Operations management

Session 3: Measures:

Capacity, Time, and More

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Previous Week

What are the key concepts learned in the last week?

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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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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

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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.

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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

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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?

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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?

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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.

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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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Utilization Rate

Capacity

used)(Capacity rate Throughputraten Utilizatio

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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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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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Utilization Rate

Can utilization rate be greater than 1?

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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

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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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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

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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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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

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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

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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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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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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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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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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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Admission Flow

The admission process

1000

50%

50%

200

100

Reject Process

Accept Process

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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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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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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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Alternative Solution

What is the average processing time?

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Admission Flow

Little’s Law holds for complicated systems.

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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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Emergency Room: Example

Imagine the following sequence of event

1,2

15 30 45 60

1 3

75

3

2

Waiting

Service

2

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Emergency Room: Example

Do we have enough capacity?

What is the utilization rate?

Why patients wait?

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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

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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

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Emergency Room

Randomness/Variability forces resource idleness and longer waiting time.

Little’s Law still holds.

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What Have We Learned

Process Measures Throughput Rate Capacity Throughput Time WIP

Little’s Law

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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.