Chapter 1. Introduction - Florida Gulf Coast University
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Transcript Chapter 1. Introduction - Florida Gulf Coast University
Chapter 5. Capacity and Bottlenecks
Outline
Bottlenecks, near bottlenecks, and non bottlenecks
Identifying Bottlenecks
Working with bottlenecks
Theory of constraints basics
Modeling a simplified process: Queuing Theory
Tradeoffs of queuing theory
Characteristics of a queuing system
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Bottlenecks, Near Bottlenecks, Non Bottlenecks
Bottleneck: a resource which has a demand requirement
greater than capacity. Planned utilization > 100%
Given process variability, even if utilization is less than 100%, a
resource/activity can become a process bottleneck.
Near bottleneck: a resource with a planned utilization of
close to 100%, but where there are other resources with a
higher utilization
Non bottlenecks: a resource with a planned utilization <<
capacity
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Working with Bottlenecks
Recognizing bottlenecks is important in order to minimize
their effect.
Critical message is: time lost in the bottleneck is lost
production time and thus lost output (profits?). Time lost on
a near bottleneck or on a non bottleneck has (in most cases)
no effect on the output.
Operations improvement should then focus on
the improvement of capacity on the bottlenecks, and
maintaining the bottleneck operating at all times.
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Working with bottlenecks: Theory of
Constraints
Basic Steps
1. Identify the system constraints. (No improvement is possible
unless the constraint or weakest link is found.)
2. Decide how to exploit the system constraint. (Make the
constraints as effective as possible.)
3. Subordinate everything else to that decision. (Align every other
part of the system to support the constraints even if this
reduces the efficiency of non-constraint resources.)
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Working with bottlenecks: Theory of
Constraints
Basic Steps
4. Elevate the system constraints. (If output is still inadequate,
acquire more of this resource so it no longer becomes a
constraint.)
5. If, in the previous steps, the constraints have been broken, go
back to step 1, but do not let the inertia become the system
constraint. (After this constraint problem is solved, go back to
the beginning and start over.)
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Working with bottlenecks: Theory of
Constraints
Operating System called: Buffer, Rope , Drum
Buffer: inventory in front of the bottleneck, Rope: signal sent
upstream to get additional inventory, Drum: refers to the
bottleneck that maintains the production rhythm
product
Start
Activity 1
Make
Q
Activity 2
Hold area (WIP)
Activity 3
The Bottleneck
Information on
the current
quantity in hold
area
Yes
If quantity in
hold area < min R
No
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Activity 4
Customer
End
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Queuing Theory and its tradeoffs
the tradeoffs costs
1600
High1400
1200
1000
Cost
Body of knowledge
that analyzes
waiting lines
QT answers question
related to the size of
the line (queue) time
waiting in line, and
the tradeoffs
between service and
waiting costs
Cost of
Service
Cost of
Waiting
Total
Cost
800
600
400
200
Low
0
1
Low
2
3
4
High5
Capacity
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Characteristics of a Queuing System
A process model that is condensed into four elements:
arrival area (of a single type of entity)
a waiting area
an activity (the transformation process)
a departure area
Entity Arrives
Waiting area
Server
(activity)
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Entity Departs
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Characteristics of a Queuing System
Entity Arrivals
Modeled as a Poisson
distribution with parameter
Waiting Line
Organized by FCFS
Customers always joins
the line and never leaves
the line
Line has infinite space
Only one line
Arrival is modeled by a rate:
5 people/minute, 11 forms/
hour
Infinite population of
customers
Each arrival is of a single
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entity.
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Characteristics of a Queuing System
Server
One entity (customer) at a time
When there are more than one server, they work in parallel
Service time is a rate: 6 people/minute, 12 forms/ hour. The
inverse is the service time (10 seconds/person)
Service time is either constant or variable. If variable, it is
modeled as an exponential distribution with parameter
Departure
Once the service is completed entities leave the system.
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Queuing Theory: Line behavior
To evaluate system alternatives we need two cost
measures:
Cost of service for each option
Cost of waiting per customer per time unit (difficult to quantify)
Performance of a system
Wq = average time in the queue (waiting)
Ws = average time in the system (waiting and in service)
Lq = average length of the queue
Ls = average total number of entities in the system
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Calculating the measures of performance
Three models. Each uses some different equations (Will use
spreadsheets for the calculations)
Model 1 - constant service times and a single server
Model 2 - exponential service times and a single server
Model 3 - exponential service times and multiple servers
Total Costs = Cost of Service + Cost of Waiting
Cost of Waiting = Number of customers through system * time
waiting per customer * cost per waiting time (for a specified
time, I.e. day, month, year)
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