Queuing Systems: basic elements
-
Upload
leilani-briggs -
Category
Documents
-
view
35 -
download
0
description
Transcript of Queuing Systems: basic elements
![Page 1: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/1.jpg)
Arrivals ServiceWaitingline
Exit
Processingorder
System
Queuing Systems: basic elements
![Page 2: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/2.jpg)
Multiple channel
Multiple phase
Queuing Systems: multiple phases
![Page 3: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/3.jpg)
Modeling with Queuing Theory
System Characteristics– Population source: finite, infinite– No. of servers– Arrival and service patterns: e.g. exponential
distribution for inter-arrival time– Queue discipline: e.g. first-come-first-serve
![Page 4: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/4.jpg)
Measuring Performance
Performance Measurement:– System utilization– Average no. of customers: in line and in system– Average waiting time: in line and in system
e.g. infinite source, single server, exponential inter-arrival and service times, first-come-first-serve: (see handout)
![Page 5: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/5.jpg)
Optimum
Cost of service capacity
Cost of service capacity
Cost of customerswaiting
Cost of customerswaiting
Total costTotal cost
Co
st
Service capacity
Totalcost
Customerwaiting cost
Capacitycost= +
Basic Tradeoff
![Page 6: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/6.jpg)
System Utilization
Av
era
ge
nu
mb
er o
n
tim
e w
ait
ing
in li
ne
0 100%
Basic Tradeoff (cont.)
![Page 7: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/7.jpg)
Applying Queuing Theory
In Process Design:– Describe the process and establish a model– Collect data on incoming and service patterns– Find formulas and/or tables, software to calculate
performance measures– Use performance measures to guide process design
decisions
![Page 8: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/8.jpg)
Applying Queuing Theory
In Operations:– Monitor performance measures– Use performance measures to guide process
improvement and operations decisions
![Page 9: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/9.jpg)
Statistical Process Control
Emphasis on the process instead of the product/material
Focus on “prevention”
![Page 10: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/10.jpg)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
UCL
LCL
Sample number
Mean
Out ofcontrol
Normal variationdue to chance
Abnormal variationdue to assignable sources
Abnormal variationdue to assignable sources
Control Chart
![Page 11: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/11.jpg)
Sample number
UCL
LCL
1 2 3 4
In-Control: random only
![Page 12: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/12.jpg)
Control Charts for Variables
Mean Chart: measuring sample means Range Chart: measuring sample ranges
i.e. max-min
![Page 13: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/13.jpg)
UCL
LCLUCL
LCL
R-chart
x-Chart Detects shift
Does notdetect shift
process mean is shifting upward
SamplingDistribution
Out-of-Control: assignable & randomshifted mean
![Page 14: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/14.jpg)
UCL
LCL
LCL
R-chart Reveals increase
x-Chart
UCL
Does notreveal increase
(process variability is increasing)SamplingDistribution
Out-of-Control: assignable & randomincreased variability
![Page 15: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/15.jpg)
Mean
LCL UCL
/2 /2
Probabilityof Type I error
Type I Error:
![Page 16: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/16.jpg)
MeanLCL UCL
Type II Error:
In-Control Out-of-Control
![Page 17: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/17.jpg)
p-Chart - Control chart used to monitor the proportion of defectives in a process
c-Chart - Control chart used to monitor the number of defects per unit
Control Charts for Attributes
![Page 18: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/18.jpg)
Counting Above/Below Median Runs (7 runs)
Counting Up/Down Runs (8 runs)
U U D U D U D U U D
B A A B A B B B A A B
Counting RunsFigure 10-11
Figure 10-12
![Page 19: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/19.jpg)
LowerSpecification
UpperSpecification
Process variability matches specifications
LowerSpecification
UpperSpecification
Process variability well within specifications
LowerSpecification
UpperSpecification
Process variability exceeds specifications
Process Capability
![Page 20: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/20.jpg)
Processmean
Lowerspecification
Upperspecification
1350 ppm 1350 ppm
1.7 ppm 1.7 ppm
+/- 3 Sigma
+/- 6 Sigma
Process Capability: 3-sigma & 6-sigma
![Page 21: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/21.jpg)
Input/Output Analysis
Change in inventory = Input - Output Average throughput time is proportional to the
level of inventory.
![Page 22: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/22.jpg)
Input flow of materials
Inventory level
Scrap flow
Output flow of materials
Flow and InventoryFlow and Inventory
Figure 11.1
![Page 23: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/23.jpg)
MRP
A general framework for MRP Inputs: Bill of Materials, Inventory Files and
Master Production Schedule MRP Processing
![Page 24: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/24.jpg)
A General Framework of MRP
Aggregate Plan
Master ProductionSchedule
MRP
Capacity RequirementsPlanning
Production Scheduling
![Page 25: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/25.jpg)
Master Production ScheduleMaster Production Schedule
Week 1 2 3 4 5 6 7 8
M1 23 23 23 23
M2 10 10 10
![Page 26: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/26.jpg)
Bill of MaterialsBill of MaterialsC (1)Seat
subassembly
H (1)Seat
frame
I (1)Seat
cushion
J (4)Seat-frame
boardsFigure 15.10
![Page 27: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/27.jpg)
Inventory Files
On-Hand Open Orders Lead Times Vendor Information Quality records, etc.
![Page 28: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/28.jpg)
MRP ExplosionMRP Explosion
Item: Seat subassemblyLot size: 230 units
Lead time: 2 weeks
Gross requirements 150150
1
230230
117117
2 3
120120
4 5
150150
6
120120
7 8
Scheduled receipts
Projected on-hand inventory
Planned receipts
Planned order releases
37
Week
117117 117117
0 00 0
00 00 000 00 0
227 227 77 187 187
230230
230230
Figure 15.11
![Page 29: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/29.jpg)
Item: Seat subassemblyLot size: 230 units
Lead time: 2 weeks
Gross requirements 150150
1 2 3
120120
4 5
150150
6
120120
7 8
Planned receipts
Planned order releases
Week
0 00 0
230
230
230
230
Item: Seat framesLot size: 300 units
Lead time: 1 week
Gross requirements 00
1
00
2 3
00
4 5 6 7 8
Scheduled receipts
Projected on-hand inventory
Planned receipts
Planned order releases
40
Week
230 2300
00 00 00300 00 0
Item: Seat cushionLot size: L4L
Lead time: 1 week
Gross requirements 00
1
00
2 3
00
4 5 6 7 8
Scheduled receipts
Projected on-hand inventory
Planned receipts
Planned order releases
0
Week
230 2300
00 00 000 00 0
Usage quantity: 1 Usage quantity: 1
MRP ExplosionMRP Explosion
Figure 15.11
![Page 30: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/30.jpg)
Issues in MRP
Two basic concepts:– Net requirements– Lead time offset
Lot size Safety stock/Safety lead time Inventory records Validity of the schedules
![Page 31: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/31.jpg)
JIT and Inventory Management
Inventory as delay in work flow Why inventory?
– Dealing with fluctuations in demand– Dealing with uncertainty– Reducing transaction costs– Taking advantage of quantity discount– Hedging against inflation, etc.
![Page 32: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/32.jpg)
JIT and Inventory Management
Inventory costs:– Holding cost– Long response time– Low flexibility– Slow feedback in the system
![Page 33: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/33.jpg)
JIT and Inventory Management
The objective of JIT: – General: reduce waste– Specific: avoid making or delivering parts before
they are needed
Strategy:– very short time window– mixed models– very small lot sizes.
![Page 34: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/34.jpg)
JIT and Inventory Management
Prerequisites:– Reduce set up time drastically– Keep a very smooth production process
Core Components:– Demand driven scheduling: the Kanban system– Elimination of buffer stock
![Page 35: Queuing Systems: basic elements](https://reader036.fdocuments.in/reader036/viewer/2022081508/56813050550346895d95fcc7/html5/thumbnails/35.jpg)
JIT and Inventory Management
Core Components: (cont.)– Process Design:
Setup time reduction Manufacturing cells Limited work in process
– Quality Improvement