LE 3D C3 Bank Inflow Little Law
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School
Clemson University *
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Course
8060
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
xlsx
Pages
14
Uploaded by SargentEnergyKouprey40
Name:
ARYAN NAHAR
Purpose of Exercise
Examine the relationship of Inventory, F
Flow Rate
"… the number of flow units that flow th
The total inflow rate is "the sum of the …
Intantaneous flow rate --R(t)
The flow rate at a specific point in time t
Inventory
"… the total number of flow units presen
I(t)
"the total number of flow units present w
Inventory Dynamics
inflow and outflow rates fluctuate over t
Instantaneous inventory accumulation (b
Total inflow rate -- R
i
(t)
Δ
R(t)
∆𝑅(𝑡)= 𝑅
Buildup Rate
Equation 3.1
Inventory Change
Equation 3.2
Inventory Change = B
Inventory Buildup Diagram
Depiction of inventory fluctuation over t
Average flow time
Stable Process
Little's Law
Equation 3.3
Average Inventory (I) = Throughput
KEY POINTS ABOUT PROCESSES
1
These are: i)
Connection (i.e., one a
shown by ii)
Buffers for waiting (w
or in a que
iii)
Activity or processing
2
a flow unit. Selection of the flo
medical process could be analy
being treated, or from the view dollars generated and dollars co
Process Flow Diagram EXERCISE
Scenario
A bank has a process in which customer
stand in a queue to wait their tu
turn they go to the bank teller a
"… the average flow time [is] the averag
specif span of time."
"A stable process
is one in which, in the
rate.
"
All work is done through proc
A process flow diagram is a sim
𝐼=𝑅×𝑇
∆𝑅(𝑡)= 𝑅
I(𝑡_2 )−𝐼(𝑡_
5
people in line waiting 4
minutes. On average
Another 8
customer p
The bank gathered the followin
About
20%
of custome
On average,
0.5
20
minutes with the loan 1
Is this system stable for this hour?
YES IT IS STABLE RI=RO
2
What is the flow unit in this example?
THE BANK CUSTOMER
3
Draw the process flow for the above sc
Use Little's Law to calculate unknown
R=
12
12
R=
0.2 per minuteper minute
I
5
R=
8 =D77
R=
0.333
R=
0.133333 per minute
T=I/R= 15.015015
4
How many customers are within the sy
(i.e., what is average inventor
8.165
5
How many customers are in process w
(i.e., what is average inventor
1.333
I
system
=
I
teller
=
Enter Front Door
Enter Back Door
teller
Teller
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6
What is the average flow time of a cus
after seeing the teller (i.e., wh
Teller Only=
19.01502
7
How many customers are in process w
1.332
8
What is the average flow time of a cus
(i.e., consider only one path)?
46.52252
9
What is the average SYSTEM flow tim
(i.e, all paths, from loan agent
Calculate this using Little's L
24.45
10
Use a second method to calculate syste
Use weighted average of path
Path
Weight
T*w
Teller->Exit
19.015
80%
15.21201
Teller->Loan Agent->Exit
46.5225
20%
9.304505
24.51652
=E133+E
I
loan agent
=
T
agent
=
T
system
=ISystem/RSystem=
Flow Time
T
system
=
Flow Time and Flow Rate in a stable system using Little's Law.
hrough a specific point in the process per unit of time…" (p. 49)
… inflow rates.. From the …entry points." (p. 49)
t (p. 49)
nt within process boundaries." (p. 49)
within process bundaries at time t", the process inventory at time t (p. 49)
time, so inventory increases (i.e., builds up) or decreases over time (p.50)
buildup) rate (p.50)
𝑅_𝑖 (𝑡)−𝑅_𝑜 (𝑡)
Buildup rate X Length of time interval (p.50)
time (p. 51)
p. 55
t (R) X Average Flow Time (T)
activity preceeds another or is in parallel and this precedence is
how they are connected); whether planned or because of delays, this can be a physical line eue of paperwork);
g. This is where something is done to a flow unit
ow unit determines our perspective. For example, the same yzed from the viewpoint of the patient of medical supplies used, or from the view of onsumed during the process.
rs may enter the bank from multiple locations. All customers enter and then urn to see the bank teller. When it is their and conduct business. During the 9 to 10 AM period, there are on average ge (of the flow times) across all flow units that exit the process during a e long run, the average inflow rate is the same as the average outflow cesses.
All processes consist of very basic steps or elements.
mplified abstraction of an actual process
.
It starts by selecting
𝑅_𝑖 (𝑡)−𝑅_𝑜 (𝑡)
_1 )= ∆𝑅×(𝑡_2−𝑡_1 )
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to be seen. The average processing time at the teller is 12
customer per hour enter the front door.
per hour enter the back door. Over a 1
hour period the inflow rate ng additional data about customers during the same time period.
ers arriving during this time leave the teller and go to a loan agent.;
customers are waiting for a loan agent. They spend
agent and then leave. The loan agents usally finish their work with these applicants ?
cenario> Use the symbols, insert variables (I,R,T) below symbols or on arrows a
n variables.
Little's Law: I = R x T, so T = I/R
I
20%
R=
0.0666
I
0.5
1.332
R=
0.067
0.067
1.333
T=I/R= 7.507508
20
0.333
I
80%
4
R=
0.266
ystem
ry in system)?
=SUM(E101,F101,I99,J99,I98)
20
with the teller
ry in one location)?
=F101
Leave?
loan agent
Loan Agent
stomer who leaves
hat is average system flow time)?
=SUM(E103:F103)
with a loan agent?
customers
=J99
stomer leaving the loan agent ?
minutes
=SUM(E103,F103,I101,J101)
me of a customer
t or teller)?
Law.
Little Law: I = R * T
minutes
=E108/O102
<---
Calculated using Little's Law
em flow time. hs
Flow Time
Weight
T*w
=E116
=K102
=C133*D133
=E123
=G95
=C134*D134
minutes
E134
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= outflow rate
before 10AM.
as appropriate..
R=
0.334
0
R=
0.333
Exit
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Most common symbols for flow charts.
This single arrow can be a connecting arrow, or it can show the throughput rate of flow Use the triangle to show units waiting in line or in storage. Do not combine waiting and
The diamond represents a decision. In practice, different flow units follow di
from this decision diamond.
The square or rectangle shows the process. It is a "Doing" step. It can repres
or it can represent a person doing something.
This represents events that are typically not par tof the actual flow. They ma
reader to know where the process starts and where it ends. They can be use
as labels during the process.
I=
R=
T=
Decision
Process
Event
units entering
d doing.
ifferent paths
sent a machine
ake it easy for the
ed
End
Teller
teller
Leave
?