


A Framework for Global Site Location

PHASE ISupply Chain

Strategy

PHASE IIRegional Facility

Configuration

PHASE IIIDesirable Sites

PHASE IVLocation Choices

Competitive STRATEGY

INTERNAL CONSTRAINTSCapital, growth strategy,existing network

PRODUCTION TECHNOLOGIESCost, Scale/Scope impact, supportrequired, flexibility

COMPETITIVEENVIRONMENT

PRODUCTION METHODSSkill needs, response time

FACTOR COSTSLabor, materials, site specific

GLOBAL COMPETITION

TARIFFS AND TAXINCENTIVES

REGIONAL DEMANDSize, growth, homogeneity,local specifications

POLITICAL, EXCHANGERATE AND DEMAND RISK

AVAILABLEINFRASTRUCTURE

LOGISTICS COSTSTransport, inventory, coordination


Comparing Locations Objectively According to McKinsey Global Institute on HBR Jun. 2006 p.91

Draw up a list of possible locations Define the decision criteria

– Six common criteria used by companies» 1. Cost of operating» 2. Availability of the skills» 3. Sales potential in the adjacent markets» 4. Risk of doing the business» 5. Attractiveness of living environments» 6. Quality of infrastructure

Collect data for each location Weight the criteria

» Fortisbank of Belgium, wants to enter new large markets, gives highest weight to 3.» Citibank, wants a location for a captive IT center, gives the highest weight to 4.

Find risk data at– Economist intelligence unit: www.eiu.com– UN Development Program: http://hdr.undp.org/statistics/data/

Rank locations according to weighted sum of their scores Assess the dynamics of the labor pool

» Availability of skilled labor– Top tier universities in the cities (How many top Business schools in Dallas?).


Analytical Models for SC Design Objective functions

» Private sector deals with total costs minimizes the sum of the distances to the customers

» Public sector deals with fairness and equity minimizes the distance to the furthest customer

– Location of emergency response units

Demand allocation» Distance vs. Price vs. Quality: Recall Hotelling model

Demand pattern over a geography: Discrete vs. Continuous

Feasibility check» Ante vs. Post

Distances» Euclidean vs. Rectilinear» Triangular inequality


Network Optimization Models

Allocating demand to production facilities Locating facilities Determining capacity

Which plants to establish? How to configure the network?

Key Costs:

•Fixed facility cost•Transportation cost•Production cost•Inventory cost•Coordination cost


A transportation networkDefined by data K, D and c

D2

m demand points

D4

D3

D1

n supply points

K1

K2

K3

c11

c12

c14

c22

c23

c31

c32

c34


Demand Allocation Model: Transportation Problem

Which market is served by which plant?

Which supply sources are used by a plant?

Given m demand points, j=1..m

with demands Dj

Given n supply points, i=1..n

with capacity Ki

Send supplies from supply points to demand points

xij = Quantity shipped from plant site i to customer j

Each unit of shipment from supply point i to demand point j costs cij

0

..

1

1

1 1

x

Kx

Dx

xc

ij

i

m

jij

j

n

iij

n

i

m

jijij

ts

Min

<See transportation.xls>


A transportation networkDefined by data K, D, c and f

m demand points

D4

D3

D2

D1

n supply points

f1,K1

f2,K2

f3,K3

c11

c12

c14

c22

c23

c31

c32

c34

Which supply point operates?

y1=yes or no

y2=yes or no

y3=yes or no


Plant Location with Multiple Sourcing

Which market is served by which plant?

Which supply sources are used by a plant?

None of the plants are open, a cost of fi is paid to open plant i

At most k plants will be opened

yi = 1 if plant is located at site i, 0 otherwise

xij = Quantity shipped from plant site i to customer j

How does cost change as k increases?

}1,0{

..

1

1

1

1 11

y

y

yKx

Dx

xcyf

i

m

ii

ii

m

jij

j

n

iij

n

i

m

jijiji

n

ii

k

ts

Min


Plant Location with Single SourcingEach customer has exactly one supplier

Which market is served by which plant?Which supply sources are used by a plant?

None of the plants are open, a cost of fi is paid to open plant i

yi = 1 if plant is located at site i, 0 otherwise

xij = 1 if market j is supplied by factory i,0 otherwise

Can a plant satisfy the demand of two or more customers with this formulation?

}1,0{,

1

..

,

1

1

1 11

jii

ii

m

jj ij

n

iij

n

i

m

jijj iji

n

ii

xy

ts

Min

yKxD

x

xcDyf


Case Study: Applichem Demand Allocation

To From

Mexico Canada Venezuela Frankfurt Gary Sunchem Capacity

Mexico $ 81 $ 92 $ 136 $ 101 $ 96 $ 101 220 Canada $ 147 $ 78 $ 135 $ 98 $ 88 $ 97 37

Venezuela $ 172 $ 106 $ 96 $ 120 $ 111 $ 117 45 Frankfurt $ 115 $ 71 $ 110 $ 59 $ 74 $ 77 470

Gary, Indiana $ 143 $ 77 $ 134 $ 91 $ 71 $ 90 185 Sunchem $ 222 $ 129 $ 205 $ 145 $ 136 $ 116 50 Demand 30 26 160 200 264 119


Applichem Demand Allocation (1982)Demand

Mexico

Canada

Frankfurt

Gary

Sunchem

Mexico 30

Canada 26

Latin America 160

Europe 200

U.S.A 264

Japan 119

30

3226

11Venezuela

220

Capacity

37

45

470

185

50

45115

20036

119185


Applichem Production Network 1982 (with duties)

Venezuela

Annual Cost = $72,916,400

Mexico

Canada

Frankfurt

Sunchem

Mexico

Canada

Latin America

Europe

U.S.A

Japan

Gary, Indiana


Applichem Production Network 1982 (without duties)

Mexico

Canada

Latin America

Mexico

Canada

Venezuela

Frankfurt

Gary

Sunchem

Europe

U.S.A

Japan

Annual Cost = 66,328,100

Without duties, Venezuela and Canada plants are closed and Frankfurt satisfies the excess Canada, Latin America and USA demand.There is consolidation without duties.


1981 Network

.Mexico

Canada

Venezuela

Frankfurt

Gary

Sunchem

Mexico

Canada

Latin America

Europe

U.S.A

Japan



1981 Network (Sunchem Closed)

Mexico

Canada

Venezuela

Frankfurt

Gary

Sunchem

Mexico

Canada

Latin America

Europe

U.S.A

Japan



Value of Adding 0.1 M Pounds Capacity (1982)

Location Shadow price or Lagrange multiplier

Mexico $0

Canada $8,300

Venezuela $36,900

Frankfurt $22,300

Gary $25,200

Sunchem $0

Capacity should be evaluated as an option and priced accordingly.

Shadow (dual) prices from LP tells you where to invest.


Gravity Methods for Location

Ton Mile-Center SolutionGiven n delivery locations, i=1..n,

ai, bi : Coordinates of delivery location i

di : Distance to delivery location i

Fi : Annual tonnage to delivery location i

Locate a warehouse at (x,y)

n

iybxaF iii1

yx, )()( 22Min

<See gravitylocation.xls>

n

i i

i

n

i i

ii

n

i i

i

n

i i

ii

d

Fd

Fb

y

d

Fd

Fa

x

1

1

1

1

)()(22

byaxd iii


Chapter 6

Network Design in an Uncertain Environment


A tree representation of uncertainty

One way to represent Uncertainty is a binomial tree Up by 1 down by -1 move with equal probability

),0( 2TNormal

T steps

1)5.0()1()5.0()1( 222

<Show Applet balldrop.htm>


Decision tree

– One column of nodes for each time period– Each node corresponds to a future state

» What is in a state? Price, demand, inflation, exchange rate, your OPRE 6366 grade

– Each path corresponds to an evolution of the states into the future

– Transition from one node to another determined by probabilities

– Evaluate the cost of a path starting from period T and work backwards in time to period 0.


Evaluating Facility Investments: AM Tires. Section 6.5 of Chopra.

Dedicated Plant Flexible Plant Plant Fixed Cost Variable Cost Fixed Cost Variable Cost

US 100,000

$1 M /year.

$15 /tire

$1.1 M /year

$15 /tire

Mexico 50,000

4 M pesos / year

110 pesos /tire

4.4 M pesos /year

110 pesos /tire

Now

U.S. Demand = 100,000; Mexico demand = 50,000. Demand is not to be met always. But selling more increases profit.

1US$ = 9 pesos.Sale price $30 in US and 240 pesos in Mexico.

FutureDemand goes up or down by 20 percent with probability 0.5 andExchange rate goes up or down by 25 per cent with probability 0.5.


AM Tires

DU=100DM=50

E=9

Period 0 Period 1 Period 2

DU=120DM = 60E=11.25

DU=120DM = 60E=6.75

DU=120DM = 40E=11.25

DU=120DM = 40E=6.75

DU=80DM = 60E=11.25

DU=80DM = 60E=6.75

DU=80DM = 40E=11.25

DU=80DM = 40E=6.75

DU=144DM = 72E=14.06

DU=144DM = 72E=8.44

DU=144DM = 48E=14.06

DU=144DM = 48E=8.44

DU=96DM = 72E=14.06

DU=96DM = 72E=8.44

DU=96DM = 48E=14.06

DU=96DM = 48E=8.44

How many states in period 2? Consider US demand 4 or 3 states Consider the rest also 4x4x4 or 3x3x3


AM Tires

Four possible capacity configurations:•Both dedicated•Both flexible•U.S. flexible, Mexico dedicated•U.S. dedicated, Mexico flexible

Consider the both flexible configurationFor each node solve the demand allocation model.

Plants Markets

U.S.

Mexico

U.S.

Mexico


AM Tires in period 2: Demand Allocation for DUS = 144; DMex = 72, E = 14.06Source

i Destination

j Variable

cost Shipping

cost E Sale price Margin($)

mij

U.S. U.S. $15 0 14.06 $30 $15 U.S. Mexico $15 $1 14.06 240 pesos $1.1

Mexico U.S. 110 pesos $1 14.06 $30 $21.2 Mexico Mexico 110 pesos 0 14.06 240 pesos $9.2

0

such that

xmMax

2

1

2

1

2

1

2

1jijij

ij

ij

ij

ji

ij

i

x

Kx

Dx Compare this formulation to the Transportation problem.We maximize the profit now.

1.1=240/14.06-15-121.2=30-110/14.06-19.2=(240-110)/14.06


AM Tires: Demand Allocation for DU = 144; DM = 72, E = 14.06; Cheap Peso

Plants Markets

U.S.

Mexico

U.S.

Mexico

100K; $15

44K; $21.2

6K; $9.2

Profit =Revenue-Cost

US Production’s contribution=100,000*15-1,100,000=$400,000Mex Production’s contribution=44,000*21.2+6000*9.2-4,400,000/14.06=$675,055Profit(DU = 144; DM = 72, E = 14.06; Period 2; Both flexible)=$1,075,055


AM Tires: Demand Allocation for DU = 144; DM = 72, E = 8.44; Expensive Peso

Plants Markets

U.S.

Mexico

U.S.

Mexico

100K; $15

44K; $16

6K; $15.4

US Production’s contribution=100,000*15-1,100,000=$400,000Mex Production’s contribution=44,000*16+6000*15.4-4,400,000/8.44 =704000+92400-521327=$275,073Profit(DU = 144; DM = 72, E = 8.44; Period 2; Both flexible)=$675,073


AM Tires: Demand Allocation for DU = 144; DM = 72, E = 5.06; Very Expensive Peso

Plants Markets

U.S.

Mexico

U.S.

Mexico

78K; $15

22K; $31.4

50K; $25.7

US Production’s contribution=78000*15+22000*31.4-1,100,000=$760,800Mex Production’s contribution=50000*25.7-4,400,000/5.06=$415,435Profit(DU = 144; DM = 72, E = 8.44; Period 2; Both flexible)=$1,176,235

Cheap Peso profit=$1,075K; Expensive Peso profit=$675K; Very Expensive Peso profit=$1,176K


Facility Decision at AM Tires

Plant Configuration United States Mexico

NPV

Dedicated Dedicated $1,629,319 Flexible Dedicated $1,514,322

Dedicated Flexible $1,722,447 Flexible Flexible $1,529,758

Make profit computations for the first year nodes one by one:Compute the profit for a node and add to that(0.9)(1/8)(Sum of the profits of all 8 nodes

connected to the current one)


Capacity Investment Strategies

Single sourcing is risky Hedging Strategy

– Risk management? » Too much capacity or too little capacity» E.g. 200 leading financial services companies are examined from 1997-

2002. Every other company struck at least once by a risky event. Source: Running with Risk. The McKinsey Quarterly. No.4. 2003.

» Managers unfamiliar with risk often focus on relatively simple accounting metrics as net income, earnings per share, return on investment, etc.

– Match revenue and cost exposure Flexible Strategy

– Excess total capacity in multiple plants– Flexible technologies

More will be said in aggregate planning chapter


Summary

Frequency decomposition Factors influencing facility decisions A strategic framework for facility location Gravity methods for location Network-LP-IP optimization models Value capacity as a real option


Location Allocation Decisions

Plants Warehouses

1

2

Which plants to establish? Which warehouses to establish?How to configure the network?

Markets


p-Median ModelInputs: A set of feasible plant locations, indexed by jA set of markets, indexed by i

Di demand of market iNo capacity limitations for plants At most p plants are to be opened

dij distance between market i and plant j

yj = 1 if plant is located at site j, 0 otherwise

xij = 1 if market i is supplied from plant site j, 0 otherwise

ji, allfor }1,0{,

i allfor 1

ji, allfor

..

,

yx

x

y

jij

jij

jji

jj

jijij

ii

yx

p

ts

xdDMin


p-Center ModelReplace the objective function in p-Median problem withMin Max {dijxij : i is a market assigned to plant j}

We are minimizing maximum distance between a market and a plantOr say minimizing maximum distance between fire stations and all the houses served by those fire stations. An example with p=3 stations and 9 houses:


p-Covering Model

xi = 1 if demand point i is covered, 0 otherwise

yj = 1 if facility j is opened, 0 otherwise

Ni facilities associated with demand point i

If j is in Ni, j can serve i

Can you read constraint (*) in English?

ji, allfor }1,0{,

y

(*) i allfor

..

jj

yx

y

ji

iNj

j

ii

i

p

x

ts

xDMax

i


Other Models

p-Choice Models– Criteria to choose the server: distance, price?

Models with multiple decision makers– Franchise model

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1 utdallas.edu/~metin SC Design Facility Location Sections 4.1, 4.2 Chapter 5 and 6.

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