Queuing Systems: basic elements
Processing
order
Arrivals
Waiting
line
Service
System
Exit
Queuing Systems: multiple phases
Multiple channel
Multiple phase
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-firstserve: (see handout)
Basic Tradeoff
Cost
Total
cost
=
Customer
waiting cost
+
Total cost
Capacity
cost
Cost of
service
capacity
Cost of
customers
waiting
Service capacity
Optimum
Average number on
time waiting in line
Basic Tradeoff (cont.)
0
System Utilization
100%
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”
Control Chart
Abnormal variation
due to assignable sources
Out of
control
UCL
Mean
Normal variation
due to chance
LCL
Abnormal variation
due to assignable sources
0
1
2
3
4
5
6
7
8
9
Sample number
10 11 12 13 14 15
In-Control: random only
UCL
LCL
1
2
Sample number
3
4
Control Charts for Variables


Mean Chart: measuring sample means
Range Chart: measuring sample ranges
i.e. max-min
Out-of-Control: assignable & random
shifted mean
process mean is
shifting upward
Sampling
Distribution
UCL
Detects shift
x-Chart
LCL
UCL
Does not
detect shift
R-chart
LCL
Out-of-Control: assignable & random
increased variability
Sampling
Distribution
(process variability is increasing)
UCL
Does not
reveal increase
x-Chart
LCL
UCL
R-chart
Reveals increase
LCL
Type I Error:
a/2
a/2
Mean
a = Probability
of Type I error
LCL
UCL
Type II Error:
In-Control
LCL
Out-of-Control
Mean
UCL
Control Charts for Attributes

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
Counting Runs
Figure 10-11
Counting Above/Below Median Runs
B A
A
B
A
B
B
B A
(7 runs)
A
B
Figure 10-12
Counting Up/Down Runs
U
U
D
U
(8 runs)
D
U
D U
U D
Process Capability
Lower
Specification
Upper
Specification
Process variability matches
specifications
Lower
Specification
Upper
Specification
Process variability well within
Lower
Upper
specifications
Specification Specification
Process variability exceeds
specifications
Process Capability: 3-sigma & 6-sigma
Upper
specification
Lower
specification
1350 ppm
1350 ppm
1.7 ppm
1.7 ppm
Process
mean
+/- 3 Sigma
+/- 6 Sigma
Input/Output Analysis


Change in inventory = Input - Output
Average throughput time is proportional to the
level of inventory.
Flow and Inventory
Input flow of materials
Inventory level
Scrap flow
Figure 11.1
Output flow of materials
MRP



A general framework for MRP
Inputs: Bill of Materials, Inventory Files and
Master Production Schedule
MRP Processing
Aggregate Plan
A General
Framework
of MRP
Master Production
Schedule
MRP
Capacity Requirements
Planning
Production Scheduling
Master Production Schedule
Week 1 2
3
M1
23
M2
23
10 10
4
5 6
7
23
23
10
8
Bill of Materials
C (1)
Seat
subassembly
H (1)
Seat
frame
Figure 15.10
J (4)
Seat-frame
boards
I (1)
Seat
cushion
Inventory Files





On-Hand
Open Orders
Lead Times
Vendor Information
Quality records, etc.
MRP Explosion
Item: Seat subassembly
Lot size: 230 units
Week
Lead
time: 2 weeks
1
2
3
4
5
6
7
8
Gross
requirements
150
0
0
120
0
150
120
0
Scheduled
receipts
230
0
0
0
0
0
0
0
117
117
117
227
227
77
187
187
Projected
on-hand
inventory
37
Planned
receipts
Planned order
releases
Figure 15.11
230
230
230
230
MRP Explosion
Item: Seat subassembly
Lot size: 230 units
Week
Lead
time: 2 weeks
Gross
requirements
1
2
3
4
5
6
7
8
150
0
0
120
0
150
120
0
Planned
receipts
230
Planned
order
releases
230
230
230
Usage quantity: 1
Usage quantity: 1
Item: Seat frames
Lot size: 300 units
Item: Seat cushion
Lot size: L4L
Week
Lead
time: 1 week
1
2
3
4
5
Gross
requirements
0
230
0
0
230
Scheduled
receipts
0
300
0
0
0
Week
6
0
7
0
8
0
Lead
time: 1 week
1
2
3
4
5
Gross
requirements
0
230
0
0
230
Scheduled
receipts
0
0
0
0
0
Projected
on-hand 40
inventory
Projected
on-hand
inventory
Planned
receipts
Planned
receipts
Planned
order
releases
Planned
order
releases
Figure 15.11
0
6
7
8
0
0
0
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