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Operations management
Session 3: Measures:
Capacity, Time, and More
Session 3 Operations Management 2
Previous Week
What are the key concepts learned in the last week?
Session 3 Operations Management 3
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
Session 3 Operations Management 4
Analyzing Business Process
InputsOutputs
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
Session 3 Operations Management 5
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
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 30000 hits per min A worker can assemble 2.22 hamburgers per min A stove can cook 20 hamburgers per min
or 0.33333 per second (Note: Units are important!)
It is a rate: Units/Time
Session 3 Operations Management 7
Process Capacity
RawMaterial 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?
Session 3 Operations Management 8
Analysis
Cooking First 20 Second 20 Third 20
1:00 2:00 3:00
10 20
1:27 1:54
Assembly
Suppose an order for 60 hamburgers is placed.What will happen?
30 40
2:27 2:54
50 60
3:27 3:54
If order continues to come, how many more hamburgers do we produce for every minute?
Session 3 Operations Management 9
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
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?
Session 3 Operations Management 11
Utilization Rate
Capacity
used)(Capacity rate Throughputraten Utilizatio
Session 3 Operations Management 12
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
Session 3 Operations Management 13
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?
Session 3 Operations Management 14
Utilization Rate
Can utilization rate be greater than 1?
Session 3 Operations Management 15
Measure: Time
How long it takes to turn patties into burgers?
Cooking First 20 Second 20 Third 20
1:00 2:00 3:00
10 20
1:27 1:54
Assembly 30 40
2:27 2:54
50 60
3:27 3:54
Session 3 Operations Management 16
Throughput Time
Different units may spend different amount time.
What is throughput time? The average time a unit stays in the system
Session 3 Operations Management 17
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?
Customer arrives Service begins Service ends
Throughput Time
Waiting Processing
Book arrives Stored Order arrives Picked Packaged Shipped
Throughput Time
Session 3 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.
Session 3 Operations Management 19
Flow Measures: Throughput rate
What is the relationship between throughput rate throughput time and WIP?
Time
WIP
Throughput rate is two unit per unit of time
Session 3 Operations Management 20
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
Little’s Law
Session 3 Operations Management 21
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?
Session 3 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
Session 3 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?
Session 3 Operations Management 24
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.
Session 3 Operations Management 25
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?
Session 3 Operations Management 26
Admission Flow
The admission process
1000
50%
50%
200
100
Reject Process
Accept Process
Session 3 Operations Management 27
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
Session 3 Operations Management 28
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.
Session 3 Operations Management 29
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?
Session 3 Operations Management 30
Alternative Solution
What is the average processing time?
Session 3 Operations Management 31
Admission Flow
Little’s Law holds for complicated systems.
Session 3 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?
Session 3 Operations Management 33
Emergency Room: Example
Imagine the following sequence of event
1,2
15 30 45 60
1 3
75
3
2
Waiting
Service
2
Session 3 Operations Management 34
Emergency Room: Example
Do we have enough capacity?
What is the utilization rate?
Why patients wait?
Session 3 Operations Management 35
Emergency Room: Example
In the waiting room,
Average WIP = (0 + 1 + 0 + 0) / 4 = 0.25
Average waiting time =
Calculate average waiting time directly
= (15 + 0 + 0)/3 = 5 minutes
Session 3 Operations Management 36
Emergency Room: Example
For the total time spent (waiting + service),
Average WIP = (0 + 2 + 1 + 1) / 4 = 1
Average waiting time =
Calculate average time spent directly
= (15 + 30 + 15)/3 = 20 minutes
Session 3 Operations Management 37
Emergency Room
Randomness/Variability forces resource idleness and longer waiting time.
Little’s Law still holds.
Session 3 Operations Management 38
What Have We Learned
Process Measures Throughput Rate Capacity Throughput Time WIP
Little’s Law
Session 3 Operations Management 39
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.