Managing Capacity Chapter 8. Chapter Objectives Be able to: Explain what capacity is, how firms...
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Transcript of Managing Capacity Chapter 8. Chapter Objectives Be able to: Explain what capacity is, how firms...
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