Managing Capacity

Chapter 8

Chapter Objectives

Be able to:Explain what capacity is, how firms measure

capacity, and the difference between theoretical and rated capacity,

Describe the pros and cons associated with three different capacity strategies: lead, lag, and match.

Apply a wide variety of analytical tools to capacity decisions, including expected value and break-even analysis, decision trees, waiting line theory, and learning curves.

Capacity Decisions

• Defining and measuring capacity

• Strategic versus tactical capacity

• Evaluating capacity alternatives

• Advanced perspectives

– Theory of Constraints

– Waiting lines

– Learning curves

Measure of an organization’s ability to provide goods or services

Jiffy Lube Oil changes per hourLaw

firm Billable hours

College Student hours per semester

Defining and Measuring Capacity

Consider:

Capacity for a PC Assembly Plant:

(800 units/shift/line)×(% Good)×(# of lines)×(# of Shifts)

1 or 2 shifts? 2 or 3 lines? Employee training? Controllable Factors

Uncontrollable FactorsSupplier problems? 98% or 100% good? Late or on time?

Strategic versus Tactical Capacity

• Strategic:– One or more years out

– “Bricks & Mortar”

– Future technologies

• Tactical:– One year or sooner

– Workforce level, schedules, inventory, etc.

Cap

acit

y

Time

Strategic Capacity Planning

• “Bricks & mortar” decisions• High-level planning• High risk

Tactical Planning

• Workforce, inventory, subcontracting decisions• Intermediate-level planning•Moderate risk

Planning & Control

•Limited ability to adjust capacity•Detailed planning•Lowest risk

Days or weeks out Months out Years out

Capacity versus Time

Capacity Strategies: When, How Much, and How?

Leader

Laggard

Demand

Lost Business

ExcessCapacity

How?

• Make or Buy (e.g., subcontracting)• One extreme: “Virtual” Business

Walden Paddlers(Marketing)

Hardigg Industries(Manufacturing)

General Composites(Design)

Independent Dealers(Direct Sales)

Evaluating Capacity Alternatives

• Economies of scale (EOS)

• Expected value analysis (EVA)

• Decision Trees

• Break-even points (BEP)

Economies of Scale

Total Cost for Fictional Line:

Fixed cost + (Variable unit cost)×(X)= $200,000 + $4X

Cost per unit for X=1? X=10,000?

$0$5,000

$10,000$15,000$20,000$25,000$30,000$35,000$40,000

5 15 25 35 45 55 65 75

Number of shipments

Sh

ipp

ing

co

sts

Common Contract Private

Fixed & Unit Cost Scenarios

Indifference Point

Compares capacity alternatives — at what volume level do they cost the same?

• Suppose one option has zero fixed cost and $750 per unit cost; the other option has $5,000 fixed cost, but only $300 per unit cost.

$0 + $750X = $5,000 + $300X

What is the volume, X, at the indifference point?

Expected Value Analysis

Forecasted demand or volume is uncertain, allows consideration of

the variability in the data

Data Requirements

Capacity cost structure(alternatives?)

Expected demand(multiple scenarios?)

Product and servicerequirements

(e.g. time standards)

EVA

Expected Value Analysis

Pennington Cabinet Company

2000 jobs per year (20% likelihood)5000 jobs per year (50%)7000 jobs per year (30%)

Each job = $1,200 revenue

We Know:

• Average job requires: 2 hours of machine time 3-1/3 hours of assembly team time

• Machines and teams work 2000 hours per year

• Each machine and team has yearly fixed cost = $200K

• 3 different capacity scenarios (see next slide!)

Effective Capacity

What is the effective capacityof each capacity alternative?

 Number of Machines

and TeamsNumber of Hours

Available Each YearMaximum Jobs per

Year

  Machines Teams Machines Teams Machines Teams

Current 3 5 6,000 10,000 3,000 3,000

Expanded 5 9 10,000 18,000 5,000 5,400

New Site 7 12 14,000 24,000 7,000 7,200

Alternate Demand Scenarios

What is the expected contribution if demand = 5000AND we decide to move to a new site?

Why does revenue for current capacity max out at $3.6 million?

Current Level Expanded New Site

Demand RevenueFixed

Expenses RevenueFixed

Expenses RevenueFixed

Expenses

2,000 $2,400,000 $1,600,000 $2,400,000 $2,800,000 $2,400,000 $3,800,000

5,000 $3,600,000 $1,600,000 $6,000,000 $2,800,000 $6,000,000 $3,800,000

7,000 $3,600,000 $1,600,000 $6,000,000 $2,800,000 $8,400,000 $3,800,000

Net Revenue Table

Demand Current Expanded New Site

3,000 $800,000 ($400,000) ($1,400,000)

5,000 $2,000,000 $3,200,000 $2,200,000

7,000 $2,000,000 $3,200,000 $4,600,000

Expected Value of Each Capacity Alternative:

Current capacity level

(20%) × $800K+(50%) × $2000K+(30%) × $2000K

= $1,760,000

Expanded capacity level

(20%) × – $400K+ (50%) × $3200K+ (30%) × $3200K

=$2,480,000

Expected Value of Each Capacity Alternative:

New Site capacity level

(20%) × – $1400K+ (50%) × $2200K+ (30%) × $4600K

= $2,200,000

Expected Value of Each Capacity Alternative:

Conclusions for Pennington

• Which alternative would you choose if you wanted to minimize the worst possible outcome (Maximin)? Maximize the best possible outcome (Maximax)?

• Why is it important to know effective capacity? How could this help future capacity decisions?

Decision Trees

• Visual tool for evaluating choices using expected value analysis

• Allows use of different outcomes and different probabilities of

success for each

Decision Tree Requirements

• Decision points represented by – Choose the best input — the highest EVA, lowest

cost, least risk, etc.

• Outcome points represented by– Summation of all inputs (outcomes) weighted by their

respective probabilities. No choice can be made at these points

• Trees drawn from final decision to the outcomes affecting that decision, then on to lower level decisions that might affect the those outcomes, then the lower level outcomes affecting those lower level decisions, and so on

Ellison Seafood Example

Here the probabilities affecting the demand level are the same for the three options considered.

But the decision tree does allow them to be different, can you think of situations where this might be true?

Decision Tree Criteria

• Book example illustrates selecting highest revenue option.

• Other option choices can be on basis of:– Using total cost for outcomes (useful when selling

price is not known)– Using estimated risk for outcomes– Outcomes reflecting a desired result (choose highest

EVA) Can you think of an example?– Outcomes reflecting undesirable results (choose

lowest EVA) Can you think of an example?

Break-Even Point (BEP)

Considers revenue and costs, at what volume level are they equal?

• Suppose each unit sells for $100, the fixed cost is $200,000 and the variable cost is $4

BEP $100X = $200,000 + $4X

What is the breakeven volume, X?

Self Test

• EBB Industries must decide whether to invest in a new machine which has a yearly fixed cost of $40,000 and a variable cost of $50 per unit.

• What is the break even point (BEP) if each unit sells for $200?

• What is the expected value, given the following demand probabilities:250 units (25%), 300 units (50%), 350 units (25%)

Advanced Perspectives

• Theory of Constraints

• Waiting lines

•Learning curves

Theory of Constraints

Concept that the throughput of a supply chain is limited (constrained) by the process step with the

lowest capacity.

Sounds logical, but what does this mean for managing the other process steps?

Theory of Constraints

• Pipeline analogy

• Which piece of the pipe is restricting the flow?

• Would making parts A or D bigger help?

Dealing with a Constraint

Identify the constraintExploit the constraint

Keep it busy!

Subordinate everything to the constraint Make supporting it the overall priority

Elevate the constraint Try to increase its capacity — more hours, screen out defective

parts from previous step, …

Find the new constraint and repeat As one step is removed as a constraint, a new one will emerge.

Which piece of the pipe on the previous slide would be the new constraint if Part C was increased in diameter?

Waiting Lines

• Waiting lines and services– Waiting and customer satisfaction– Factors affecting satisfaction

• Waiting Line Theory– Terminology and assumptions– Illustrative example

Waiting at Outback Steakhouse...

Waiting to get food...

Waiting to pay bill ...

Leavingrestaurant

Waiting outside or in bar

Key Points

• Waiting time DECREASES value-added experience

• On the other hand, adding serving capacity INCREASES costs

• Businesses must have a way to analyze the impact of capacity decisions in environments where waiting occurs

Waiting and Customer Satisfaction

Cost ofwaiting

Cost ofservice

CO

ST

Waiting time

Lost customers

Cost of Waiting = f(Satisfaction)

Factors Affecting Satisfaction

1. Firm-related factors

2. Customer-related factors

Firm-Related Factors

• “Unfair” versus “fair” waits

• Uncomfortable versus comfortable waits

• Initial versus subsequent waits

• Capacity decisions

Waiting Line (Queuing) Theory

• Application of statistics to allow us to perform a detailed analysis of system

– Utilization levels, line lengths, etc.

• Terminology and assumptions

Terminology and Assumptions I

?

Service

System

Line Phase

Terminology and Assumptions II

?

Service

Single-ChannelSingle-Phase

?

Service

?

Service

Multiple-ChannelSingle-Phase

Terminology and Assumptions III

Complex service environment ...

Howwould

youdescribe

this?

?

Service

?

Service

?

Service

?

Service

?

Service

Terminology and Assumptions IV

• Population: Infinite or Finite

• Arrival rates: Random or constant rate– Random rates typically defined by Poisson

distribution for infinite population

• Service Rates: Random or constant– Random service rates typically described by

exponential distribution

• Priority rules (aka “Queue Discipline”)

• Permissible queue length

Example

• A single drive-in window for Bank

• Arrival rate

– 15 per hour, on average

• Service rate

– 20 per hour, on average

• How many channels? Phases?

• What kinds of questions might we have?

Drive-In Bank

= arrival rate = 15 cars per hour

= service rate = 20 cars per hour

Average utilization of the system:

= = 0.75

Drive-In Bank

Probability of n arrivals during period T is:

Tn

n enT

P !)(

%87.0!4

)75.015( 75.0154

4 eP

e.g., probability of only 4 arrivals during a45-minute period is:

Drive-In Bank

Average number of cars in the system:(waiting plus being served)

carsCs 0.3)1520(

15)(

Drive-In BankAverage number of cars waiting:

carsC

CC

w

sw

25.2100225

)1520(2015

)()(

2

2

Drive-In Bank

Average time spent in the system:(waiting plus being served)

minutes122.0)1520(

1)(

1

hoursTs

(How do we know the answer is in hours?)

Drive-In Bank

Average time spent in the line:

minutes92.075.0)(

hoursTT sW

(How do we know the answer is in hours?)

Question?What happens as the arrival rate

approaches the service rate?

Suppose is now 19 cars per hour

One Answer:

Average number of cars waiting:

Implications? What are we assuming here?

carsCw 05.18)1920(20

19)(

22

Other Types of Systems(Discussed in the supplement to Chapter 8)

• Single-channel, single-phase with constant service time

– Example: Automatic car wash

• Multiple-channel, multiple-phase (hospital)

– Usually best handled usingsimulation analysis

Self Test I

• Look back at the drive-in window example. How can we have an average line length > 1 while the average number of cars being served is < 1?

• Similarly, what happens as the arrival rate approaches the service rate?

• Suppose the teller at the drive-in window is given training and can now handle 25 cars an hour (a 25% increase in service rate). What happens to the average length of the line?

Self Test II

• Look back at the Outback Steakhouse example. What kind of queuing system is it?

Question?

How can capacity change, even when we do not hire new people

or put in new equipment?

Learning Curves

• Recognize that people (and often equipment) become more productive over time due to learning.

• First observed in aircraft production during World War II

• Getting more emphasis as companies outsource more activities

A Formal Definition

For every doubling of cumulative output, there will bea set percentage improvement in time per unit or someother measure of input

1 2 4 8 16Output

Timeperunit

10 hrs.

8 hrs.

6.4 hrs.

5.12 hrs.4.096 hrs.

80% learning curve -Where does the name come from?

A Formal Definition (cont’d)

Where: Tn = time for the nth unit

T1 = time for the first unit

b = ln(learning percent) / ln2

b1n nTT

Example

• Reservation clerk at Delta Airlines• First call (while training) takes 8 minutes• Second call takes 6 minutes• What is the learning rate?• How long would you expect the 4th call to

take? The 16th? The 32nd?

Key Points

• Quick improvements early on, followed by more and more gradual improvements

• The lower the percentage, the steeper the learning curve

• Practically speaking, there is a floor• Estimates of effective capacity must consider

learning effects!

Another Question . . .

How could learning curves be used in long-term purchasing

contracts?

Johnston Controls I

• Johnston Controls won a contract to produce 2 prototype units for a new type of computer.

• First unit took 5,000 hrs. to produce and $250K of materials

• Second unit took 3,500 hrs. to produce and $200K of materials

• Labor costs are $30/hour

Johnston Controls II

• The customer has asked Johnston Controls to prepare a bid for an additional 10 units.

• What are Johnston’s expected costs?

Johnston Controls III

• Labor learning rate:

3500 hours / 5000 hours = 70%

• Materials learning rate:

$200K / $250K = 80%

Johnston Controls IV

• “Additional 10 units” means the third through twelfth units.

• Total labor for units 3 through 12:

= 5,000 hours × (5.501 – 1.7)= 19,005 hrs

5.501 is sum of nb for 12 units1.7 is the sum of nb for the first two units

Johnston Controls V

• Total material for units 3 through 12:

= $250,000 × (7.227 – 1.8)

= $1,356,750

Johnston Controls VI

• Total cost for “additional 10 units”:

= $30 × (19,005 hours) + $1,356,750

= $1,926,900

What if there is a significant delay before the second contract?

Self-Test

• Assume that there WILL BE a significant delay before Johnston Controls makes the next 10 units. Assuming that Johnston has to “start over” with regard to learning, estimate total cost for these additional 10 units.

Case Study in Managing Capacity

Forster’s Market