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OPIM 204: Lecture #1 Introduction to OM

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Page 1: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

OPIM 204: Lecture #1

Introduction to OM

Page 2: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

OPIM 204 Operations Management

• Instructor: Jose M. Cruz• Office: Room 332• Phone: (203) 236-9945 • E-mail: [email protected]• Web: www.sba.uconn.edu/Users/Mnunez/OPIM204_F2003.htm

Page 3: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

How to get help?

• Read syllabus• Go to course web page• Attend office hours:

M, Th 4-6 pm, • Send e-mail• Phone call during office hours

Page 4: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Textbook & Software Requirements

• Russell & Taylor– Operations management– Prentice-Hall, fourth edition, 2002.

• Make sure that it includes free student CD-ROM with Excel OM, we will use it a lot in class!

• MS Excel Solver Add-in (middle of the semester).

Page 5: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Objectives

• Learn about OM:– How OM activities are performed– How goods and services are produced– What operations managers do– How OM affects costs in any organization

• Develop qualitative and quantitative decision-making skills in operations

• Learn basic OM Excel tools

Page 6: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Subjects/Schedule

Subject/Activity Reading DatesIntroduction to O.M. & Decision Analysis Ch 1 , 2 & Supp 2 Sept 2Products & Services Ch 3 Sep 9Processes & Technologies Ch 4 Sep 16Forecasting Ch 8 Sep 23Statistical Control Ch 15 Sep 30Quality Ch 14 Oct 7First Examination Oct 14Supply Chain & Transportation Problem Ch 7 Oct 21Facilities & Facility Location Ch 5 & Supp 5 Oct 28Inventory Management Ch 10 Nov 4Second Examination Nov 11Waiting Line Models Ch 16 Nov 18Project Planning Ch 6 Dec 2Capacity & Aggregate Planning Ch 9 Dec 9Final Examination Dec

Page 7: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Evaluation and Course Policy

• Class Participation: 5%• Take-Home Assignments: 20%• First Partial Examination: 25%• Second Partial Examination: 25%• Final Examination: 25%

Page 8: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 1 - 2© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

The Operations Function

• Operations as a transformation process

• Operations as a basic function

• Operations as the technical core

Page 9: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 1 - 3© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Operations As A Transformation Process

OUTPUT

MaterialMachinesLaborManagementCapital

Goods or Services

INPUT Transformationprocess

Feedback

Page 10: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 1 - 4© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Transformation Processes

• Physical (manufacturing)• Locational (transport/storage)• Exchange (retail)• Physiological (healthcare)• Psychological (entertainment)• Informational (communications)

Page 11: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 1 - 5© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Operations As A Basic Function

MARKETING FINANCE

OPERATIONS

Page 12: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Computer Exercise: Histograms

• South Laser Inc.: Manufacturer of custom laser transmitters

• Lasers: low-volume, high-end product, usually hand made

• Problem: A very sensitive module can easily break. Number of broken modules has increased recently.

Page 13: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Alternative Explanations

• Operator inexperience• Production shifts• Assembly room temperature• Welder maintenance: tuning up tools

Page 14: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Solution Through Histograms

• Histogram: frequency chart that can be used to understand data ranges and points of concentration

Page 15: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 1 - 29© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Issues & Trends In Operations

1. Intense competition2. Global markets, global sourcing,

and global financing3. Importance of strategy4. Product variety and mass customization5. More services

Page 16: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 1 - 30© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Issues & Trends In Operations

6. Emphasis on quality7. Flexibility8. Advances in technology9. Worker involvement10. Environmental and ethical concerns

Page 17: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 1 - 34©2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 2/e

Strategy Of Productive Systems

–1. Introduction to Operations & competitiveness–2. Operations strategy–3. Quality management–4. Statistical quality control

0

10

20

30

40

50

60

70

0 1 2 3 4 5 6 7

Page 18: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 1 - 35© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Designing Productive Systems

–5. Product & service design–6. Process planning, analysis and reengineering–7. Facility layout–8. Human resources in operations management–9. Supply chain management

Page 19: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 1 - 36©2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Operating Productive Systems–10. Forecasting–11. Capacity planning & aggregate production

planning–12. Inventory management–13. Materials requirements planning–14. Scheduling–15. Just-in-time systems–16. Waiting line models for service improvement–17. Project management

Page 20: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 2 - 3© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Competing On Cost

• Eliminate all waste• Invest in

–updated facilities & equipment–streamlining operations–training & development

Page 21: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 2 - 4© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Competing On Quality

Please the customer–Understand customer attitudes toward and expectations of quality

Page 22: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 2 - 5© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Competing On Flexibility

• Produce wide variety of products• Introduce new products• Modify existing products quickly• Respond to customer needs

Page 23: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

Ch 2 - 6© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Competing On Speed

• Fast moves

• Fast adaptations

• Tight linkages

Page 24: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 2© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Decision Analysis

• A set of quantitative decision-making techniques for decision situations where uncertainty exists

Page 25: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 3© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Decision Making

• States of nature– events that may occur in the future– decision maker is uncertain which state of nature

will occur– decision maker has no control over the states of

nature

Page 26: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 4© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Payoff Table

• A method of organizing & illustrating the payoffs from different decisions given various states of nature

• A payoff is the outcome of the decision

Page 27: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 5© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Payoff Table

States Of NatureDecision a b

1 Payoff 1a Payoff 1b2 Payoff 2a Payoff 2b

Page 28: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 6© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Decision-making Criteria Under Uncertainty

• Maximax criterion– choose decision with the maximum of the maximum

payoffs• Maximin criterion

– choose decision with the maximum of the minimum payoffs

• Minimax regret criterion– choose decision with the minimum of the maximum

regrets for each alternative

Page 29: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 7© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

• Hurwicz criterion– choose decision in which decision payoffs are weighted

by a coefficient of optimism, – coefficient of optimism () is a measure of a decision

maker’s optimism, from 0 (completely pessimistic) to 1 (completely optimistic)

• Equal likelihood (La Place) criterion – choose decision in which each state of nature is

weighted equally

Page 30: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 8© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Decision-making Under Uncertainty Example

Expand$ 800,000 $ 500,000Maintain status quo 1,300,000 -150,000Sell now320,000 320,000

States Of Nature

Good Foreign Poor Foreign

Decision Competitive Conditions Competitive Conditions

Page 31: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 9© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Maximax Solution

Expand: $800,000Status quo: 1,300,000

-- MaximumSell: 320,000

Decision: Maintain status quo

Page 32: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 10© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Maximin Solution

Expand: $500,000 -- Maximum

Status quo: -150,000Sell: 320,000

Decision: Expand

Page 33: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 11© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Minimax Regret Solution

$ 1,300,000 - 800,000 = 500,000 $ 500,000 - $500,000 = 01,300,000 - 1,300,000 = 0 500,000 - (-150,000) = 650,0001,300,000 - 320,000 = 980,000 500,000 - 320,000 = 180,000

Good Foreign Poor Foreign

Competitive Conditions Competitive Conditions

Expand: $500,000 -- MaximumStatus quo: 650,000Sell: 980,000Decision: Expand

Regret Value

Page 34: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 12© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Hurwicz Solution

= 0.3, 1- = 0.7

Expand: $ 800,000 (0.3) + 500,000 (0.7) = $590,000 -- MaximumStatus quo: 1,300,000 (0.3) -150,000 (0.7) = 285,000Sell: 320,000 (0.3) + 320,000 (0.7) = 320,000

Decision: Expand

Page 35: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 13© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Equal Likelihood Solution

Two decisions, weight = 0.50 for each state of nature

Expand: $ 800,000 (0.50) + 500,000 (0.50) = $650,000 -- MaximumStatus quo: 1,300,000 (0.50) -150,000 (0.50) = 575,000Sell: 320,000 (0.50) + 320,000 (0.50) = 320,000

Decision: Expand

Page 36: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 14© 2000by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Decisionmaking With Probabilities

• Risk involves assigning probabilities to states of nature

• Expected value is a weighted average of decision outcomes in which each future state of nature is assigned a probability of occurrence

Page 37: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

EV x p ix ixi

n

where

ix outcome i

p ix probability of outco

( )

1

me i

C2 Supp - 15© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Expected Value

Page 38: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 16© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Expected Value Example

70% probability of good foreign competition30% probability of poor foreign competition

EV(expand) = $ 800,000 (0.70) + 500,000 (0.30) = $710,000EV(status quo) = 1,300,000 (0.70) -150,000 (0.30) = 865,000 -- MaximumEV(sell) = 320,000 (0.70) + 320,000 (0.30) = 320,000

Decision: Maintain status quo

Page 39: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 17© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Expected Value Of Perfect Information

• The maximum value of perfect information to the decision maker

• EVPI = (expected value given perfect information) - (expected value without perfect information)

Page 40: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 18© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

EVPI ExampleGood conditions will exist 70% of the time, choose maintain status quo

with payoff of $1,300,000

Poor conditions will exist 30% of the time, choose expand with payoff of $500,000

Expected value given perfect information = $1,300,000 (0.70) + 500,000 (0.30) = $1,060,000

EVPI = $1,060,000 - 865,000 = $195,000

Page 41: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 19© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Sequential Decision Trees

• A graphical method for analyzing decision situations that require a sequence of decisions over time

• Decision tree consists of– Square nodes - indicating decision points– Circles nodes - indicating states of nature– Arcs - connecting nodes

Page 42: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 20© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

2

1

3

4

5

6

7

Expand(-$800,000)

Purchase Land(-$200,000)

Expand(-$800,000)

Warehouse(-$600,000)

0.60

0.40No market

growth$225,000

Market growth$2,000,000

$3,000,000

$700,000

$2,300,000

$1,000,000

$210,000

Marketgrowth

Marketgrowth

No marketgrowth

No marketgrowthSell land

Sell land

0.80

0.40

0.70

0.30

No marketgrowth (3 years,

$0 payoff)

Marketgrowth (3 years,

$0 payoff)

0.20

0.60

Decision Tree Example

Page 43: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 21© 2000by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

Evaluations At Nodes

Compute EV at nodes 6 & 7EV(node 6) = 0.80($3,000,000) + 0.20($700,000) = $2,540,000EV(node 6) = 0.30($2,300,000) + 0.70($1,000,000) = $1,390,000

Expected values written above nodes 6 & 7

Decision at node 4 is between $2,540,000 for Expand and $450,000 for Sell land

Choose Expand

Repeat expected value calculations and decisions at remaining nodes

Page 44: OPIM 204: Lecture #1 Introduction to OM OPIM 204 Operations Management Instructor: Jose M. Cruz Office: Room 332 Phone: (203) 236-9945 E-mail: Jose.Cruz@business.uconn.eduJose.Cruz@business.uconn.edu

C2 Supp - 22© 2000 by Prentice-Hall IncRussell/Taylor Oper Mgt 3/e

2

1

3

4

5

6

7

Expand(-$800,000)

Purchase Land(-$200,000)

$1,160,000

$1,360,000$790,000

$1,390,000

$1,740,000

$2,540,000Expand

(-$800,000)

Warehouse(-$600,000)

0.60

0.40No market

growth$225,000

Market growth$2,000,000

$3,000,000

$700,000

$2,300,000

$1,000,000

$210,000

Marketgrowth

Marketgrowth

No marketgrowth

No marketgrowthSell land

Sell land

0.80

0.40

0.70

0.30

No marketgrowth (3 years,

$0 payoff)

Marketgrowth (3 years,

$0 payoff)

$1,290,000

0.20

0.60

Decision Tree Solution