MGT530 M6-Discussion Forum: Reliability and Decision Theory

7/5/23, 11:31 AM

Operations Management

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Discussion 25

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Demonstrates
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Decision Theory

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You should be able to:
LO 5s.1
LO 5s.2
LO 5s.3
LO 5s.4
LO 5s.5
LO 5s.6
LO 5s.7

Outline the steps in the decision process
Name some causes of poor decisions
Describe and use techniques that apply to decision making
under uncertainty
Describe and use the expected-value approach
Construct a decision tree and use it to analyze a problem
Compute the expected value of perfect information
Conduct sensitivity analysis on a simple decision problem

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5s-2

 A general approach to decision making that is suitable

to a wide range of operations management decisions
 Capacity planning
 Product and service design
 Equipment selection
 Location planning

LO 5s.1

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5s-3

 Characteristics of decisions that are suitable for using

decision theory
 A set of possible future conditions that will have a

bearing on the results of the decision
 A list of alternatives from which to choose
 A known payoff for each alternative under each possible
future condition

LO 5s.1

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5s-4

1.
2.
3.
4.
5.

Identify the possible future states of nature
Develop a list of possible alternatives
Estimate the payoff for each alternative for each possible
future state of nature
If possible, estimate the likelihood of each possible future
state of nature
Evaluate alternatives according to some decision criterion
and select the best alternative

LO 5s.1

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5s-5



A table showing the expected payoffs for each
alternative in every possible state of nature
Possible Future Demand
Alternatives

Low

Moderate

High

Small facility

$10

$10

$10

Medium facility

7

12

12

Large Facility

(4)

2

16

• A decision is being made concerning which size facility
should be constructed
• The present value (in millions) for each alternative under
each state of nature is expressed in the body of the above
payoff table

LO 5s.1

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5s-6

 Steps:
1.
Identify the problem
2. Specify objectives and criteria for a solution
3. Develop suitable alternatives
4. Analyze and compare alternatives
5. Select the best alternative
6. Implement the solution
7. Monitor to see that the desired result is achieved

LO 5s.1

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5s-7

 Decisions occasionally turn out poorly due to

unforeseeable circumstances; however, this is not the
norm
 More frequently poor decisions are the result of a
combination of
 Mistakes in the decision process
 Bounded rationality
 Suboptimization

LO 5s.2

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5s-8

 Errors in the Decision Process

Failure to recognize the importance of each step

Skipping a step

Failure to complete a step before jumping to the next step

Failure to admit mistakes

Inability to make a decision

LO 5s.2

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5s-9

 Bounded rationality
 The limitations on decision making caused by costs,

human abilities, time, technology, and availability of
information
 Suboptimization
 The results of different departments each attempting to

reach a solution that is optimum for that department

LO 5s.2

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5s-10

 There are three general environment categories:
 Certainty
 Environment in which relevant parameters have known
values
 Risk
 Environment in which certain future events have
probabilistic outcomes
 Uncertainty
 Environment in which it is impossible to assess the likelihood
of various possible future events

LO 5s.3

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5s-11

 Sometimes we know the exact outcome or

environment. Under those situations, making a
decision is easy. For example, if Investment 1 gives a
return of 3.4% and Investment 2 gives a return of 5.6%,
then we know what to do.
 Uncertainty comes when there is a risk involved, for
instance, Investment 1 could be the return on a CD
which is guaranteed, but Investment 2 could be a
mutual fund whose returned can’t be guaranteed.

LO 5s.3

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5s-12

 Decisions are sometimes made under complete

uncertainty: No information is available on how likely
the various states of nature are.
 Decision criteria:
 Maximin
 Choose the alternative with the best of the worst possible payoffs

 Maximax
 Choose the alternative with the best possible payoff

 Laplace
 Choose the alternative with the best average payoff

 Minimax regret
 Choose the alternative that has the least of the worst regrets

LO 5s.3

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5s-13

Possible Future Demand

Alternatives

Low

Moderate

High

Small Facility

$10

$10

$10

Medium Facility

7

12

12

Large Facility

(4)

2

16

•The worst payoff for each alternative is
Small facility:
$10 million
Medium facility
$7 million
Large facility
-$4 million
•Choose to construct a small facility

LO 5s.3

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5s-14

Possible Future Demand

Alternatives

Low

Moderate

High

Small Facility

$10

$10

$10

Medium Facility

7

12

12

Large Facility

(4)

2

16

•The best payoff for each alternative is
Small facility:
$10 million
Medium facility
$12 million
Large facility
$16 million
•Choose to construct a large facility

LO 5s.3

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5s-15

Possible Future Demand

Alternatives

Low

Moderate

High

Small Facility

$10

$10

$10

Medium Facility

7

12

12

Large Facility

(4)

2

16

•The average payoff for each alternative is
Small facility:
(10 + 10 + 10) ÷ 3 = $10 million
Medium facility
(7 + 12 + 12) ÷ 3 = $10.33 million
Large facility
(−4 + 2 + 16) ÷ 3 = $4.67 million
•Choose to construct a medium facility

LO 5s.3

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5s-16

Possible Future Demand

Alternatives

Low

Moderate

High

Small Facility

$10

$10

$10

Medium Facility

7

12

12

Large Facility

(4)

2

16

•Construct a regret (or opportunity loss) table
•The difference between a given payoff and the best
payoff for a state of nature
Regrets

LO 5s.3

Alternatives

Low

Moderate

High

Small Facility

$0

$2

$6

Medium Facility

3

0

4

Large Facility

14

10

0

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5s-17

Regrets

Alternatives

Low

Moderate

High

Small Facility

$0

$2

$6

Medium Facility

3

0

4

Large Facility

14

10

0

•Identify the worst regret for each alternative
•Small facility
$6 million
•Medium facility
$4 million
•Large facility
$14 million
•Select the alternative with the minimum of the maximum
regrets
•Build a medium facility

LO 5s.3

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5s-18

 Decisions made under the condition that the

probability of occurrence for each state of nature can
be estimated
 A widely applied criterion is expected monetary value
(EMV)
 EMV
 Determine the expected payoff of each alternative, and choose

the alternative that has the best expected payoff
 This approach is most appropriate when the decision maker is
neither risk averse nor risk seeking

LO 5s.4

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5s-19

Possible Future Demand

Alternatives

Low (.30)

Moderate (.50)

High (.20)

Small Facility

$10

$10

$10

Medium Facility

7

12

12

Large Facility

(4)

2

16

EMVsmall = .30(10) +.50(10) +.20(10) = 10
EMVmedium = .30(7) + .50(12) + .20(12) = 10.5
EMVlarge = .30(-4) + .50(2) + .20(16) = $3
Build a medium facility

LO 5s.4

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5s-20

 Decision tree
 A schematic representation of the available alternatives and their
possible consequences
 Useful for analyzing sequential decisions

LO 5s.5

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5s-21

 Composed of
 Nodes
 Decisions – represented by square nodes
 Chance events – represented by circular nodes

 Branches
 Alternatives – branches leaving a square node
 Chance events – branches leaving a circular node
 Analyze from right to left

 For each decision, choose the alternative that will yield

the greatest return
 If chance events follow a decision, choose the alternative
that has the highest expected monetary value (or lowest
expected cost)
LO 5s.5

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5s-22

 A manager must decide on the size of a video arcade to construct. The manager

has narrowed the choices to two: large or small. Information has been collected
on payoffs, and a decision tree has been constructed. Analyze the decision tree
and determine which initial alternative (build small or build large) should be
chosen in order to maximize expected monetary value.
$40
$40

2

Overtime

$50
$55

1

($10)

2
$50

$70

LO 5s.5

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5s-23

$40
$40

2

Overtime

$50
$55

1

($10)

2
$50

$70

EVSmall = .4(40) + .6(55) = $49
EVLarge = .4(50) + .6(70) = $62
Build the large facility
LO 5s.5

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5s-24

 Expected value of perfect information (EVPI)
 The difference between the expected payoff with perfect
information and the expected payoff under risk
 Two methods for calculating EVPI
 EVPI = expected payoff under certainty – expected payoff under risk
 EVPI = minimum expected regret

LO 5s.6

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5s-25

Possible Future Demand

Alternatives

Low (.30)

Moderate (.50)

High (.20)

Small Facility

$10

$10

$10

Medium Facility

7

12

12

Large Facility

(4)

2

16

EVwith perfect information = .30(10) + .50(12) + .20(16) = $12.2
EMV = $10.5
EVPI = EVwith perfect information – EMV
= $12.2 – 10.5
= $1.7
You would be willing to spend up to $1.7 million to obtain
perfect information
LO 5s.6

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5s-26

Regrets

Alternatives

Low (.30)

Moderate (.50)

High (.20)

Small Facility

$0

$2

$6

Medium Facility

3

0

4

Large Facility

14

10

0

• Expected Opportunity Loss
• EOLSmall = .30(0) + .50(2) + .20(6) = $2.2
• EOLMedium = .30(3) + .50(0) + .20(4) = $1.7
• EOLLarge = .30(14) + .50(10) + .20(0) = $9.2
• The minimum EOL is associated with the building the
medium size facility. This is equal to the EVPI, $1.7
million.
LO 5s.6

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5s-27

 Sensitivity analysis
 Determining the range of probability for which an

alternative has the best expected payoff
 The approach illustrated is useful when there are two
states of nature
 It involves constructing a graph and then using algebra to

determine a range of probabilities over which a given solution
is best

LO 5s.7

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5s-28

State of
Nature
Alternative

#1

#2

Slope

Equation

A

4

12

12 – 4 = +8

4 + 8P(2)

B

16

2

2 – 16 = −14

16 – 14P(2)

C

12

8

8 − 12 = −4

12 – 4P(2)

LO 5s.7

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5s-29

16 − 14P(2) = 12 − 4P(2)
Rearranging terms yields
4 = 10P(2)
Solving yields P(2) = .40.
Thus, alternative B is best from P(2) = 0 up to
P(2) = .40. B and C are equivalent at P(2) = .40.

Similar analysis can be used for alternative A
and C
4 + 8P(2) = 12 − 4P(2 )
Solving yields P(2) = .67.
Thus, alternative C is best from P(2) > .40 up to
P(2) = .67, where A and C are equivalent. For
values of P(2) greater than .67 up to P(2) = 1.0,
A is best.

LO 5s.7

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5s-30

Strategic Capacity
Planning for
Products and
Services

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written consent of McGraw-Hill Education.

5-1

You should be able to:
LO 5.1 Name the three key questions in capacity planning
LO 5.2
Explain the importance of capacity planning
LO 5.3
Describe ways of defining and measuring
capacity
LO 5.4
Name several determinants of effective
capacity
LO 5.5
Discuss factors to consider when deciding
whether to perform in-house or outsource
LO 5.6
Discuss the major considerations related to
developing capacity alternatives
LO 5.7
Describe the steps used to resolve constraint
issues
LO 5.8Copyright ©2021 McGraw-Hill
Briefly
describe approaches that are useful for
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evaluating capacity alternatives

5-2

 Capacity
 The upper limit or ceiling on the load that an operating

unit can handle
 Capacity needs include
 Equipment

 Space
 Employee skills

LO 5.1

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5-3

 Goal
 To achieve a match between the long-term supply

capabilities of an organization and the predicted level of
long-term demand
 Overcapacity → operating costs that are too high

 Undercapacity → strained resources and possible loss of

customers

LO 5.1

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5-4

 Key questions:
 What kind of capacity is needed?
 How much is needed to match demand?
 When is it needed?
 Related questions:
 How much will it cost?
 What are the potential benefits and risks?
 Are there sustainability issues?
 Should capacity be changed all at once, or through several smaller
changes?
 Can the supply chain handle the necessary changes?

LO 5.1

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5-5

 Capacity decisions
1.
Impact the ability of the organization to meet future demands
2. Affect operating costs
3. Are a major determinant of initial cost
4. Often involve long-term commitment of resources
5. Can affect competitiveness
6. Affect the ease of management
7. Have become more important and complex due to globalization
8. Need to be planned for in advance due to their consumption of
financial and other resources

LO 5.2

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5-6

 Measure capacity in units that do not require

updating
 Why is measuring capacity in dollars problematic?

 Two useful definitions of capacity
 Design capacity
 The maximum output rate or service capacity an operation,
process, or facility is designed for
 Effective capacity
 Design capacity minus allowances such as personal time and
maintenance

LO 5.3

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5-7

Business

Inputs

Outputs

Auto
manufacturing

Labor hours,
machine hours

Number of cars per shift

Steel mill

Furnace size

Tons of steel per day

Oil refinery

Refinery size
Number of acres,
number of cows

Gallons of fuel per day
Bushels of grain per acre per
year, gallons of milk per day

Restaurant

Number of tables,
seating capacity

Theater

Number of seats

Number of meals served per
day
Number of tickets sold per
performance

Retail sales

Square feet of floor
space

Farming

Revenue generated per day

TABLE 5.1 Measures of capacity

LO 5.3

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5-8

 Actual output
 The rate of output actually achieved
 It cannot exceed effective capacity

 Efficiency

actual output
Efficiency =
effective capacity

 Utilization

actual output
Utilizatio n =
design capacity
Measured as percentages
LO 5.3

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5-9

 Design Capacity = 50 trucks per day
 Effective Capacity = 40 trucks per day
 Actual Output = 36 trucks per day

actual output
36
Efficiency =
=
= 90%
effective capacity 40
actual output
36
Utilizatio n =
=
= 72%
design capacity 50
LO 5.3

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5-10

 Facilities
 Product and service factors
 Process factors
 Human factors

 Policy factors
 Operational factors
 Supply chain factors

 External factors

LO 5.4

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5-11

TABLE 5.2 Factors that determine effective capacity

LO 5.4

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5-12

 Strategies are typically based on assumptions and

predictions about:
 Long-term demand patterns
 Technological change
 Competitor behavior

LO 5.4

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5-13

 Leading
 Build capacity in anticipation of future demand increases
 Following
 Build capacity when demand exceeds current capacity
 Tracking
 Similar to the following strategy, but adds capacity in relatively
small increments to keep pace with increasing demand

LO 5.4

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5-14

 Capacity cushion
 Extra capacity used to offset demand uncertainty
 Capacity cushion = 100% − utilization
 Capacity cushion strategy
 Organizations that have greater demand uncertainty typically
have greater capacity cushions
 Organizations that have standard products and services
generally have smaller capacity cushions

LO 5.4

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5-15

1.

Estimate future capacity requirements

2.

Evaluate existing capacity and facilities; identify gaps

3.

Identify alternatives for meeting requirements

4.

Conduct financial analyses

5.

Assess key qualitative issues

6.

Select the best alternative for the long term

7.

Implement alternative chosen

8.

Monitor results

LO 5.4

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5-16

 Long-term considerations relate to overall level of

capacity requirements
 Require forecasting demand over a time horizon and

converting those needs into capacity requirements
 Short-term considerations relate to probable

variations in capacity requirements
 Less concerned with cycles and trends than with

seasonal variations and other variations from average

LO 5.4

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5-17

 Calculating processing requirements requires

reasonably accurate demand forecasts, standard
processing times, and available work time
k

pD

N R = i =1

i

i

T

where
N R = number of required machines
pi = standard processing time for product i
Di = demand for product i during the planning horizon
T = processing time available during the planning horizon
LO 5.4

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5-18

 Service capacity planning can present a number of

challenges related to:
 The need to be near customers
 Convenience
 The inability to store services
 Cannot store services for consumption later
 The degree of demand volatility
 Volume and timing of demand
 Time required to service individual customers

LO 5.4

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5-19

 Strategies used to offset capacity limitations and that

are intended to achieve a closer match between supply
and demand
 Pricing
 Promotions
 Discounts
 Other tactics to shift demand from peak periods into

slow periods

LO 5.4

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5-20

 Once capacity requirements are determined, the organization

must decide whether to produce a good or service itself or
outsource
 Factors to consider:
 Available capacity
 Expertise
 Quality considerations
 The nature of demand
 Cost
 Risks

LO 5.5

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5-21

 Things that can be done to enhance capacity management:
 Design flexibility into systems
 Take stage of life cycle into account
 Take a “big-picture” approach to capacity changes
 Prepare to deal with capacity “chunks”
 Attempt to smooth capacity requirements
 Identify the optimal operating level
 Choose a strategy if expansion is involved

LO 5.6

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5-22

 An operation in a

sequence of operations
whose capacity is lower
than that of the other
operations

LO 5.6

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McGraw-Hill Education.

5-23

Average cost per unit

Minimum
cost

Optimal
Output
rate

LO 5.6

Rate of output

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McGraw-Hill Education.

5-24

 Economies of scale
 If output rate is less than the optimal level, increasing

the output rate results in decreasing average per unit
costs
 Diseconomies of scale
 If the output rate is more than the optimal level,

increasing the output rate results in increasing average
costs per unit

LO 5.6

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McGraw-Hill Education.

5-25

 Economies of scale
 If output rate is less than the optimal level, increasing

the output rate results in decreasing average per unit
costs
 Reasons for economies of scale:
 Fixed costs are spread over a larger number of units
 Construction costs increase at a decreasing rate as facility size

increases
 Processing costs decrease due to standardization

LO 5.6

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McGraw-Hill Education.

5-26

 Diseconomies of scale
 If the output rate is more than the optimal level, increasing the
output rate results in increasing average per unit costs
 Reasons for diseconomies of scale
 Distribution costs increase due to traffic congestion and
shipping from a centralized facility rather than multiple smaller
facilities
 Complexity increases costs
 Inflexibility can be an issue
 Additional levels of bureaucracy

LO 5.6

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McGraw-Hill Education.

5-27

Average cost per unit

Minimum cost & optimal operating rate are
functions of size of production unit.

Small
plant

Medium
plant

Large
plant

Output rate

LO 5.6

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McGraw-Hill Education.

5-28

 Constraint
 Something that limits the performance of a process or system in
achieving its goals
 Categories
 Market
 Resource
 Material
 Financial
 Knowledge or competency
 Policy

LO 5.7

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McGraw-Hill Education.

5-29

1.
2.
3.
4.
5.

Identify the most pressing constraint
Change the operation to achieve maximum benefit, given
the constraint
Make sure other portions of the process are supportive of
the constraint
Explore and evaluate ways to overcome the constraint
Repeat the process until the constraint levels are at
acceptable levels

LO 5.7

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McGraw-Hill Education.

5-30

 Alternatives should be evaluated from varying

perspectives
 Economic
 Is it economically feasible?
 How much will it cost?
 How soon can we have it?
 What will operating and maintenance costs be?
 What will its useful life be?
 Will it be compatible with present personnel and present
operations?
 Non-economic
 Public opinion
LO 5.8

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McGraw-Hill Education.

5-31

 Techniques for Evaluating Alternatives
 Cost-volume analysis
 Financial analysis
 Decision theory
 Waiting-line analysis
 Simulation

LO 5.8

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McGraw-Hill Education.

5-32

 Cost-volume analysis
 Focuses on the relationship between cost, revenue, and

volume of output
 Fixed Costs (FC)
 Tend to remain constant regardless of output volume

 Variable Costs (VC)
 Vary directly with volume of output
 VC = Quantity(Q) × variable cost per unit (v)

 Total Cost
 TC = FC + VC

 Total Revenue (TR)
 TR = revenue per unit (R) × Q

LO 5.8

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McGraw-Hill Education.

5-33

 BEP
 The volume of output at which total cost and total

revenue are equal
 Profit (P) = TR – TC = R × Q – (FC + v × Q)
= Q(R – v) – FC

FC
QBEP =
R−v

LO 5.8

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McGraw-Hill Education.

5-34

.

LO 5.8

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McGraw-Hill Education.

5-35

 Capacity alternatives may involve step costs, which are

costs that increase stepwise as potential volume
increases
 The implication of such a situation is the possible occurrence of

multiple break-even quantities
LO 5.8

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McGraw-Hill Education.

5-36

 Cost-volume analysis is a viable tool for comparing

capacity alternatives if certain assumptions are
satisfied
 One product is involved
 Everything produced can be sold
 The variable cost per unit is the same regardless of volume
 Fixed costs do not change with volume changes, or they are step

changes
 The revenue per unit is the same regardless of volume
 Revenue per unit exceeds variable cost per unit

LO 5.8

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McGraw-Hill Education.

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 Cash flow
 The difference between cash received from sales and

other sources and cash outflow for labor, material,
overhead, and taxes
 Present value
 The sum, in current value, of all future cash flow of an

investment proposal

LO 5.8

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McGraw-Hill Education.

5-38

 Capacity planning impacts all areas of the organization
 It determines the conditions under which operations will have to function
 Flexibility allows an organization to be agile
 It reduces the organization’s dependence on forecast accuracy and reliability
 Many organizations utilize capacity cushions to achieve flexibility
 Bottleneck management is one way by which organizations can enhance

their effective capacities
 Capacity expansion strategies are important organizational considerations
 Expand-early strategy
 Wait-and-see strategy

 Capacity contraction is sometimes necessary
 Capacity disposal strategies become important under these
conditions

LO 5.8

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McGraw-Hill Education.

5-39

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