1. Managing Capacity

2. 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.
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3. Capacity Decisions Defining and measuring capacity
Strategic versus tactical capacity
Evaluating capacity alternatives
Advanced perspectives
Theory of Constraints
Waiting lines
Learning curves
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4. Defining and Measuring Capacity
Measure of an organization’s ability to provide goods or services
Jiffy Lube  Oil changes per hour Law firm  Billable hours College  Student hours per semester
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5. Consider: Capacity for a PC Assembly Plant: Controllable Factors
(800 units/shift/line)×(% Good)×(# of lines)×(# of Shifts)
Controllable Factors
1 or 2 shifts? 2 or 3 lines? Employee training?
Uncontrollable Factors
Supplier problems? 98% or 100% good? Late or on time?
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6. Strategic versus Tactical Capacity
One or more years out
“Bricks & Mortar”
Future technologies
Tactical:
One year or sooner
Workforce level, schedules, inventory, etc.
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7. Capacity versus Time Capacity Time Days or weeks out Months out
Planning & Control
Limited ability
to adjust
capacity
Detailed planning
Lowest risk
Tactical Planning
Workforce, inventory,
subcontracting decisions
Intermediate-level
planning
Moderate risk
Strategic Capacity Planning
“Bricks &
mortar” decisions
High-level planning
High risk
Capacity
Time
Days or weeks out
Months out
Years out
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8. Capacity Strategies: When, How Much, and How?
Demand
Leader
Excess
Capacity
Lost Business
Laggard
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9. How? Make or Buy (e.g., subcontracting)
One extreme: “Virtual” Business
Walden Paddlers
(Marketing)
Hardigg Industries
(Manufacturing)
Independent Dealers
(Direct Sales)
General Composites
(Design)
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10. Evaluating Capacity Alternatives
Economies of scale (EOS)
Expected value analysis (EVA)
Decision Trees
Break-even points (BEP)
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11. 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?
X = 1: $200,004
X= 10,000: $24
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12. Fixed & Unit Cost Scenarios
Page 214 in text.
Common Carrier: Fixed cost = 0, unit cost = $750
Contract Carrier: Fixed cost = $5,000, unit cost = $300
Private Carrier: Fixed cost = $21,000, unit cost = $50
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13. 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?
X = or about 11
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14. Expected Value Analysis
Forecasted demand or volume is uncertain, allows consideration of the variability in the data

15. Capacity cost structure
Data Requirements
Capacity cost structure
(alternatives?)
Expected demand
(multiple scenarios?)
EVA
Product and service
requirements
(e.g. time standards)
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16. Expected Value Analysis
Pennington Cabinet Company jobs per year (20% likelihood) 5000 jobs per year (50%) jobs per year (30%)
Each job = $1,200 revenue
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17. We Know:
Average job requires: hours of machine time /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!)
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18. Number of Machines and Teams Number of Hours Available Each Year
Effective Capacity
Number of Machines and Teams
Number of Hours Available Each Year
Maximum Jobs per Year
Machines
Teams
Current 3 5
6,000
10,000
3,000
Expanded 9
18,000
5,000
5,400
New Site 7 12
14,000
24,000
7,000
7,200
Effective capacity is limited by machine capacity
What is the effective capacity
of each capacity alternative?
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19. Alternate Demand Scenarios
Current Level
Expanded
New Site
Demand
Revenue
Fixed
Expenses
2,000
$2,400,000
$1,600,000
$2,800,000
$3,800,000
5,000
$3,600,000
$6,000,000
7,000
$8,400,000
What is the expected contribution if demand = 5000
AND we decide to move to a new site?
Why does revenue for current capacity max out at $3.6 million?
$2,200,000
Cannot handle a demand greater than 3,000
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20. 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
$4,600,000
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21. Expected Value of Each Capacity Alternative:
Current capacity level (20%) × $800K +(50%) × $2000K +(30%) × $2000K = $1,760,000
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22. Expected Value of Each Capacity Alternative:
Expanded capacity level (20%) × – $400K + (50%) × $3200K + (30%) × $3200K = $2,480,000
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23. Expected Value of Each Capacity Alternative:
New Site capacity level (20%) × – $1400K + (50%) × $2200K + (30%) × $4600K = $2,200,000
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24. 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?
Maximin: Current site at $800,000
Maximax: New site at $4,600,000
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25. Visual tool for evaluating choices using expected value analysis
Decision Trees
Visual tool for evaluating choices using expected value analysis
Allows use of different outcomes and different probabilities of success for each

26. 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
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27. 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?
Refer students to the text, Example 8.3, Figures 8.4 and 8.5, for this discussion
Different probabilities because of location differences, market size differences, product mix differences, technology differences, etc.
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28. 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?
Desirable examples: Market share, potential market size, product volume times price, projected reliability, project completion time…
Undesirable examples: yield loss, projected failure rate, holding costs, quality costs, time-to-market, etc.
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29. 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 $ BEP  $100X = $200,000 + $4X What is the breakeven volume, X?
BEP: X = 2,084
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30. 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: units (25%), 300 units (50%), 350 units (25%)
BEP at ($200 - $50)X = $40,000, that is, X = = 267
Net for 250 units = <$2,500>
Net for 300 units = $5,000
Net for 350 units = $12,500
EMV = 0.25 x (-$2,500) x $5, x $12,500 = $5,000
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31. Advanced Perspectives
Theory of Constraints
Waiting lines
Learning curves

32. 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?

33. Theory of Constraints Pipeline analogy
Which piece of the pipe is restricting the flow?
Would making parts A or D bigger help?
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34. Dealing with a Constraint
Identify the constraint
Exploit 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?
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35. Waiting Lines Waiting lines and services Waiting Line Theory
Waiting and customer satisfaction
Factors affecting satisfaction
Waiting Line Theory
Terminology and assumptions
Illustrative example
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36. Waiting at Outback Steakhouse...
Waiting outside or in bar
Waiting to get food...
Leaving
restaurant
Waiting to pay bill ...
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37. 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
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38. Waiting and Customer Satisfaction
Cost of
service
Cost of
waiting
Lost customers
COST
Waiting time
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39. Cost of Waiting = f(Satisfaction)
Factors Affecting Satisfaction
Firm-related factors
Customer-related factors
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40. Firm-Related Factors “Unfair” versus “fair” waits
Uncomfortable versus comfortable waits
Initial versus subsequent waits
Capacity decisions
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41. 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
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42. Terminology and Assumptions I
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43. Terminology and Assumptions II
Single-Channel
Single-Phase
Multiple-Channel
Single-Phase
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44. Terminology and Assumptions III
Complex service environment ...
How
would
you
describe
this?
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45. 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
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46. Example A single drive-in window for Bank Arrival rate Service rate
15 per hour, on average
Service rate
20 per hour, on average
How many channels? Phases?
What kinds of questions might we have?
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47.  = arrival rate = 15 cars per hour
Drive-In Bank
 = arrival rate = 15 cars per hour
 = service rate = 20 cars per hour
Average utilization of the system:
 =  = 0.75
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48. Drive-In Bank Probability of n arrivals during period T is:
e.g., probability of only 4 arrivals during a 45-minute period is:
Note: Discuss with students about need to keep time references to the same period. Here, since l is in cars per hour,
45 minutes must be converted to 0.75 hours.
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49. Drive-In Bank
Average number of cars in the system: (waiting plus being served)
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50. Drive-In Bank Average number of cars waiting:
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51. Drive-In Bank
Average time spent in the system: (waiting plus being served)
(How do we know the answer is in hours?)
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52. Drive-In Bank Average time spent in the line:
(How do we know the answer is in hours?)
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53. Suppose l is now 19 cars per hour
Question? What happens as the arrival rate approaches the service rate?
Suppose l is now 19 cars per hour

54. One Answer: Average number of cars waiting:
Implications? What are we assuming here?
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55. 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 using simulation analysis
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56. 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?
Length of the line for a service rate of 25 cars per hour is 225/[25(25-15)] =0.9 cars, a decrease from 2.25 cars
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57. Self Test II
Look back at the Outback Steakhouse example. What kind of queuing system is it?
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58. Question?
How can capacity change, even when we do not hire new people or put in new equipment?

59. 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
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60. A Formal Definition 80% learning curve -
For every doubling of cumulative output, there will be
a set percentage improvement in time per unit or some
other measure of input
Output
Time
per
unit
10 hrs.
8 hrs.
6.4 hrs.
5.12 hrs.
4.096 hrs.
80% learning curve -
Where does the name come from?
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61. A Formal Definition (cont’d)
Where: Tn = time for the nth unit
T1 = time for the first unit
b = ln(learning percent) / ln2
Explain to students that ln represents the natural logarithm
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62. 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?
Learning rate = 6min/8min = 75%
Using Table 8.6 in textbook: Learning rate = 6/8 = 75%
4th call is x 8 min = minutes
16th call is x 8 min = minutes
32nd call is x 8 min = min or 0.75 of 16th call time = x 0.75 = min
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63. 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!
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64. How could learning curves be used in long-term purchasing contracts?
Another Question . . .
How could learning curves be used in long-term purchasing contracts?

65. 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
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66. Johnston Controls II
The customer has asked Johnston Controls to prepare a bid for an additional 10 units.
What are Johnston’s expected costs?
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67. Johnston Controls III
Labor learning rate: hours / 5000 hours = 70%
Materials learning rate: $200K / $250K = 80%
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68. 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 units
1.7 is the sum of nb for the first two units
Refer to Table 8.6 in textbook for 70% learning curve data
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69. Johnston Controls V
Total material for units 3 through 12: = $250,000 × (7.227 – 1.8) = $1,356,750
Refer to Table 8.6 in textbook for 80% learning curve data
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70. Johnston Controls VI
Total cost for “additional 10 units”: = $30 × (19,005 hours) + $1,356, = $1,926,900
What if there is a significant delay before the second contract?
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71. 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.
Assume same learning curve percentages, but start anew.
Hence, using sum of nb for first 10 units, hours will be 5,000 x = 24,660 and hours cost will be $30 x 24,660 = $739,800
Materials cost will be $250,000 x = $1,578,750
Total cost will $2,318,550 compared to cost of $1,926,200 if we order right away, a savings of $392,350!
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72. Case Study in Managing Capacity
Forster’s Market