1. Operations management
Session 3: Measures:
Capacity, Time, and More

2. Operations Management
Previous Week
What are the key concepts learned in the last week?
Session 3
Operations Management

3. Operations Management
Class Objectives
Review of the last week
How do we quantitatively evaluate a process?
Capacity
Time
Other?
Little’s Law
A general rule that links various performance measures
Examples
Summary
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Operations Management

4. Analyzing Business Process
Inputs Outputs
Our purpose is to examine a transformation process from the perspective of flows.
The unit being transformed is typically referred to as a job and can represent a customer, an order, material, money, information, etc.
Transformation Process
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Operations Management

5. Operations Management
Throughput Rate
In general, the inflow rate and the outflow rate fluctuate over time. Define the average in (out) flow rates as the long-run average number of jobs that flow into (out of) the system.
In a stable environment, the average inflow rate is equal to the average outflow rate
The average flow rate through the system is referred to as the throughput rate assessed as the number of jobs per unit time.
Session 3
Operations Management

6. Operations Management
Measure: Capacity
Definition: The number of units, per unit of time, that can be processed.
Examples:
A casher can serve 20 customers per hour
The capacity of a server is hits per min
A worker can assemble 2.22 hamburgers per min
A stove can cook 20 hamburgers per min
or per second (Note: Units are important!)
It is a rate: Units/Time
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Operations Management

7. Operations Management
Process Capacity
Raw
Material
Cook
Assemble
Deliver
Patties cook in 60 seconds; the stove holds 20 patties.
Assembly of a hamburger takes 27 seconds per hamburger.
10 workers are available to assemble hamburgers.
What is the capacity of the cooking stage? What is the capacity of the assembling stage?
What is the capacity of the process?
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Operations Management

8. Operations Management
Analysis
Suppose an order for 60 hamburgers is placed.
What will happen?
1:27
1:54
2:27
2:54
3:27
3:54 10 20 30 40 50 60
Assembly
First 20
Second 20
Third 20
Cooking
1:00
2:00
3:00
If order continues to come, how many more hamburgers
do we produce for every minute?
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Operations Management

9. Operations Management
Bottleneck Analysis
The stove, operating 100% of the time, can push out: 20 hamburgers / 1 minute = 20 hamburgers per minute.
The workers, operating 100% of the time, can push out: 10 hamburgers / 27 seconds = 22.2 hamburgers per minute.
The stove is the bottleneck resource; it pushes out the slowest amount of hamburgers per time period.
Session 3
Operations Management

10. Operations Management
Calculating Capacity
The capacity of a process is determined by the slowest (bottleneck) resource.
To calculate the bottleneck resource, calculate the amount of “stuff” each resource can push out per unit time. The bottleneck resource is the resource that pushes out the least amount of “stuff” per unit time.
Would hiring an additional worker increase the revenue?
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Operations Management

11. Operations Management
Utilization Rate
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Operations Management

12. Operations Management
Utilization Rate
Utilization rate is a measure of efficiency.
It measures the percentage of products/services that the process is producing what it is designed (suppose) to do.
An example:
The capacity of a cashier in Starbucks is 96 customers per shift.
The cashier’s throughput rate is only 72 customers per shift.
What is the capacity utilization? 72/96 = 0.75
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Operations Management

13. Operations Management
Utilization Rate
What is the meaning of the number 0.75?
The cashier is busy only 75% of the time.
25% of the time the cashier is idle and not doing any productive work.
What are the managerial implications?
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Operations Management

14. Operations Management
Utilization Rate
Can utilization rate be greater than 1?
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Operations Management

15. Operations Management
Measure: Time
How long it takes to turn patties into burgers?
1:27
1:54
2:27
2:54
3:27
3:54 10 20 30 40 50 60
Assembly
First 20
Second 20
Third 20
Cooking
1:00
2:00
3:00
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Operations Management

16. Operations Management
Throughput Time
Different units may spend different amount time.
What is throughput time?
The average time a unit stays in the system
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Operations Management

17. Operations Management
Throughput Time
Average time a customer spends in a bank
Average time a book stays at the Amazon.com’s warehouse
How do we measure throughput time?
Waiting
Processing
Customer arrives
Service begins
Service ends
Throughput Time
Book arrives
Stored
Order arrives
Picked
Packaged
Shipped
Throughput Time
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Operations Management

18. Flow Measures: Work in Process
Work in Process (WIP) Inventory: the number of units at a point of time.
Example 1: The WIP in Disneyland is the number of customers waiting, eating, resting, or playing in Disneyland.
Example 2: The WIP in Space Mountain is the number of customers waiting for or riding in Space Mountain.
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Operations Management

19. Flow Measures: Throughput rate
What is the relationship between throughput rate throughput time and WIP?
WIP
Throughput rate is two
unit per unit of time
Time
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Operations Management

20. Operations Management
Little’s Law
Throughput Time = (Average) WIP / Throughput Rate
Example: Bank Teller
Average WIP: 6 customers
Throughput rate: 12 customers per hour
Throughput time: 6/12 = 0.5
A customer spends (on average) 0.5 hours in the bank
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Operations Management

21. Operations Management
Little’s Law
In the bank example on the previous overhead …
Does this mean each customer spends 0.5 hours in the bank?
How many customers arrive on average in an hour?
How many customers leave on average in an hour?
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Operations Management

22. Implications of Little’s Law
Given average WIP and throughput rate, we can calculate throughput time
Relatively easy to measure WIP and throughput rate
Keeping WIP fixed, reducing throughput time results in a higher throughput rate.
Throughput Rate = Average WIP / Throughput Time
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Operations Management

23. Implications of Little’s Law
Average number of customers in a restaurant: 50
Average number of customers arriving (and leaving) per hour: 30
The throughput time is 50/30 = 1.66
A customer spends (on average) 1hr and 40 mins.
The restaurant is losing money. How can an OM person help?
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Operations Management

24. Operations Management
Admission Flow
Marshall provides higher education to executives and receives about 1000 applications per month.
The evaluation starts with a preliminary classification with basic information:
Group A: Applicants with desired recommendations, working experience, etc. (50% of the applicants)
Group B: Other applicants. (50% of the applicants)
Applicants in group A will be further considered through an advanced review.
Applicants in group B will be rejected.
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Operations Management

25. Operations Management
Admission Flow
On average there were:
200 applications in the preliminary review stage
100 applications in the advanced review stage
How long does group A spend in the application process?
How long does group B spend in the application process?
How long is the average process time?
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Operations Management

26. Operations Management
Admission Flow
The admission process
100
50%
Accept Process
1000
200
50%
Reject Process
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Operations Management

27. Operations Management
Admission Flow
Let us do a detailed analysis
How long do the applicants spend in the preliminary review stage?
TT = WIP/TR=200/1000 = 0.2 * 30 days = 6 days
Applicants spend 6 days in the first stage
Applicants from group B receive an answer in 6 days on average
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Operations Management

28. Operations Management
Admission Flow
How long do the applicants from group A spend in the advanced review stage?
TT = WIP/TR=100/(1000*50%) = 0.2
Applicants from group A spend 6 days on average in the advanced review stage.
Applicants from group A receive answer in 12 days (6 + 6) on average.
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Operations Management

29. Operations Management
Admission Flow
What is the average processing time?
6*0.5+12*0.5 = 9 days
Is there an alternative way to calculate the average waiting time?
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Operations Management

30. Operations Management
Alternative Solution
What is the average processing time?
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Operations Management

31. Operations Management
Admission Flow
Little’s Law holds for complicated systems.
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Operations Management

32. Emergency Room: Example
Let us calculate the average waiting time in an emergency room.
Imagine a system in which a patient can be treated in exactly 15 minutes.
Two patients arrive at minute 15, and one patient arrives at minute 45.
What is the average waiting time?
Is there enough capacity?
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Operations Management

33. Emergency Room: Example
Imagine the following sequence of event
Service 1 2 3
Waiting 2 15 30 45 60 75
1,2 3
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Operations Management

34. Emergency Room: Example
Do we have enough capacity?
What is the utilization rate?
Why patients wait?
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Operations Management

35. Emergency Room: Example
In the waiting room,
Average WIP = ( ) / 4 = 0.25
Average waiting time =
Calculate average waiting time directly
= ( )/3 = 5 minutes
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Operations Management

36. Emergency Room: Example
For the total time spent (waiting + service),
Average WIP = ( ) / 4 = 1
Average waiting time =
Calculate average time spent directly
= ( )/3 = 20 minutes
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Operations Management

37. Operations Management
Emergency Room
Randomness/Variability forces resource idleness and longer waiting time.
Little’s Law still holds.
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Operations Management

38. Operations Management
What Have We Learned
Process Measures
Throughput Rate
Capacity
Throughput Time
WIP
Little’s Law
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Operations Management

39. Operations Management
Next Time
Kristen’s Cookie Company
Everybody: read the case and be prepared for class discussion
Presenting teams: prepare a write-up and presentation for 10 minutes (exactly)
Note that Kristen’s cookies case slides (and all case slides) will not be posted to Blackboard.
Session 3
Operations Management