reinertsen+lkce+2012+wip+constraints (1)

The Science ofWIP ConstraintsLean Kanban Central Europe

Vienna, AustriaOctober 23, 2012

Donald G. ReinertsenReinertsen & Associates

600 Via Monte D’OroRedondo Beach, CA 90277 U.S.A.

(310)-373-5332Internet: [email protected]

www.ReinertsenAssociates.com

No part of this presentation may be reproducedwithout the written permission of the author.

2Copyright 2012, Reinertsen & Associates

Objectives• What is the science behind WIP constraints?• How do WIP constraints affect economics?• What is the difference between a WIP

constraint and PULL?• What is the difference between WIP control and

WIP constraints?


SomeBackground


The TPS Emergency Room

• We desire to rigorouslyimitate the practices ofToyota.

• We will set a strictupper limit on WIP.

• When we reach ourlimit, no new patientscan enter until anotherdeparts.


Two Approaches• We can treat WIP constraints with two approaches:

• Science-based• Faith-based

• A science-based approach:• Forces you to understand underlying

mechanisms of action.• Permits you to engineer specific solutions for

different and changing contexts.• A faith-based approach:

• Requires much less thinking.• Works well in stable contexts like manufacturing.


Thus, since the Toyota Production System hasbeen created from actual practices in thefactories of Toyota, it has a strong feature ofemphasizing practical effects, and actualpractice and implementation over theoreticalanalysis. – Taiichi Ohno

From Foreword to 1983 FirstEdition of Toyota ProductionSystem by Yasuhiro Monden


The Science


Queueing Theory

• The key to a science-based approach isqueueing theory.

• Queues form when processes withvariability are loaded to high levels ofutilization.

• Queues are not intrinsically evil.• They create quantifiable economic costs.• By understanding the behavior of queues

we can discover how to control them.

Traffic at rush hourillustrates the classiccharacteristics of aqueueing system.

Pho

to C

opyr

ight

200

0 C

omst

ock,

Inc.


The Effect of Capacity Utilization

Queue Size vs. Capacity Utilization

0

5

10

15

20

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%Capacity Utilization

Que

ue S

ize Deterministic

Stochastic

Notes: Assumes M/M/1/ Queue, = Capacity Utilization

1

2

qL


Total Cost

Cost of Delay

Cost of Excess Capacity

The Economics of Queues

Excess Product Development Resource

Dollars

To Maximize Profits,Minimize Total Cost

How many product developers can draw the red curve?


Arrivals

Departures

Time in Queue

Quantityin Queue

QueueTime

CumulativeQuantity

Cumulative Flow Diagram


Arrivals

Queue

Time

CumulativeQuantity

Little’s Formula

You can calculate size of thequeue either by integratinghorizontal or vertical slices.

Departures

)( tTimeat Queuein Customers ofNumber

)( Customer nth for Queuein Wait time

)()( 1

tL

nW

dttLnW

q

q

N

n

b

aqq

Rate Departure Average

)(Queuein Customers ofNumber Average

Queuein Time Wait Average

tL

W

LW

q

q

qq


How WIP Constraints Work• Queueing systems randomly drift into

high queue states.• These high queue states can be relatively

persistent and, when present, they candelay many jobs for a long time.

• If we prevent a system from entering thesehigh queue states, we will producesignificant cycle time benefits at relativelylow cost.


• We flip a coin 1000 times, add 1 for each head,subtract 1 for each tail, and keep track of ourcumulative total.

• What is your best estimate of:• How many times the cumulative total will return to

the zero line during the 1000 flips?

Random Processes

Time

H T T H H HTCumulativeTotal


Cumulative

-10

0

10

20

30

40

50

0 250 500 750 1000

Note: +1 for each head, -1 for each tailBased on example from “Introduction to Probability Theory and Its Applications”, by William Feller. John Wiley: 1968

One Thousand Coin Tosses

1st Half Crossings = 382nd Half Crossings = 0

Average Time Between Crossings = 25.6

Maximum Time Between Crossings = 732


Early

Late

Cumulative Totals Diffuse

Value of Random Variable

Prob

abili

ty

1. Zero is always most probable value.2. But, it becomes less probable with time.3. For large N, a binomial distribution approaches anormal distribution.

Notes:


Probability of High Queue States

Number of Items in Queue

Prob

abili

ty

n1State Probability =

for M/M/1/ Queue


Impact of High Queue States

Number of Items in Queue (Queue State)

Prob

abili

tyState Probability

Impact onCycle Time

for M/M/1/ QueueA State’s Cycle Time Impact = pn(n)/

Cyc

le T

ime

Impa

ct


So, Why Not Chop Off theTail?

Number of Items in Queue

Prob

abili

ty

State Probability

Impact onCycle Time


The Economics


How WIP Constraints Work• WIP constraints affect three important

economically important factors:• They decrease average cycle time. (+)• They generate blocking costs. (-)• They create underutilization costs. (-)

• We need an economic framework toassess their impact.


The M/M/1/k Queue

WIPCAP 1 2 5 10 20 InfiniteAverage Cycle Time 1.0 1.5 2.8 4.6 7.2 10.0 Time in Queue 0 0.5 1.8 3.6 6.2 9.0

Utlilization Percent 47% 63% 79% 85% 89% 90%Empty Percent 53% 37% 21% 15% 11% 10%Blocking Percent 47% 30% 13% 5% 1% 0%

Note: Assumes 90 percent utilization.

WIP constraints tradeoff reductions in cycle timeagainst blocking and underutilization costs.


Effect of WIPCAPS

72%

52%

28%

21%

5%

1%

13%

5%

1%

0% 20% 40% 60% 80%

0.5x

1x

2x

WIPCAP

Percent Change

Delay Reduction Underutilization Blocking

Consequences of WIP Constraints

Note: WIPCAP relative to average WIP for M/M/1/ queue loaded to 90 percent utilization.


The Big Idea!

We can get significant cycle timereduction, for a relatively low price,by reducing the amount of time ourprocess spends in high queue states.

But, some practical details remain...


SomePracticalities


What Should I Constrain?

• The span of the WIP constraint can be:• Local - e.g. Kanban• Regional - e.g. QRM• Global - e.g. TOC

• Larger spans require less total inventory,but they can create local WIP starvation.

• Larger spans can cause feedback delayswhich lead to long loop closure times.


Setting the Constraint

• WIP constraints are cheap, effective,incremental, and reversible.

• Some useful heuristics:• Start at 2x average unconstrained WIP.• Drop the limit by 20-30 percent.

• You can always reverse direction.• We can use a combination of WIP

constraints and time-slicing to differentiateservice levels for different workstreams.


PULL vs. WIPConstraints


Classic Pull• Items are removed from inventory whenever

the customer chooses.• The removal of an item triggers the

production of a replacement item.• This protocol will strictly balance inflows and

outflows and therefore intrinsically maintainsconstant WIP.

• Thus, classic pull entangles two ideas:• A process to trigger replenishment orders• Stabilization of WIP levels


Implications of Classic Pull

• Flows are tightly coupled.• The instantaneous rate of replenishment is

equal to the instantaneous rate of removal.• The batch size of replenishment is equal to the

batch size of removal.• This stabilizes inventory as a secondary effect.

Hamburger Chute


Classic Push• Classic Push uses forecasts to trigger

removal and replenishment of inventory.• In Push, the balance between inflows and

outflows is neither prescribed, nor prohibited.• Likewise, the synchronization of inflow and

outflow is neither prescribed nor prohibited.• However, unbalanced inflows and outflows

are common, which leads to uncontrolledrandom variation in inventory levels.

• Thus, we could choose to constrain WIP in aPush system.


Is Pull Intrinsically Superior?

“Pull in simplest terms means thatno one upstream should produce agood or service until the customerdownstream asks for it…”

- Womack and Jones


Jean-Pierre’sBoulangerie

• We could not help noticing that your inventoryof baguettes varies widely between 7 AM and10 AM.

• And, because you are using what are, quitefrankly, medieval methods, you must get upinsanely early to start baking bread.

• We recommend you use customer orders,instead of forecasts, to trigger production.


WIP Control


Where Pull Fits

Pull WIP Constraints

WIP Control


Demand-focusedApproaches

Block Entry

Purge WIP

Redefine theEndpoint

T-ShapedResources

Supply-focusedApproaches

WIP Control

Methods of WIP Control

ResourcePulling

Part-timeResources

FlexibleExperts

SkillOverlap

Mix-focusedApproach

ChangeMix

Toyota’s Kanban Method


Finding Better Ideas

• In my opinion, the most advancedWIP control techniques appear intelecommunications systems.

• Let’s take one example.


Controlling Internet Flows

Sender Receiver

Packet from Sender

Acknowledgement (ACK) from Receiver

Data Network

Packets + ACKs < Window SizeWindow Size Limits Number of Unacknowledged Packets


Congestion Avoidance vs. Control

0

100

Probabilityof

DroppingPacket TCP

RED

REM

RED = Random Early Deletion, REM = Random Early Marking

Quantity in Buffer


Contrasting Flow Control Strategies

Toyota Production System• On/Off Flow Control• Static WIP Limits• One Service Level

• Local Feedback Loops

• Static Routing

• Constrains Variability

INTERNET• Progressive Throttling• Dynamic WIP Limits• Multiple Service Levels

• Local and GlobalFeedback Loops

• Dynamic Routing

• Tolerates Variability

Which system is a better fit with the needs of product development?


Summary• WIP constraints are cost-effective way to

prevent the accumulation of variability.• Their economic trade-offs favor progressive

tightening.• There are many alternatives to completely

stopping flow when a WIP limit is reached.• Look to telecommunication systems, not

factories, for the most advanced approaches.

1991 / 1997 1997 2009

Going Further

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