queuing systems: basic elements
DESCRIPTION
Processing order. Arrivals. Waiting line. Service. Exit. System. Queuing Systems: basic elements. Queuing Systems: multiple phases. Multiple channel. Multiple phase. Modeling with Queuing Theory. System Characteristics Population source: finite, infinite No. of servers - PowerPoint PPT PresentationTRANSCRIPT
Arrivals ServiceWaitingline
Exit
Processingorder
System
Queuing Systems: basic elements
Multiple channel
Multiple phase
Queuing Systems: multiple phases
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
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)
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
System Utilization
Av
era
ge
nu
mb
er o
n
tim
e w
ait
ing
in li
ne
0 100%
Basic Tradeoff (cont.)
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
Applying Queuing Theory
In Operations:– Monitor performance measures– Use performance measures to guide process
improvement and operations decisions
Statistical Process Control
Emphasis on the process instead of the product/material
Focus on “prevention”
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
Sample number
UCL
LCL
1 2 3 4
In-Control: random only
Control Charts for Variables
Mean Chart: measuring sample means Range Chart: measuring sample ranges
i.e. max-min
UCL
LCLUCL
LCL
R-chart
x-Chart Detects shift
Does notdetect shift
process mean is shifting upward
SamplingDistribution
Out-of-Control: assignable & randomshifted mean
UCL
LCL
LCL
R-chart Reveals increase
x-Chart
UCL
Does notreveal increase
(process variability is increasing)SamplingDistribution
Out-of-Control: assignable & randomincreased variability
Mean
LCL UCL
/2 /2
Probabilityof Type I error
Type I Error:
MeanLCL UCL
Type II Error:
In-Control Out-of-Control
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
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
LowerSpecification
UpperSpecification
Process variability matches specifications
LowerSpecification
UpperSpecification
Process variability well within specifications
LowerSpecification
UpperSpecification
Process variability exceeds specifications
Process Capability
Processmean
Lowerspecification
Upperspecification
1350 ppm 1350 ppm
1.7 ppm 1.7 ppm
+/- 3 Sigma
+/- 6 Sigma
Process Capability: 3-sigma & 6-sigma
Input/Output Analysis
Change in inventory = Input - Output Average throughput time is proportional to the
level of inventory.
Input flow of materials
Inventory level
Scrap flow
Output flow of materials
Flow and InventoryFlow and Inventory
Figure 11.1
MRP
A general framework for MRP Inputs: Bill of Materials, Inventory Files and
Master Production Schedule MRP Processing
A General Framework of MRP
Aggregate Plan
Master ProductionSchedule
MRP
Capacity RequirementsPlanning
Production Scheduling
Master Production ScheduleMaster Production Schedule
Week 1 2 3 4 5 6 7 8
M1 23 23 23 23
M2 10 10 10
Bill of MaterialsBill of MaterialsC (1)Seat
subassembly
H (1)Seat
frame
I (1)Seat
cushion
J (4)Seat-frame
boardsFigure 15.10
Inventory Files
On-Hand Open Orders Lead Times Vendor Information Quality records, etc.
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
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
Issues in MRP
Two basic concepts:– Net requirements– Lead time offset
Lot size Safety stock/Safety lead time Inventory records Validity of the schedules
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.
JIT and Inventory Management
Inventory costs:– Holding cost– Long response time– Low flexibility– Slow feedback in the system
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.
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
JIT and Inventory Management
Core Components: (cont.)– Process Design:
Setup time reduction Manufacturing cells Limited work in process
– Quality Improvement