Unformatted text preview: Overview
• Throughput Concepts Throughput Concepts, Flow
Time, and Little’s Law • What is it Worth to Increase Throughput? • Flow time and Lead time Peter L. Jackson
Professor
School of O.R. and I.E.
1/29/2012 Industrial Data and Systems Analysis • Little’s Law
• What is it Worth to Reduce Flow Time? 1/29/2012 1 What is Throughput?
is Throughput? Definition of ‘cycle time’ is not consistent: even within the same company! • Takt time
• Inverse of throughput rate
• Units of time per
unit of output
• Time between
successive
outputs
• Toyota System • Measure of interest: throughput rate
• Flights per hour, outpatients per day,
per hour out
per day gallons per second, messages per hour,
etc.
Industrial Data and Systems Analysis 2 What is ‘Cycle Time’?
is Cycle Time • Activity of a repetitive process
of repetitive process
• Output = input (∴ throughput), unless... 1/29/2012 Industrial Data and Systems Analysis 3 1/29/2012 • Flow time
• Time spent in
spent in
system by single
unit (includes
queue time) Industrial Data and Systems Analysis 4 Throughput Detractors
Throughput Detractors The M.F.D. THRUPUT Game
M.F.D. THRUPUT Game • Unscheduled time
• Starved / blocked by production control system • Speed loss
• Quality loss
• Scrap, rework • Breakdowns
• Setup time
• Planned downtime
• partial shifts
• maintenance
• meetings, training
training
1/29/2012 Industrial Data and Systems Analysis 5 1/29/2012 Industrial Data and Systems Analysis Throughput Targets
Targets Will the Process Achieve the
Target? • DGR (daily going rate): units per day required to
(daily going rate): units per day required to 6 • Begin with throughput rate achievable
with throughput rate achievable support final assembly schedule (level schedule) under ideal operating conditions
• Adjust for breakdowns, setups, quality
for breakdowns setups quality
loss, speed loss • Cycle time (Takt time): time allowed between successive units of output to achieve DGR • Ex. Adjust for speed loss:
Adjust for speed loss:
• Equipment runs at 100y% speed
• Throughput rate adjusted for efficiency = • Takt time = effective daily operating time / DGR unadjusted rate * y • Stated as requirement: process must be • Adjust for planned downtime designed and operated to achieve these targets 1/29/2012 Industrial Data and Systems Analysis 7 1/29/2012 Industrial Data and Systems Analysis 8 Adjust for Repair Cycles
Adjust for Repair Cycles
operational repair Adjust for Setup Cycles
for Setup Cycles
setup repair Setup
time TTF TTR Industrial Data and Systems Analysis 100(1x)% Run time rate
• Setup cycle length = Setup time + run time
cycle length Setup time run time
• Fraction of time equipment is running =
Run time / (Setup cycle length)
• Throughput rate adjusted for setups =
unadjusted rate * run time / cycle length
9 Adjust for Scrap
for Scrap
I setup • Run time = average lot size / production
ti MTTF: mean time to fail (when running)
MTTR: mean time to repair
Mean repair cycle length = MTTR+MTTF
Fraction of time equipment is operational
= MTTF / (MTTR+MTTF)
MTTF (MTTR+MTTF)
• Throughput rate adjusted for repair =
Unadjusted rate MTTF (MTTR
Unadjusted rate * MTTF / (MTTR+MTTF)
•
•
•
• 1/29/2012 run 1/29/2012 Industrial Data and Systems Analysis 10 Adjust for Rework Cycles
for Rework Cycles
I O 100x% 100(1x)% O 100x% • Output rate is 100(1x)% of input rate
• Throughput rate adjusted for scrap = • Suppose reject rate applies to reworked parts as well unadjusted throughput rate * (1x) • Expected number of work and rework cycles per
∞ part
part = x=1/(1x)
1/(1
n n=0 • Throughput rate adjusted for rework = unadjusted rate * (1x) 1/29/2012 Industrial Data and Systems Analysis 11 1/29/2012 Industrial Data and Systems Analysis 12 Aside: Rework analysis
Aside: Rework analysis Aside: Rework Analysis (cont’d)
Rework Analysis (cont • Let N= number of work + rework cycles • Unadjusted time per piece = 1/unadjusted
time per piece 1/unadjusted ∞ E[ N ] = P{N > n} since N is nonnegative r.v. n =0 P{N > 0} = 1 since every part has at least one cycle
P{N > n} = x n , n ≥ 1 i.e. part must fail n times in a row
∞ E[ N ] = 1 + x + x + x + = x n =
2 3 n =0 1/29/2012 1
1− x Industrial Data and Systems Analysis 13 Adjust for Planned Downtime
for Planned Downtime throughput rate
• Adjusted time per piece =
E[N]/unadjusted throughput rate
• Adjusted throughput rate = 1/adjusted
time per piece = unadjusted throughput
rate / E[N]
• Adjusted throughput rate = unadjusted
throughput rate * (1x)
1/29/2012 MultiStage Throughput
Throughput • Begin with 24 hour clock
• Subtract planned downtime to get 1 available hours
• Multiply throughput per hour by available
hours to get achievable throughput per
day (nominal
day (nominal t’put)
• Compare to DGR Blocked
operation Bottleneck
operation 3
Starved
operation with the lowest throughput rate
determines the throughput rate of the
system as a whole inadequate • Downstream operations will be starved
• Upstream operations will be blocked
operations will be blocked • If DGR < nominal t’put then process will be idle (unscheduled time)
(unscheduled time) Industrial Data and Systems Analysis 2 • In a series of operations, the operation
series of operations the operation • If DGR > nominal t’put then design is
DGR nominal
then design is 1/29/2012 14 Industrial Data and Systems Analysis 15 1/29/2012 Industrial Data and Systems Analysis 16 Sample Problem
Sample Problem 1
• •
•
•
•
• Speed and Quality Losses
and Quality Losses
• What is effective throughput rate of the
is effective throughput rate of the The engineering specifications indicate that an
automated lathe can turn a certain metal part at a rate of
100 pieces per hour.
However, in practice the lathe is run at only 95% of that
speed.
The scrap rate from the machine is only about 1 part in
10,000.
Rework occurs at about the same rate.
On average the machine is out of service for repairs 30
minutes for every 20 hours of operation.
Furthermore, jobs arrive in batches of 250 units and
there is a setup time required of 15 minutes for each job. 1/29/2012 lathe considering speed loss, scrap, and
rework? (pieces per hour)
• Assume rework % expressed in terms of non scrapped units
• i.e. apply rework adjustment after scrap
adjustment 17 Industrial Data and Systems Analysis Breakdown Losses
Losses 1/29/2012 In service In service 18 Transitions (Setups)
(Setups) Down for repairs In service Industrial Data and Systems Analysis In service In service … • What fraction of time in service is spent in
fraction of time in service is spent in In service
In service production (rather than in setup)? • What fraction of potential operational time is the equipment available for
service? 1/29/2012 Industrial Data and Systems Analysis 19 1/29/2012 Industrial Data and Systems Analysis 20 Net Effect
Net Effect Sample Problem 2
Problem • What is the effective throughput rate of
is the effective throughput rate of •
•
•
• the lathe considering all effects of speed,
quality, reliability, and transition? •
•
•
• Automobile assembly plant
Production rate: 40 jobs per hour
Sales rate per week: 3,040 vehicles
Plant operates 5 days per week, two shifts per
day + overtime
Daily going rate: 608 vehicles
Hours per shift: 8
Planned downtime per shift: 20 minutes
Compute:
• Operating hours per day: 15.333
• Takt time: 1.513 minutes per vehicle 1/29/2012 Industrial Data and Systems Analysis 21 1/29/2012 Industrial Data and Systems Analysis 22 Actual Performance
Performance Performance Against Target
Against Target • There are quality problems if we run the
are quality problems if we run the • Effective throughput: 34.1 vehicles per hour
• Takt time: 1.513 minutes per vehicle
• Effective cycle time: 1.759 minutes per •
•
•
•
• line too fast
We have slowed the line speed by 10%
There are lots of little interruptions on the
line that cause it to slow down
Duration of interruption: 20 seconds
Frequency of interruption: 10 per hour
of interruption: 10 per hour
Uninterrupted hours per hour of
operation: 0.947 1/29/2012 Industrial Data and Systems Analysis vehicle
• “Measure” : a quantity describing
performance (ex. effective cycle time)
ti
• “Metric”: a measure used as a standard (ex.
takt time)
takt time)
• Our cycle times in the plant are 16% too
high, compared to our metric
23 1/29/2012 Industrial Data and Systems Analysis 24 What is it Worth to Increase
Th
Throughput? What Does Overtime Cost?
Does Overtime Cost? • Approach:
pp
• assume production target is fixed
• As throughput rate increases, time required decreases
• Time is money: compute wages saved • Available regular time hours per week:
ti 76.67
• Available regular time production per week:
regular time production per week:
2614.7
• Overtime hours required: 12.47
hours required: 12
1/29/2012 Industrial Data and Systems Analysis 25 What is it Worth to Increase
Th
Throughput? •
•
•
•
•
•
•
• Workers per line per shift: 50
per line per shift: 50
Salaries+benefits per year: $70,000
Weeks per year: 50
per year: 50
Salary+benefits per workerweek: $1,400
Benefit rate: 25%
rate: 25%
Salary per hour: $28
Overtime per hour: $42 (no benefits)
per hour: $42 (no benefits)
Total cost per overtime hour: $2,100 1/29/2012 Industrial Data and Systems Analysis 26 What are Other Ways to Measure
Benefit of Increasing Throughput?
Th • Current predicted overtime cost: $26,185
predicted overtime cost: $26,185 per week
• Annualized cost: $1,309,259
• What is impact of cutting speed loss in
half (without hurting quality)? $492,593
per year
• What is impact of cutting interruption
frequency (or duration) in half? $246,296
per year
1/29/2012 Industrial Data and Systems Analysis 27 1/29/2012 Industrial Data and Systems Analysis 28 How Can You Increase
Th
Throughput? Overview • Continuous improvement
improvement
• Measure, Analyze, Act
• Observe factory, interview workers and staff, • Throughput Concepts
• What is it Worth to Increase Throughput? collect data on problems
• Brainstorm solutions, implement and test • Flow time and Lead time • Recitation this week
• Use SQL to analyze instances of throughput • Little’s Law problems
problems 1/29/2012 • What is it Worth to Reduce Flow Time? Industrial Data and Systems Analysis 29 What is Flow Time?
is Flow Time? 1/29/2012 Industrial Data and Systems Analysis 30 Accounting for Lead Time
for Lead Time
• Lead time: the time
time: the time • Cycle time
• Inverse of throughput rate
throughput rate
• Ex. Oven cycle
time: 32 min.
• Two trays of 8
trays of
cookies per cycle
• Cookie cycle time: 2
min./cookie
1/29/2012 from when you trigger
an action until you see
the result
• Typically, lead time is
duration of time
between order
placement and order
placement and order
fulfillment (delivery) • Flow time
• Time spent in
spent in
system by single
unit (includes
queue time)
• Cookie flow time:
flow time:
32 min. + queue
time Industrial Data and Systems Analysis 31 1/29/2012 Industrial Data and Systems Analysis 32 Lead Time Analysis
Lead Time Analysis
Order Sent
Sent
Credit
Approved Schedule
Released Queue Factor
Factor
Long Haul
Haul
Transport
Drop Shipments
Consolidated Material
Picked /
Produced • Order lead time is flow time of order through the entire system (order processing, factory
scheduling, production, packing, shipping, and
receiving)
• Distinguish between valueadded time and nonvalue added time Material
Received /
Inspected /
Order
Verified Order Lead Time Order
Scheduled
Order
Received Material
Packed /
Shipped • Valueadded time: material transformation + transport to
time: material transformation transport to Short Haul
Haul
Delivery customer Production Lead Time
Pick Materials Operation 1 Operation 2 • Nonvalueadded time: queue time+internal transport time Operation 3 • Queue factor: (time in queue+value added time) /
factor: (time in queue+value added time) value added time Operation Lead Time
Production
Transport
Queue
Queue 1/29/2012 Setup Run • If measured rigorously, queue time is many orders Transport
Queue
Queue Industrial Data and Systems Analysis of magnitude larger than value
of magnitude larger than valueadded time
time 33 1/29/2012 Industrial Data and Systems Analysis How to Reduce Lead Times
to Reduce Lead Times Overview • Continuous improvement 34 • Throughput Concepts • Measure, Analyze, Act • What is it Worth to Increase Throughput? • How to reduce valueadded time:
• Flow time and Lead time • Increase speed of operations • How to reduce queue time • Little’s Law • Increase frequency of operations
• Reduce variability 1/29/2012 Industrial Data and Systems Analysis • What is it Worth to Reduce Flow Time? 35 1/29/2012 Industrial Data and Systems Analysis 36 Unit Flowing Through a
System
0 a unit enters the
system 1/29/2012 Unit Spending Time in a
System
Time 0 a unit leaves the
system W, time spent in
the system (flow
time lead time
time, lead time,
waiting time,…) 37 Industrial Data and Systems Analysis Units Flowing Through a
System
0 next unit enters
the system Time 1/29/2012 38 Industrial Data and Systems Analysis Units Arriving (and Leaving) at
Some Rat
te
Time 0 next unit leaves
the system 1 Time 1 unit of time λ, input rate ( = output rate =
throughput rate) 1/29/2012 Industrial Data and Systems Analysis 39 1/29/2012 Industrial Data and Systems Analysis 40 In Steady State, How Many
Units Are in the System?
th Average Units in System
Units in System W • Average Units in System = Throughput
Units in System Throughput λ
1 L, average
number of units in
the system rate * Unit Flow Time
• Little’s Law: L = λW • Applicable in wide variety of systems
in wide variety of systems
• When is it not applicable? 1/29/2012 Industrial Data and Systems Analysis 41 1/29/2012 Industrial Data and Systems Analysis 42 Little’s Law
Law How Much Money is Tied Up in
Inventory? • 600 students admitted annually to four • Automotive example continued:
• Sales: 3,040 vehicles per week
• Production and transport time per vehicle: 8 year degree program • 2400 students in program, on average •
•
•
•
• • 15 days for ship to cross Pacific Ocean, 700 vehicles per ship, one ship per week
• 1500 vehicles in oceanic transit, on average 1/29/2012 Industrial Data and Systems Analysis 43 days
Pipeline inventory: 3,474.3 vehicles
Vehicle cost: $12,000
Pipeline inventory investment: $41,691,429
Interest rate to finance investment: 12%
fi
12%
Annual pipeline inventory interest charge:
$5
$5,002,971 1/29/2012 Industrial Data and Systems Analysis 44 What is it Worth to Reduce
Fl
Flow Time?
Ti What are Other Benefits of Reducing
Fl
Flow Times and Lead Times?
Ti
Ti • Reducing material flow time reduces inventory (“pipeline inventory”)
• Reducing production and transportation
flow time by 1 day would reduce pipeline
inventory by 12
inventory by 12.5 %
• Interest savings per year: $625,371 1/29/2012 Industrial Data and Systems Analysis 45 Overview
• Throughput Concepts
• What is it Worth to Increase Throughput? • Flow time and Lead time
• Little’s Law
• What is it Worth to Reduce Flow Time? 1/29/2012 Industrial Data and Systems Analysis 47 1/29/2012 Industrial Data and Systems Analysis 46 ...
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 Spring '09
 JACKSON

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