operations management
jenny2000000
6_LittlesLawandNCCpreparation.pptxClass 6 Process Flow Analysis III
Instructor: Mani Lakshmanan
P300 Introduction to Operations Management
Class 5 Review
Demand rate and inventory buildup
Demand Rate always < Capacity Rate:
No inventory buildup;
Existing inventory is processed at rate (capacity rate – demand rate)
Demand Rate > Capacity Rate:
Inventory accumulation at rate (demand rate –capacity rate)
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...
...
...
...
...
Input
Output
Demand rate, D
[units/hr]
Capacity rate
[units/hr]
Actual Flow Time
Actual Flow Time
= waiting time + theoretical flow time
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Capacity rate,
[units/hr]
...
...
...
...
...
Input
Output
Demand rate, D
[units/hr]
Actual Flow Time
Theoretical vs. Actual Flow Time
*Flow time efficiency = Theoretical flow time / Actual flow time
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By default, flow time = actual flow time
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In fact, let me show you more examples. The table here lists the values of the flow time efficiency for a variety of processes. We just got surprisingly low flow time efficiency. This implies how important to reduce the waiting time and to improve the flow time performance. To know how to reduce the waiting time, we need to first fully understand how waiting time is generated. What factors will determine the length of the waiting time. This is our job in the class’s remaining time.
Ok, will we see waiting time in steady state process? No, since there is no inventory, every arrived job is processed immediately. So waiting time occurs in non-steady state process. What is also appeared in non-steady state process? Inventory. So intuitively, we will think there is certain relationship between waiting and inventory.
Outline
Little’s Law
The relationship between Flow Time, Inventory and Throughput Rate
Introduction to Case 2: National Cranberry Cooperative
Demand Rate,
Capacity Rate
Inventory
Flow Time
Throughput Rate
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Minimum (
)
Little’s Law
Throughput rate:
The average rate that orders/items flow through a process
Equals minimum(Capacity Rate, Demand Rate).
Little’s law:
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...
...
...
...
...
Input
Output
Demand rate, D
[units/hr]
Throughput rate,
Flow Time, T
Inventory, I
Capacity rate, C
[units/hr]
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Little’s Law Example
The Travelers Insurance Company processes 10,000 claims per year. The average processing time is 3 weeks. Assuming 50 weeks in a year, what is the average number of claims “in process?”
Answer: 600
Number in process?
10,000 claims per year
3 weeks
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Now let us try some examples. Please work on these problems. And I will ask somebody to help me to explain how the Little’s law should be applied.
Little’s Law Example – E-mail
A student Sara receives 50 messages each day to which she must generate a response.
Suppose that she replies about 50 messages each day.
Sara removes a message from her InBox once she has responded to it. Then the remaining messages in her InBox are the messages that are waiting to be answered. Over the last semester, the size of the InBox has varied between one and two hundred messages with an average of 150 messages.
How long on average we need to wait for Sara to Reply a E-mail?
Answer: 3 days
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Little’s Law Example – Housing Market
The local real estate agent in your community estimates that it takes 120 days on average to sell a house; whereas this number changes some with the economy and season, it has been fairly stable over the past decade.
You observe from monitoring the classified ads that over the past year the number of houses for sale has ranged from 20 to 30 at any point in time, with an average of 25.
What can we say about the number of transactions in the past 360 days?
Answer: 75 transactions
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Little’s Law Example – Doughnut Shop
From your daily morning trip to the doughnut shop, you know they have a healthy business, at least financially speaking. As you might want to invest in a franchise, you wonder what amount of revenue they generate.
Over the course of several months; you visit the shop at random times between 6:00AM and 9:00 AM; you observe that the queue averages about 10 customers, and that it takes you about 3 min to get in and out of the shop.
Assume your experience is typical, and each order generates revenue of $10.
Apply Little's Law to estimate the doughnut shop’s revenue for the morning period 6:00AM ~ 9:00 AM.
Answer: 200 customers/hour
Revenue of $6000 for one morning
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Little’s Law Example – U.S. Yearly Births
How many people are born on average in U.S. per year?
Assume steady state: birth rate = death rate
U.S. population = 316.6 million*
(* U.S. POPClock Projection, U.S. Census Bureau, 2013)
U.S. life expectancy at birth = 78.37 years**
(** "CIA - The World Factbook". Cia.gov. Retrieved 2012-03-22.)
I = 316.6 million
T = 78.37 yrs
R = I / T ≈ 4.0 million/yr
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12.7 birth per 1000 people per year***
(*** World Development Indicators, The World Bank, 2012)
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Here I have an interview question asked by McKinsey Consulting. How many people are born worldwide in average per year? If you are not that knowledgeable, you can still figure out this question quickly. This actually requires for a birth rate. Let us assume the birth rate is equal to death rate. So the world population is in a steady state. How many people are there world wide? Let us say 7 billion. What is your estimate of people’s average lifespan?
70 years. All right, now do you know how to apply Little’s Law to get the result? 7billion/70years = 100 million/yr
Little’s Law
What is exactly in the box?
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Throughput rate,
Flow Time, T
Inventory, I
WIP
Orders
WIP
Input
Output
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Little’s Law
A relationship based on AVERAGE
I, average amount of items in the box
T, average time for one item to flow through the box from beginning to end
R, average rate to see items get out of the box
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Throughput rate,
Flow Time, T
Inventory, I
Input
Output
What if demand rate changes over time?
[units]
[hrs]
[units/hr]
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Little’s Law
Any limitation?
Over a long enough period of time, total input equals to total output
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Throughput rate,
Flow Time, T
Inventory, I
Input
Output
WIP
Burn CD
CAPACITY:
20 CDs/ hour
Demand rate: 15 CDs/hr
30 CDs/hr
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Improvements Based on Little’s Law
Consider the breakfast milk in the refrigerators of two students:
Student1:
Consumption Rate = 0.2 box/day
Inventory = 1 box
Flow Time =
Student 2:
Throughput Rate = 0.2 box/day
Inventory = 4 boxes
Flow Time =
If you were them, which would you prefer?
What would you do?
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20 days
5 day
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Which system is better?
How many students have more than 1 box of milk on average?
Improvements Based on Little’s Law
Usually want to improve system responsiveness or liquidity
This means the same or better throughput, but shorter flow time
Little’s law tells us
Shorten flow time increase throughput rate (R), or
decrease inventory (I)
Little’s Law is a diagnostic tool, not a prescriptive tool
Do help to identify what causes inventory or flow time to grow
Do not tell what levers we can use to decrease
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Since system 1 remains the same throughput rate, and at the same time, a better responsiveness. If we want to improve system responsiveness, Little’s law tells us, we can two things. Either increase throughput rate or decrease inventory. But Little’s Law is only a diagnostic tool. It tells you what are the reasons for a big inventory or for a long flow time. On what issues you might put your efforts on. However, it cannot tell you, you should use what levers to achieve your goal.
But do you have any idea of what levers we can use to shorten the flow time or to reduce the delay?
Outline
Little’s Law
The relationship between Flow Time, Inventory and Throughput Rate
Intro to Case 2: National Cranberry Cooperative
Min (Demand Rate,
Capacity Rate)
Inventory
Flow Time
Throughput Rate
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National Cranberry Cooperative
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A Process with Mixed Products
Two inputs from two mechanisms of cranberry harvesting
Water harvesting
Dry harvesting
Compute capacity rate of the process for EACH Product
Potential “resource sharing” problem
Two inputs occupy a same resource / activity
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The process we are going to analyze in the case is about raw cranberry processing. Basically, the input is raw cranberry, and the output is clean & dry cranberry that is ready for further production, such as making cranberry juice.
The difference of this process from those we have analyzed is… Each of them has exclusive activities in the process, while they also share some resource or activities.
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Example
Look at the following process:
A
B
A&B
A&B
A&B
1000 units/hour
200 units/hour
800 units/hour
400 units/hour to A
400 units/hour to B
500 units/hour
600 units/hour
O1
O2
O3
O4
O5
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In this example, there are five activities (O1~O5), and two products (A and B). Activity O1, O3 and O5 are shared by A and B, O2 is dedicated to A, and O4 is dedicated to B.
O3 is slightly different from O1 and O5: The capacity of O3 is specifically allocated (400 for A and 400 for B). In other words, although O3’s capacity is 800 units/hour, there is no way that the throughput of A can exceeds 400 units/hour.
How to figure out the capacity rate of this process for product A and B, respectively?
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Example
Separate & Combine
A
B
A&B
A&B
A&B
1000 units/hour
200 units/hour
800 units/hour
400 units/hour to A
400 units/hour to B
500 units/hour
600 units/hour
O1
O2
O3
O4
O5
Isolate the path for Product A:
Capacity Rate for A = 200 units/hour
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In this example, there are five activities (O1~O5), and two products (A and B). Activity O1, O3 and O5 are shared by A and B, O2 is dedicated to A, and O4 is dedicated to B.
O3 is slightly different from O1 and O5: The capacity of O3 is specifically allocated (400 for A and 400 for B). In other words, although O3’s capacity is 800 units/hour, there is no way that the throughput of A can exceeds 400 units/hour.
How to figure out the capacity rate of this process for product A and B, respectively?
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Example
Separate & Combine
A
A&B
A&B
A&B
1000 units/hour
200 units/hour
800 units/hour
400 units/hour to A
400 units/hour to B
500 units/hour
600 units/hour
O1
O2
O3
O4
O5
Isolate the path for Product B:
Capacity Rate for B = 400 units/hour
B
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In this example, there are five activities (O1~O5), and two products (A and B). Activity O1, O3 and O5 are shared by A and B, O2 is dedicated to A, and O4 is dedicated to B.
O3 is slightly different from O1 and O5: The capacity of O3 is specifically allocated (400 for A and 400 for B). In other words, although O3’s capacity is 800 units/hour, there is no way that the throughput of A can exceeds 400 units/hour.
How to figure out the capacity rate of this process for product A and B, respectively?
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Example
Combine to see whether there are conflictions:
A
B
A&B
A&B
A&B
1000 units/hour
200 units/hour
500 units/hour
600 units/hour
Capacity Rate for A = 200 units/hour
Capacity Rate for B= 400 units/hour
>600
=600
800 units/hour
400 units/hour to A
400 units/hour to B
O1
O2
O3
O4
O5
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Now, we put the two isolated paths together, and check whether there are conflictions of resource for those activities that are shared by A and B.
Here, O1 can finish 1000 units/hour. Even if we produce both A and B at their isolated capacity rates (which is the best we can do), we only need to occupy 600 units/hour from O1. Therefore, there is no confliction at O1.
Similar for O5, whose capacity rate is exactly 600 units/hour.
Therefore, there are no conflictions of resources in this process, and the “real” capacity rates of A and B are equal with their isolated capacity rates.
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Example
What if there is confliction?
Different capacity combinations are possible.
A
B
A&B
A&B
A&B
1000 units/hour
200 units/hour
500 units/hour
500 units/hour
<600
Total: 500 units/hour
A
B
800 units/hour
400 units/hour to A
400 units/hour to B
Capacity Rate for A = 200 units/hour
Capacity Rate for B= 400 units/hour
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What if we decrease the capacity rate of O5 down to 500 units/hour? There will be confliction at O5 in this case: Suppose we produce both A and B at their isolated capacity rates, it won’t work since we require 600 units/hour at O5.
Therefore, the allocation of resource at O5 determines the “real” capacity rates for A and B. For example, if we allocate 200 units/hour of O5 for A, and 300 units/hour of O5 for B, the real capacity rate will be 200 units/hour for A and 300 units/hour for B (rather than 400 units for B).
What are the efficient ways to allocate the resource at O5? For example, if we allocate 300 units/hour of O5 for A, it is inefficient since the capacity rate of A is still 200 units/hour (capped by the isolate capacity rate or, in other words, capped by O2). Hence, any allocation is inefficient if we allocate more than 200 units/hour for A. Similarly, any allocation is inefficient if we allocated less than 100 units/hour for A, which results into more than 400 units/hour for B (400 units/hour is the isolated capacity rate for B). Hence, efficient allocation for A ranges from 100 units/hour to 200 units/hour.
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NCC Case
Q1: Analyze the current process
Flow Diagram provided. Only need to fill capacity rate for each activity and identify the capacity rate of the process for each product.
No need to consider resource cycle time.
Q2: Maximum throughput rate
The definition of throughput rate.
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NCC Case
Q3: Inventory build-up diagram for bins and trucks
Consider wet and dry cranberry separately.
Q4: What are the possible capital investments considered by NCC?
Identify from case text
Q5: Quantify the costs and benefits for NCC’s investment for the fifth Kiwanee dumper in 1980.
Q6: Quantify the costs and benefits of “converting dry berry holding bins into wet/dry berry holding bins.”
How is the flow time / bottleneck affected?
How many bins to convert?
How much savings for truck drivers?
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NCC Case
Instruction file on Canvas
Due Sunday Midnight (Refer Canvas )
One report for each team
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Industry Process
Average
Flow Time
Theoretical
Flow Time
Flow Time
Efficiency*
Life Insurance
New Policy
Application
72 hrs. 7 min. 0.16%
Consumer
Packaging
New Graphic
Design
18 days 2 hrs. 0.14%
Commercial Bank
Consumer
Loan
24 hrs. 34 min. 2.36%
Hospital Patient Billing
10 days 3 hrs. 3.75%
Automobile
Manufacture
Financial
Closing
11 days 5 hrs 5.60%
|
Industry |
Process |
Average Flow Time |
Theoretical Flow Time |
Flow Time Efficiency* |
|
Life Insurance |
New Policy Application |
72 hrs. |
7 min. |
0.16% |
|
Consumer Packaging |
New Graphic Design |
18 days |
2 hrs. |
0.14% |
|
Commercial Bank |
Consumer Loan |
24 hrs. |
34 min. |
2.36% |
|
Hospital |
Patient Billing |
10 days |
3 hrs. |
3.75% |
|
Automobile Manufacture |
Financial Closing |
11 days |
5 hrs |
5.60% |
