copyright © 2010 pearson education, inc. publishing as prentice hall. chapter 5 network design in...

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Chapter 5Network

Design in the Supply Chain

5-1


Outline

The Role of Network Design in the Supply Chain Factors Influencing Network Design Decisions Framework for Network Design Decisions Models for Facility Location and Capacity

Allocation The Role of IT in Network Design Making Network Design Decisions in Practice

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Network Design Decisions

Facility role Facility location Capacity allocation Market and supply allocation

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Factors InfluencingNetwork Design Decisions

Strategic Technological Macroeconomic Political Infrastructure Competitive Logistics and facility costs

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Strategic Factors

Firm’s competitive strategy– Cost– Responsiveness




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Competitor location

0 1A 1-B


Competitor location

0 1A 1-B

D1 = A + (1 – B – A)/2D2 = (1+ B – A)/2




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Service and Number of Facilities

Number of Facilities

ResponseTime

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Costs and Number of Facilities

Costs

Number of facilities

Inventory

Transportation

Facility costs

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TransportationTransportation

Cost Buildup as a Function of FacilitiesC

ost

of O

per

atio

ns

Cos

t of

Op

erat

ion

s

Number of FacilitiesNumber of Facilities

InventoryInventory

FacilitiesFacilities

Total CostsTotal Costs

LaborLabor

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Framework for Network Design Decisions

Phase I – Supply Chain Strategy Phase II – Regional Facility Configuration Phase III – Desirable Sites Phase IV – Location Choices

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A Framework forNetwork Design Decisions

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

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Linear programming (LP)

Optimization of linear objective functions

Normally formulated:– Maximize X– Subject to y < z


LP example (Joe’s chop shop)

Joe takes plain vans and converts them into custom vans and can produce either fine or fancy vans. Both types require a $25,000 plain van. Fancy vans sell for $37,000 and Joe uses $10,000 in parts to customize them yielding a profit margin of $2,000. Fine vans use $6,000 in parts and sell for $32,700 yielding profits of $1,700. Joe figures the shop can work on no more than 12 vans in a week. Joe hires 7 people including himself and operates 8 hours per day, 5 days a week and thus has at most 280 hours of labor available in a week. Joe also estimates that a fancy van will take 25 hours of labor, while a fine van will take 20 hours.

To maximize profit, how many of each van should Joe produce?


LP Example (Joe’s chop shop)

Maximize Z = 2000 Xfancy + 1700 Xfine




Subject to:Xfancy ≥ 0

Xfine ≥ 0




Subject to:Xfancy ≥ 0

Xfine ≥ 0

Xfancy + Xfine ≤ 12

25 Xfancy + 20 Xfine ≤ 280


12

12

10

10

8

8

6

6

4

4

2

20

Xfancy + Xfine ≤ 12

Xfancy

Xfine


12

12

10

10

8

8

6

6

4

4

2

20

25 Xfancy + 20 Xfine ≤ 280

Xfancy

Xfine


12

12

10

10

8

8

6

6

4

4

2

20

Xfancy

Xfine


12

12

10

10

8

8

6

6

4

4

2

20

2000 Xfancy + 1700 Xfine

Xfancy

Xfine


12

12

10

10

8

8

6

6

4

4

2

20

Xfancy

Xfine


Steps to add the Solver add-in in Excel 2007

1. Click the Microsoft Office Button , and then click Excel Options.2. Click Add-Ins, and then in the Manage box, select Excel Add-ins.3. Click Go.4. In the Add-Ins available box, select the Solver Add-in check box, and then click OK.

Tip: If Solver Add-in is not listed in the Add-Ins available box, click Browse to locate the add-in. If you get prompted that the Solver Add-in is not currently installed on your computer, click Yes to install it.After you load the Solver Add-in, the Solver command is available in the Analysis group on the Data tab

LP Example- Excel Solver


LP Example


# of Fancy produced

# of Fine produced

Subject to

Xfancy + Xfine <= 12 0

25 Xfancy + 20Xfine <= 280 0


LP Example

Maximize Z = 2000 Xfancy + 1700 Xfine 22800

# of Fancy produced 8

# of Fine produced 4

Subject toXfancy + Xfine <= 12 12

25 Xfancy + 20Xfine <= 280 280


LP example #2 (calculators)

A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day.

If each scientific calculator sold results in a $2 loss, but each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?


LP Example #2 (Calculators)

Maximize Z = -2 Xscientific + 5 Xgraphing

Subject to:Xscientific ≥ 100

Xgraphing ≥ 80

Xscientific + Xgraphing ≤ 200

Xscientific ≤ 200

Xgraphing ≤ 170


LP Example #2 (Calculators)

Maximize Z = -2 Xsci + 5 Xgraph 650

# of Sci produced 100

# of Graph produced 170

Subject toXsci + Xgraph <= 200 270


Network Optimization Models

Allocating demand to production facilities Locating facilities and allocating capacity

Which plants to establish? How to configure the network?

Key Costs:

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

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Plant Location with Multiple Sourcing

}1,0{;

,...,1,

,...,1,

..

1

1

1

1 11

yy

yKx

Dx

xcyf

i

m

ii

ii

n

jij

j

n

iij

n

i

m

jijiji

n

ii

k

ni

mj

ts

Min

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Figure 5-3

Inputs - Costs, Capacities, Demands

Demand Region

Production and Transportation Cost per 1,000,000 Units Fixed Low Fixed High

Supply Region N. America S. America Europe Asia Africa Cost ($) Capacity Cost ($) Capacity

N. America 81 92 101 130 115 6,000 10 9,000 20

S. America 117 77 108 98 100 4,500 10 6,750 20

Europe 102 105 95 119 111 6,500 10 9,750 20

Asia 115 125 90 59 74 4,100 10 6,150 20

Africa 142 100 103 105 71 4,000 10 6,000 20

Demand 12 8 14 16 7


Figure 5-4

Decision Variables

Demand Region - Production Allocation (1000 Units) Plants Plants

Supply Region N. America S. America Europe Asia Africa (1=open) (1=open)

N. America 0 0 0 0 0 0 0

S. America 0 0 0 0 0 0 0

Europe 0 0 0 0 0 0 0

Asia 0 0 0 0 0 0 0

Africa 0 0 0 0 0 0 0


Figure 5-5

Constraints

Supply Region Excess Capacity

N. America 0

S. America 0

Europe 0

Asia 0

Africa 0

N. America S. America Europe Asia Africa

Unmet Demand 12 8 14 16 7

Objective Function

Cost = $ -


Figure 5-6

Constraints:All decision variables are ≥ 0

All excess capacity is ≥ 0

All unmet demand = 0

Plants are open or closed (0,1)


Figure 5-7Inputs - Costs, Capacities, Demands

Demand Region

Production and Transportation Cost per 1,000,000 Units Fixed Low Fixed High

Supply Region N. America S. America Europe Asia Africa Cost ($) Capacity Cost ($) CapacityN. America 81 92 101 130 115 6,000 10 9,000 20S. America 117 77 108 98 100 4,500 10 6,750 20Europe 102 105 95 119 111 6,500 10 9,750 20Asia 115 125 90 59 74 4,100 10 6,150 20Africa 142 100 103 105 71 4,000 10 6,000 20Demand 12 8 14 16 7 Decision Variables Demand Region - Production Allocation (1000 Units) Plants Plants

Supply Region N. America S. America Europe Asia Africa (1=open) (1=open)N. America 0 0 0 0 0 0 0S. America 12 8 0 0 0 0 1Europe 0 0 0 0 0 0 0Asia 0 0 4 16 0 0 1Africa 0 0 10 0 7 0 1

ConstraintsSupply Region Excess Capacity N. America 0S. America 0Europe 0Asia 0Africa 3 N. America S. America Europe Asia AfricaUnmet Demand 0 0 0 0 0

Objective FunctionCost = $ 23,751


Gravity Method

C

C

C

C


x = (60x5000) + (15x1000) + (80x3000)

5000+ 1000 + 3000

y = (15x5000) + (70x1000) + (110x3000)

5000+ 1000 + 3000

x = 555000/9000 ≈ 62

y = 475000/9000 ≈ 53

k

nn

k

nnny

k

nn

k

nnnx

V

Vdy

V

Vdx

1

1

1

1 ,


Gravity Method

10

20

30

40

50

60

70

80

90

100

10 20 30 40 50 60 70 80 90 100 110 120 130 140

C

C

C

C


Gravity Method

10

20

30

40

50

60

70

80

90

100

10 20 30 40 50 60 70 80 90 100 110 120 130 140

C

C

C

C

Customer x y demandIdaho 75 40 500Arizona 35 40 2000Texas 25 80 1200Ohio 65 105 600


Gravity Method

Ton Mile-Center Solution– x : X coordinate center of gravity

– y : Y coordinate center of gravity

– dnx : X coordinate of the nth

location

– dny : Y coordinate of the nth

location

– Vn : Annual tonnage to delivery

location n

k

nn

k

nnny

k

nn

k

nnnx

V

Vdy

V

Vdx

1

1

1

1

5-50


x = (75x500) + (35x2000) + (25x1200) + (65x600)

500+ 2000 + 1200 + 600

y = (40x500) + (40x2000) + (80x1200) + (105x600)

500+ 2000 + 1200 + 600

x = 176500/4300 = 41

y = 259000/4300 = 60

k

nn

k

nnny

k

nn

k

nnnx

V

Vdy

V

Vdx

1

1

1

1 ,


Gravity Method

10

20

30

40

50

60

70

80

90

100

10 20 30 40 50 60 70 80 90 100 110 120 130 140

C

C

C


k

nn

k

nnny

k

nn

k

nnnx

V

Vdy

V

Vdx

1

1

1

1 ,

Customer x y demand

California 60 15 5000

Texas 15 70 1000

New York 80 110 3000


QUESTION>>>

QUESTION…. What is the location 41/70 Oklahoma (62/53 Colorado)XX 55/71 Kansas 73/82 Iowa


Gravity Method

C

C

C

C


x = (60x5000) + (15x1000) + (80x3000)

5000+ 1000 + 3000

y = (15x5000) + (70x1000) + (110x3000)

5000+ 1000 + 3000

x = 555000/9000 ≈ 62

y = 475000/9000 ≈ 53

k

nn

k

nnny

k

nn

k

nnnx

V

Vdy

V

Vdx

1

1

1

1 ,


Exercise #2 DryIce, Inc., is a manufacturer of air conditioners that ha seen its demand

grow significantly. The company anticipates nationwide demand for the year 2010 to be 180,000 in the South, 120,000 units in the Midwest, 110,000 in the East, and 100,000 units in the West. Managers at DryIce are designing the manufacturing network and have selected four potential sites- New York, Atlanta, Chicago, and San Diego. Plants could have a capacity of either 200,000 or 400,000 units. The annual fixed costs are the four locations are shown in the table below, along with the cost of producing and shipping an air conditioner to each of the four markets. Where should DryIce build its factories and how large should they be?

New York Atlanta Chicago San Diego

Fixed Costs

200k 6,000,000 5,500,000 5,600,000 6,100,000

400k 10,000,000 9,200,000 9,300,000 10,200,000

Variable Costs

East 211 232 238 299

South 232 212 230 280

Midwest 240 230 215 270

West 300 280 270 225


Exercise #2

Objective function:Minimize Z = fixed costs + Variable costs

Subject to :All shipments are positive integers (≥0)

All shipments are ≤ 400000

All shipment add up to the 2010 requirements.


Question

Question

Answer is: **265740 250150 231000 276090


Exercise #2 New York

Shipped from NY Atlanta

Shipped from Atlanta Chicago

Shipped from

Chicago San Diego

Shipped from San

Diego Requirements Supply

Fixed Costs

200k 6,000,000 5,500,000 5,600,000 6,100,000

400k 10,000,000 9,200,000 9,300,000 10,200,000

Variable Costs

East 211

110,000

232

-

238

-

299

-

110,000 110,000

South 232

-

212

180,000

230

-

280

-

180,000 180,000

Midwest 240

-

230

-

215

120,000

270

-

120,000 120,000

West 300

-

280

-

270

-

225

100,000

100,000 100,000

23,210,000 110,000 38,160,000 180,000 25,800,000 120,000 22,500,000 100,000

Fixed 6,000,000 5,500,000 5,600,000 6,100,000

29,210,000 43,660,000 31,400,000 28,600,000 132,870,000

TOTAL SYSTEM COST

265,740,000

Cells that are changed

All non negative integers


The Role of IT in Network Design

IT systems help with network design by:1. Making the modeling of the network design

problems easier

2. Containing high-performance optimization technologies

3. Allowing for “what-if” scenarios

4. Interfacing with planning and operational software

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Making Network Design Decisions In Practice

Do not underestimate the life span of facilities Do not gloss over the cultural implications Do not ignore quality of life issues Focus on tariffs and tax incentives when

locating facilities

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Summary of Learning Objectives

What is the role of network design decisions in the supply chain?

What are the factors influencing supply chain network design decisions?

Describe a strategic framework for facility location.

How are the following optimization methods used for facility location and capacity allocation decisions?– Gravity methods for location– Network optimization models

5-64

copyright © 2010 pearson education, inc. publishing as prentice hall. chapter 5 network design in...

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competitor location