"the goal" discussion guide

The Goal

Discussion Guide

Craig Paxson

The Goal Discussion Guide Craig Paxson

The Goal Discussion Guide

© Craig Paxson 2015

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Introduction

Early in 2015, I volunteered to lead a reading discussion group at work. The book I chose to read

was “The Goal” by Eliyahu Goldratt. I scoured the internet for a reading and discussion guide

appropriate for a weekly group session and could not discover any. I found plenty of synopses

and some college syllabi, but not any discussion guides. So I decided to create one. This booklet

is the discussion guide I created.

Because “The Goal” uses the Socratic Method - “ask - tell - ask”, I decided to create the readings

in that same method. Each week’s reading begins with Alex asking a question of Jonah, then

Jonah’s response, Alex learning from that answer, and then the next question posed by Alex.

The discussion guide is broken into 7 weeks of reading. Each week has questions to be answered

by the participants. Some weeks have exercises (for instance, the dice game played on the hike)

to further illustrate the concepts discussed in the book. It will be helpful if the leader can

customize the discussion questions and exercises to the organization.


Leaders Guide

How to Lead a Discussion of “The Goal”

Written in a fast-paced thriller style, “The Goal”, a gripping novel, is transforming management

thinking throughout the world. It is a book to recommend to your friends in industry - even to

your bosses - but not to your competitors. Alex Rogo is a harried plant manager working ever

more desperately to try improve performance. His factory is rapidly heading for disaster. So is

his marriage. He has ninety days to save his plant - or it will be closed by corporate HQ, with

hundreds of job losses. It takes a chance meeting with a professor from student days - Jonah - to

help him break out of conventional ways of thinking to see what needs to be done. The story of

Alex's fight to save his plant is more than compulsive reading. It contains a serious message for

all managers in industry and explains the ideas, which underline the Theory of Constraints

(TOC), developed by Eli Goldratt.

This is a seven week discussion of “The Goal.” Each week, you will read a selected set of

chapters. “The Goal” is written using the Socratic Method - Ask - Tell - Ask. The chapter are

selected based on the question that Jonah poses to Alex, what Alex learns and Alex’s next

questions. As you read each section, think about the following questions:

1. What is the current situation? What did Alex learn?

2. What questions does Alex currently have?

3. What hints does Jonah give Alex?

4. What answers will Alex will discover?

5. How does this apply to my organization?


As discussion facilitator, you will ask questions to review the previous week’s reading and may

present exercises to enhance learning.

Reading Schedule

Intro – Chap 4

Chaps 5 – 8

Chaps 9 – 11

Chaps 12 – 19

Chaps 20 – 25

Chaps 26 – 31

Chaps 32 – 40


Introduction – Chapter 4

1. Why does Alex think the robots are so successful when he first talks to Jonah?

- because their localized cost per part had gone down

2. How does Jonah indicate that the robots were not successful?

- sales had not increased, labor had not decreased and inventory had gone up

3. How does Jonah define productivity?

- the act of bringing an organization closer to its goal. Every action that brings an

organization closer to its goal is productive. Every action that does not bring an

organization closer to its goal is not productive.

Next Meeting: Chapters 5 - 8


Chapter 5 – 8

Review of Intro – Chapter 4

1. What is The Goal?

- Make Money

2. What does your process manufacture?

3. What three common financial measures express the goal to "make money"?

- Net Profit, Return on Investment and Cash Flow

4. Express the “goal” in terms of those financial measures

- Increase net profit while simultaneously increasing both ROI and cash flow

5. What three measures are useful at the operational level to express the goal?

- Throughput, Inventory and Operational Expense

6. Define throughput, inventory, and operational expense.

- Throughput - the rate at which the system generates money through sales

- Inventory - all the money the system has invested in purchasing things which it intends

to sell

- Operational Expense - all the money the system spends in order to turn inventory into

throughput

7. Jonah claims the common financial measures are related to the operational measures. How?

- Net Profit = Throughput – Operating Expense

- ROI = (Throughput – Operating Expense) / Inventory

- Cash Flow = Throughput –– Operating Expense ± ΔInventory


8. Define the measurements in your process’ terms

- Throughput

- Inventory

- Operating Expense

9. What questions does Jonah leave Alex with? What do you think Alex will discover?

- Local Optimums

- Operational Rules



Chapter 9 – 11

Review – Definitions Quiz Cards

1. Express the "goal" in terms of throughput, inventory, and operational expense.

- Increase throughput while simultaneously decreasing inventory and cash flow

2. What is the result of high efficiencies on a non-constraint machine?

- Excess inventory

3. Do high efficiencies necessarily imply higher profit?

- No – high efficiencies lead to increased inventory, unless that inventory is turned into

throughput

4. Why is it important that throughput be defined in terms of sales rather than production?

- We don’t get paid for finished goods

5. What causes a balanced plant to fail?

- Inventory, and the carrying cost of inventory goes up because of statistical fluctuations and

dependent events

6. What are the type of operational operating expenses?

- Variable and Fixed or

- Controllable and Uncontrollable

7. What is the equation for Productivity?

- Productivity = Throughput / Operating Expense


Next Meeting: Chapters 12 – 19


Definitions

Productivity – any action that moves the organization closer to the goal

The Goal in financial measures - Increase net profit while simultaneously increasing both ROI

and cash flow

Operational Measures

Throughput - the rate at which the system generates money through sales

Inventory - all the money the system has invested in purchasing things which it intends to

sell

Operational Expense - all the money the system spends in order to turn inventory into

throughput

The Goal in operational measures - Increase throughput while simultaneously decreasing

inventory and cash flow

Financial Measure Equations

Net Profit = Throughput – Operating Expense

ROI = (Throughput – Operating Expense) / Inventory

Cash Flow = Throughput – Operating Expense ± ΔInventory

Productivity = Throughput / Operating Expense


Chapters 12 - 19

Play the Dice Game (Appendix 2)

1. Why does the spread of the line of boy scouts discussed on page 100 always become longer

as time goes on?

- the leaders are going faster than Herbie

2. What characteristics of the hiking troop relate to the production characteristics of throughput,

inventory, and operational expense?

- Throughput – the distance covered by the last scout in the troop

- Inventory – the total length of the line

- Operational Expense –– energy expended by the troop

3. Using the hike analogy on page 113, what happens in a plant if the fastest operations are put

at the beginning of the production process, the slowest operations are put at the end, and all

workers produce at a high efficiency?

- inventory goes up

4. What is Herbie in terms of TOC?

- the Bottleneck or Constraint

5. In terms of TOC what has been done when Herbie goes to the front of the line?

- exploiting the constraint, letting the constraint dictate throughput

6. In terms of TOC what has been done when items are removed from Herbie's pack?

- elevating the constraint – making it go faster

7. Why was Pete so happy even through the order was not delivered on time?

- Pete produced the 100 parts needed even though the total throughput was less

8. Define a bottleneck

- any resource where capacity is less than demand


9. Why does Jonah say “balance flow not capacities”?

- Each resource should only produce as much as the constraint



Chapters 20 – 25

1. Why does Jonah say a plant should have bottlenecks?

- Every production line has a bottleneck. It is impossible to not have one, so we should strive

to utilize the bottleneck to meet operational goals

2. What does lost time at a bottleneck cost?

- The throughput (revenue) or profit that could have been generated

3. What two things can be done to optimize a bottleneck?

- Only work on things that contribute to throughput

- Ensure there are always materials for the bottleneck to work on

4. What is the effect of the "efficient" operation of non-bottleneck machines?

- Excess inventory

5. What determines the level of utilization of a non-bottleneck machine?

- the level of utilization of a non-bottleneck is not determined by its own potential, but by

some other constraint in the system

6. What are the combinations of production flow through a bottleneck and non-bottleneck?

a. N -> B – non-bottleneck feeding bottleneck

b. B -> N – bottleneck feeding non-bottleneck

c. B and N -> Assembly – bottleneck and non-bottleneck feeding assembly

d. B -> market and N -> market

7. What is the difference between activating a resource and utilizing a resource?


8. Which resources in the system should we seek to optimize? Which should we not?

a. Only optimize the bottlenecks – constrain every other resource to the throughput of

the bottleneck

9. What does Jonah suggest is the actual constraint in the system?

- Policy – he says “you created this monster by the decisions you made” and “

10. What do you think is the solution Jonah is proposing?



Chapters 26 – 31

1. What is the function of the drum and rope if used on a hike?

- Keep everyone walking at the same pace, and keep everyone from getting spread out

2. What is the drum for the production facility?

- The pace of the bottleneck

3. What is the rope for the production facility?

- The total amount of work in process inventory

4. Why is a rope needed for assembly operations?

- To ensure the correct amount of WIP and ensure bottlenecks do not run out of work.

5. What is the next logical step after establishing the drum and rope for the production

process?

- Cut batch sizes – cutting WIP improves throughput (see Little’s Law, Appendix 4)

6. What does cutting batch sizes in half for non-bottleneck operations accomplish?

- Eases cash flow because less cash is tied in inventory

- Improves throughput


7. How can the time material spends in plant be classified into four types?

- Setup – time spent waiting for a resource while the resource is being prepared

- Process – time spent being worked on

- Queue – waiting on a resource while that resource is busy on something else

- Wait – for another part

8. What is time saved on a non-bottleneck machine?

- A mirage

This is a good time to bring up the concept of Little’s Law. See the Appendix on Little’s

Law.

Play the Dot Game (Appendix 3) to illustrate the effect Work In Process inventory has on

throughput, cycle time and cost.



Chapters 32 - 40

1. What are the 5 Focusing Steps?

1. Identify the system constraint

2. Exploit the constraint

3. Subordinate everything to the constraint

4. Elevate the constraint

5. If a constraint has been broken, go back to Step 1, but do not allow inertia to cause a

constraint

2. What is the Process of Change?

1. What to Change

2. What to Change To

3. How to Cause the Change

4. Alex and his team have moved from the Cost world to the Throughput world.

5. In each world, what is the relative importance of Inventory (I), Operating Expense (OE) and

Throughput (T) and why?

Cost World Throughput World

1. Operating Expense

2. Throughput

3. Inventory

1. Throughput

2. Inventory

3. Operating Expense

What are your most important learnings?


Author Bio

Eli Goldratt is an educator, author, scientist, philosopher, and business leader. But he is, first and

foremost, a thinker who provokes others to think. Often characterized as unconventional,

stimulating, and "a slayer of sacred cows," Dr. Goldratt exhorts his audience to examine and

reassess their business practices with a fresh, new vision.

He obtained his Bachelor of Science degree from Tel Aviv University and his Masters of

Science, and Doctorate of Philosophy from Bar-Ilan University. In addition to his pioneering

work in Business Management and education, he holds patents in a number of areas ranging

from medical devices to drip irrigation to temperature sensors.


Appendix 1: Week 1 Quiz Cards

What is the definition of Productivity? Express The Goal in operational

measures

Express The Goal in financial measures What is the equation for Net Profit in

operational terms

What is the definition of Throughput? What is the equation for ROI in

operational terms

What is the definition of Inventory? What is the equation for Cash Flow

in operational terms

What is the definition of Operational

Expense?


Appendix 2: The Dice Game

Adapted from the game played on the hike in Chapter 12

Purpose:

The dice game will demonstrate how variability and dependent events impact throughput.

Materials Required:

1 6-sided die

4 - 6 cups or bowls representing stages in the production process

Matches, pennies, poker chips or other items to move from bowl to bowl (minimum of 40).

Procedure:

Setup:

1. Set up a production line of 5 - 6 cups or bowls.

2. Place the tokens into the first bowl.

Game Play:

1. Worker 1 will roll the die and move the resulting number to the second cup in the line.

2. Worker 2 will roll the die and move the resulting number of tokens to the next cup in the

process.

3. Repeat the procedure for the remaining workers. The last worker moves the tokens to

“finished goods.”

4. Each worker rolling the die and moving tokens counts as “1 day.” You will play the game for

10 days.

5. Each student will record their roll and the number of tokens they moved during each turn.


Statistically, a single die can only roll six values, one each of 1, 2, and 3,4,5,6. The average value

for one roll is 3.5 (1+2+3+4+5+6=21/6=3.5).

With 10 days of production, on average we would expect to move 3.5 tokens per day for a total

of 35 tokens produced.

Discussion Questions:

1. How many tokens did the line produce? Versus expected?

2. How many tokens did each station produce versus expected?


Appendix 3: The Dot Game

Adapted from the Lean Manufacturing Cup Game

Purpose

The Dot game simulates a simple manufacturing system and demonstrates how work in process

(WIP) inventory affects throughput, cycle time and cost.

Materials Required

2.5” x 2.5” Post-It Notes

4 colors of 3/4” round stickers

Pen and Paper or Flipboard

Procedure

1. The game requires between 4 and 6 players. Larger groups can have multiple “lines” or

observers.

2. The “line” will manufacture a Post-It that looks like the one below. Make an example

product and post it for the team to see.


3. The line is broken into between 4 and 6 stations. You can adjust the number of stations

based on the number of players.

1. Station 1 - Raw Materials. This player will tear off the requisite number of Post-

Its and pass to the next station.

2. Station 2 - Red. This player will put on the one red dot.

3. Station 3- Blue. This player will put on the two blue dots.

4. Station 4 - Green. This player will put on the two green dots.

5. Station 5 - Yellow. This player will put on the one yellow dot.

6. Station 6 - Inspection. This player will inspect the Post-It and make sure it meets

standard.

4. The game is played in multiple rounds. Each round will be timed for 5 minutes.

1. Round 1 - Batches of 6. Each player will complete 6 Post Its prior to passing the

entire batch of 6 to the next station. Record the number of Post-Its completed, the

number remaining in WIP and the time for the first Post-It to be completed (Cycle

Time).

2. Round 2 - Batches of 1. Each player will complete 1 Post-It and pass it to the next

station. Record the number of Post-Its completed, the number remaining in WIP

and the time for the first Post-It to be completed.

Discussion:

1. What effect did batch size have on Throughput?

2. Cycle Time

3. Cost?


Appendix 4: Little’s Law

Little’s Law states that inventory (I) is equal to cycle time (CT) multiplied by throughput (T).

The equation looks like this:

Inventory (I) = Cycle Time (CT) * Throughput(T).

Alternatively, the law can represent Cycle Time:

CT = I / T

Or Throughput:

T = I / CT

The implications of Little’s Law are that Inventory management can control Cycle Time and

Throughput. We also know that as Inventory rises, so does Operating Expense (because of

carrying costs).

We also know from chapters 5 - 11 that:

Net Profit = Throughput – Operating Expense

ROI = (Throughput – Operating Expense) / Inventory

Cash Flow = Throughput –– Operating Expense ± ΔInventory

Productivity = Throughput / Operating Expense

Can you describe how Cycle Time fits into Jonah’s operation terms and how it might

affect Productivity and Net Profit?

See the following article for a more in-depth discussion.

he many ways to improve operations include increasing output per peri-od, decreasing average inventory, decreasing flow time and reducingdefects.

Little’s Law states inventory is equal to flow time multiplied by flow rate. It isdeceptively simple and has application in the areas of reduction of flow times,safety inventory and safety capacity. The theory of constraints (TOC) has appli-cation for improving production processes when sales are limited by plant capac-ity. It focuses on identifying the bottleneck and then exploiting and elevating it.

TOC and Little’s Law are important tools for both Six Sigma and lean. In theoperations management major at the University of Wisconsin Oshkosh, we wantour graduates to be apply Six Sigma, lean, TOC and Little’s Law to improve opera-tions at their companies. For our students to learn how to apply these techniqueseffectively, it often is necessary for us to start with simple processes and then moveto more complex and realistic processes after they have grasped the basic concepts.

This approach can be particularly useful for understanding Little’s Law andTOC. Little’s Law generally is best understood when it is used to reduce cycletimes (flow times), while TOC leads quickly to being able to identify and elevatea physical constraint (bottleneck) to increase throughput (flow rates).

In a recent article, Robert Gerst warned, “Little’s Law is everywhere.”1 TOC isalso everywhere, particularly when an improvement project focuses directly onincreasing flow rates.

We have used two models to provide a framework for moving from the basics toa more complete understanding of both Little’s Law and TOC. The first model issimple and deterministic. The second model is also simple, but it is stochastic,involving random elements for both arrivals and processing times.

Little’s Law

While decreasing cycle or flow time can be instrumental in improving customerservice, you must be careful not to ignore the throughput (flow rate) of the system.Both measures are directly related to average inventory as defined by Little’s Law.2, 3

Little’s Law defines the relationship among the three variables of flow rate(throughput), inventory and flow time (cycle time). A notation in a recently pub-lished book provides the following equation:4

I = R x Twhere: I = average inventory; R = average flow rate; T = average flow time.

In any system, when one of these variables changes value, a second variable(and possibly a third) also must change value. The issue of which variableschange value depends on the structure of the system.

The capacity of the system determines the average flow rate for the system. Fora system operating at capacity, an increase in inventory will result in a propor-tional increase in average flow time, with average flow rate remaining relativelyconstant. Obviously this is an undesirable result because the revenue from thesystem, which is proportional to flow rate, remains constant while carrying cost,

C Y C L E T I M E R E D U C T I O N

Applying Little’s Law And the Theory of ConstraintsTHEY CAN BE USED

IN SIX SIGMA AND

LEAN PROJECTS

TO IMPROVE

OPERATIONS.

T

By Michael R.

Godfrey and D.

Brent Bandy,

University

of Wisconsin

Oshkosh

S I X S I G M A F O R U M M A G A Z I N E I F E B R U A R Y 2 0 0 5 I 37

App ly ing L i t t le ’s Law and the Theor y o f Const ra in ts

which is proportional to inventory, increases. On the other hand, when a system has either excess

(or variable) capacity, it is possible for an increase ininventory in the system to result in a proportionalincrease in flow rate, with flow time remaining constant.

This is a positive outcome because the flow rate andinventory—and thus the revenue and holding cost—will increase by the same percentage. This being a pos-itive outcome is based on assuming the revenue perunit exceeds the holding cost per unit. If this is notthe case, however, then the system will operate at a lossand should be shut down.

Finally, given a third scenario in which the systemhas either excess (or variable) capacity, it is possiblean increase in inventory will result in changes inboth flow rate and flow time. Of course, the values ofthe three variables will still satisfy Little’s Law. Butwhether an increase in inventory will lead to a desir-able result depends on the relative changes of thethree values.

Theory of Constraints

TOC is a system improvement methodology thatfocuses on the system constraint. Applying TOCentails answering the following questions:5

• What should be changed?

• What should it be changed to?

• How can the change be brought about? Eli Goldratt created five focusing steps to drive

improvement efforts at the constraint: 1. Identify the constraint (physical or policy).

2. Decide how to exploit the constraint (get themost out of it).

3. Subordinate everything else (adjust the rest ofthe system to enable the constraint to operateeffectively).

4. Elevate the constraint (invest time, energy andmoney to eliminate the constraint).

5. Go back to step one, but beware of inertia. These five focusing steps help answer the three ear-

lier questions.6 A physical constraint within a process,also called a bottleneck, determines the flow rate orcapacity of that process.

Flow Rate and Flow Time Measures

Flow time and the flow rate measures are relatedbut different. When discussing physical constraintswithin an organization’s operations, you must exer-

cise care when distinguishing between activities thatdetermine flow times and resources that are physicalconstraints.

Some systems use a simple linear flow, in which eachsequential activity is performed by a different resource.In such systems, the longest activity is, by definition,performed by the physical constraint (assuming all re-sources are available whenever the system is operating).

In a three-station line, for example, with each sta-tion staffed by a different person, the workstation withthe longest processing time would determine the flowrate of the line. There would be a single path on theline; therefore the flow time would be the summationof the individual workstation processing times on thiscritical path.

In this situation, increasing flow rates by applyingTOC principles would decrease flow times. The fol-lowing actions would lead to increased flow rate at theconstraint:

• Decreasing downtimes at the constraint.

• Improving job scheduling at the constraint.

• Eliminating processing steps at the constraint.

• Shifting processing steps from the constraint toother resources.

• Adding more units of the constraint resource. Likewise, you could apply Little’s Law to reduce

flow time, for example, by reducing the processingtimes of tasks on the single path, including those per-formed by the constraint. If you reduce flow time onthe path, then you also would increase flow rate. Youalso could reduce flow time by moving tasks off thissingle path.

In more complex operations—for example, those inwhich parallel workstations exist or a process branchesto different paths—the physical constraint may not per-form an activity on the critical path. If this is the case,increasing flow rate at the constraint will not decreaseflow time, nor will attempts to reduce flow time increaseflow rate. The following two examples help highlightthe differences between flow rate and flow time.

Example One

Consider a simple deterministic system to demon-strate three scenarios:

1. System operating at capacity.

2. System operating at less than capacity (flow ratechanges).

3. System operating at less than capacity (both flowrate and flow time change).

38 I F E B R U A R Y 2 0 0 5 I W W W . A S Q . O R G


With this deterministic system, a student entersevery two minutes, and a student leaves every two min-utes. Five students are inside the system, with eachspending 10 minutes there. Note that Little’s Law issatisfied by the system, as it must be. The inventory(five students) is equal to flow rate (0.5 students perminute) times flow time (10 minutes).

Scenario one—system operating at capacity. In thefirst scenario, the capacity of the system is fixed at 0.5students per minute. For this scenario, a machine pro-duces a ticket every two minutes. One student is at themachine and four students stand in line waiting. Thewaiting line is a buffer in front of the ticket machine.As soon as a student has a ticket, he or she is allowedto exit, and at exactly the same time, another studententers.

What happens if you double the inventory by put-ting five more students into the system? The changeinside the system is that nine students are in thebuffer, and the flow time doubles from 10 to 20 min-utes. For this system, the optimal inventory is one,which results in a flow time of two minutes.

Scenario two—system operating at less than capacity(flow rate changes). The second scenario is the one inwhich the capacity of the system is underutilized. Forthis scenario, there are 20 10-minute timers inside thesystem. Each student picks up an unused timer uponentering the system. When the timer goes off, the stu-dent exits the system, leaving the timer in the system.At any point in time, five students are holding timersinside the system, and there are 15 unused timers.

What happens if you double the inventory by put-ting five more students into the system? The changeinside the system is that there are now 10 studentsholding timers and 10 unused timers. Thus, in thiscase, the flow time remains at 10 minutes and the flowrate doubles from 0.5 students per minute to 1.0 stu-dent per minute.

Note also you can double the inventory again (up to20) and have the flow rate double again. However, at20, you reach the capacity of the system, which isdetermined by the constraint (timers), and thenrevert to a point at which the flow rate will remain con-stant if inventory is increased beyond 20. Thus, for thissystem, the optimal inventory is 20, which results in a

flow rate of two students per minute.Scenario three—system operating at less than capac-

ity (both flow rate and flow time change). The thirdscenario is the one for which both flow rate and flowtime change as inventory in the system increases.

For this scenario, the students must go through twophases inside the system. In the first phase, studentsuse 8.5-minute timers. There are 20 timers in the sys-tem. As soon as a student’s timer beeps, he or she pro-ceeds to the second phase and uses the timer to starta machine that requires 1.5 minutes to produce theticket to leave the system.

There is one machine for producing tickets. Thecapacity of the timer resource is 2.35 (20/8.5) stu-dents per minute. The capacity of the ticket machineis 0.67 (1/1.5) students per minute. Therefore, theticket machine determines capacity, but because it isnot fully utilized, flow rate is less than capacity.

We can use Little’s Law to determine the averageinventory in each phase of the system. The averageinventory of students using the ticket machine is 0.75(the flow rate of 0.5 per minute times the flow time of1.5 minutes). Because there are five students in thesystem, the average number of students holdingtimers is 4.25 (5 – 0.75). After we double the invento-ry in the system to 10 students, the status of the systemwill change, but determining the new status is not asstraightforward as for the first two scenarios.

Because the system is not at capacity with five stu-dents in it, let’s assume as a first attempt the flow timein the system will not change and the inventory foreach phase of the system will double. However, we canimmediately see this is not possible for the secondphase of the system because the machine can handleonly one student at a time.

Therefore, our first assumption was wrong, and weassume the system is now at capacity. So there willalways be one student using the ticket machine, andthe other nine either will be holding a timer or wait-ing in the buffer for the ticket machine.

The system flow rate will be the capacity of the tick-et machine—0.67 students per minute. The flow timefor the system will be 15 minutes (inventory of 10divided by flow rate of 0.67), and each student willspend five minutes waiting in the buffer. Therefore,


YOU MUST EXERCISE CARE WHEN DISTINGUISHING BETWEEN ACTIVITIES THAT

DETERMINE FLOW TIMES AND RESOURCES THAT ARE PHYSICAL CONSTRAINTS.


the average inventories in the system are 5.67 studentswith timers, 3.33 students waiting in the buffer andone student at the ticket machine. To summarize,doubling the inventory in the system from five to 10increases the flow rate from 0.50 to 0.67 students perminute and increases the flow time from 10 to 15 min-utes.

The optimal approach for this scenario can bedetermined by eliminating the wait in the buffer,which results in an optimal inventory of 6.67 students.In essence, the system has excess capacity, similar toscenario two in which there are fewer than 6.67 stu-dents in the system, and is at capacity, similar to sce-nario one in which there are 6.67 or more students inthe system.

Example Two

In reality, almost all systems have variability and aremuch more complex than the system in example one.That example, with its three scenarios, demonstratedthe moderate difficulty of applying Little’s Law andTOC to relatively simple systems.

For the second example, we made the system fromthe third scenario of the previous example more com-plex by adding variability. Simulation is especiallyhelpful in the analysis of systems with variability.

For example, a recent article reported the use ofsimulation modeling of call center operations inlaunching a new fee based technical support programthat guaranteed paying customers would wait less thanone minute on hold.7

We used ProModel 8 to develop a simulation modelfor this system with the ticket machine and the 20timers. We then introduced variability by using a nor-mal probability distribution for the times associatedwith both the timer and the ticket machine.

To avoid making the example too complex, we usedthe same value for the coefficient of variation for boththe timer and the ticket machine. Thus, using c to rep-resent the coefficient of variation, the times in the sim-ulation for the timer were sampled from the normalprobability distribution with a mean of 8.5 (minutes)and a standard deviation of 8.5c. For the ticketmachine, the times were sampled from the normalprobability distribution with a mean of 1.5 (minutes)and a standard deviation of 1.5c.

We then ran the simulation for values of c from 0.0up to 0.5 in increments of 0.1 and for system invento-ries from 5 to 10. The simulation used a 10-hourwarmup period and a run time of 100 hours. Theresults for the average values over the 100 hours for

average flow rate per minute are shown in Figure 1.The impact of variability on flow rate and thus on

flow time (from Little’s Law) can be seen clearly. At agiven value for inventory, increasing variabilitydecreases flow rate and increases flow time.

Interestingly, this simple example can be used toshed light on the impact of increasing variability onsystems that are and are not operating at capacity.When the inventory is five, the system is not at capaci-ty, which corresponds to systems in which the just-in-time manufacturing approach is effective.9

When there is no variability, there is no waiting timefor the entities as they flow through the system. As thelevel of variability increases, entities start encounter-ing waiting time in the buffer because the previousentity is still using the ticket machine. As a result, aver-age flow time increases and flow rate decreases.

Of course, real just-in-time systems do not behavelike this because they operate in such a way that flowrate is maintained. However, the model demonstratesthat for a system with no wait time, when variabilityincreases to the point there is waiting, both averageflow time and average inventory will increase.

When the inventory is eight, the system is at capaci-ty, and TOC is appropriate. As variability increases, thebuffer in front of the ticket machine (the constraint)will at times be empty when it finishes working on theprior entity. Based on TOC concepts, we know the sys-tem’s average flow rate will decrease, and from Little’sLaw, we know the average flow time will increase.

The system being considered does not correspondto what happens in real life TOC systems. Such sys-tems have a given level of variability, and essentially,what needs to be done is to determine the optimalinventory for operating the system.

40 I F E B R U A R Y 2 0 0 5 I W W W . A S Q . O R G

0.70

0.65

0.00.10.20.30.40.5

0.60

0.55

0.50

0.45

0.405 6 7 8 9 10

Inventory

Thro

ughp

ut p

er m

inut

e

Figure 1. Throughput vs. Inventory as aFunction of Coefficient of Variation

Fortunately, the simulation model also can be usedto depict that approach. In fact, if you assume inven-tory must be an integer value, it is not necessary tomake more runs with the model. All you need to do isto look at the results from the standpoint of a givenlevel of variability rather than from a given level ofinventory as was done in Figure 1.

To do this, you need to assign economic values forinventory, flow time and flow rate. Again, let’s take asimplified approach and assign economic values of +50for each unit per minute increase in flow rate, -1 foreach additional unit of inventory and -1 for each addi-tional minute of flow time. Now let’s use these values todetermine the optimal inventory for a value of 0.2 forthe coefficient of variation. The pertinent values areshown in Table 1, where you can see the optimal levelof inventory is eight units. We carried out similar analy-sis for each of the other values for the coefficient ofvariation. The results are shown in Table 2.

If there is very little variability, the optimal invento-ry is therefore seven. For fairly small levels of variabil-ity (values of c from 0.1 to 0.3), the optimal inventoryis eight. Finally, for larger levels of variability (values ofc from 0.4 to 0.5), the optimal inventory is nine.

Manufacturing and Nonmanufacturing

Both Little’s Law and TOC are relevant tools as partof broader Six Sigma or lean projects and can beapplied to these projects in any type of operations sys-tem. Our students have applied Little’s Law to reduceflow times in a variety of systems, including a hospital,an order processing system at a manufacturer and anoperation for processing insurance applications.

Some of our students also have applied TOC con-cepts in the same projects in which they reduced flow

times. When the critical path of activities includes anactivity performed by the constraint resource, increas-ing flow rate at the constraint will then reduce flowtime.

When the critical path does not include an activityperformed by the constraint, separate but relatedprojects have to be undertaken—one to increase theflow rate of the constraint and a second to reduce flowtime on the critical path.

These students and most practitioners must learn toapply Little’s Law and TOC appropriately. Further-more, the use of process modeling, simulation andoptimization can aid in applying these techniques tosystems, which in turn can lead to significant improve-ments in operations.

REFERENCES AND NOTES

1. Robert Gerst, “The Little Known Law,” Six Sigma Forum Magazine, Vol. 3,No. 2, pp. 18-23.

2. John D.C. Little, “A Proof for the Queuing Formula: L = lW,” OperationsResearch, Vol. 9, No. 3, pp. 383-387.

3. Ravi Anupindi, Sunil Chopra, Sudhakar D. Desmukh, Jan A. Van Mieghemand Eitan Zemel, Managing Business Process Flows, Prentice Hall, 1999, p. 42.

4. Ibid.

5. H. William Dettmer, Goldratt’s Theory of Constraints: A Systems Approach toContinuous Improvement, ASQ Quality Press, 1997, p. 11.

6. Ibid., pp. 13-15.

7. Robert M. Saltzman and Vijay Mehrotra, “A Call Center Uses SimulationTo Drive Strategic Change,” Interfaces, Vol. 31, No. 3, pp. 87-101.

8. Information on ProModel, a discrete even simulation software, can befound at www.promodel.com/products/promodel.

9. Just-in-time manufacturing is an optimal material requirement planningsystem for a manufacturing process in which there is little or no manufac-turing material inventory on hand at the manufacturing site and little or noincoming inspection.



WHAT DO YOU THINK OF THIS ARTICLE? Please share

your comments and thoughts with the editor by e-mailing

[email protected].

Table 1. Economic Analysis For a Coefficient of Variation of 0.2

Average Averagethroughput in cycle time Economic

Inventory units per minute in minutes value

5 0.4720 10.59 31.61

6 0.5507 10.89 38.18

7 0.6172 11.34 43.38

8 0.6553 12.20 45.33

9 0.6652 13.53 43.99

10 0.6662 15.01 41.61

Table 2. Optimal Inventory as a Function Of Coefficient of Variation

Coefficient of variation 0.0 0.1 0.2 0.3 0.4 0.5

Optimal inventory 7 8 8 8 9 9


Participants Guide

How to Read “The Goal”

Written in a fast-paced thriller style, The Goal, a gripping novel, is transforming management

thinking throughout the world. It is a book to recommend to your friends in industry - even to

your bosses - but not to your competitors. Alex Rogo is a harried plant manager working ever

more desperately to try improve performance. His factory is rapidly heading for disaster. So is

his marriage. He has ninety days to save his plant - or it will be closed by corporate HQ, with

hundreds of job losses. It takes a chance meeting with a professor from student days - Jonah - to

help him break out of conventional ways of thinking to see what needs to be done. The story of

Alex's fight to save his plant is more than compulsive reading. It contains a serious message for

all managers in industry and explains the ideas, which underline the Theory of Constraints

(TOC), developed by Eli Goldratt.

This is a seven week discussion of “The Goal.” Each week, you will read a selected set of

chapters. The Goal is written using the Socratic Method - Ask - Tell - Ask. The chapter are

selected based on the question that Jonah poses to Alex, what Alex learns and Alex’s next

questions. As you read, each section, think about the following questions:

1. What is the current situation? What did Alex learn?

2. What questions does Alex currently have?

3. What hints does Jonah give Alex?

4. What do you think the answers Alex will discover are?

5. How does this apply to my organization?


Your discussion facilitator will ask questions to review the previous week’s reading and may

present exercises to enhance your learning.

Reading Schedule

Intro – Chap 4

Chaps 5 – 8

Chaps 9 – 11

Chaps 12 – 19

Chaps 20 – 25

Chaps 26 – 31

Chaps 32 – 40


Intro – Chapter 4

1. Why does Alex think the robots are so successful when he first talks to Jonah?

2. How does Jonah indicate that the robots were not successful?

3. How does Jonah define productivity?



Chapter 5 – 8

1. What is the goal?

2. What does your process manufacture?

3. What three common financial measures express the goal to "make money"?

4. Express the “goal” in terms of those financial measures

5. What three measures are useful at the operational level to express the goal?

6. Define throughput, inventory, and operational expense.

7. Jonah claims the common financial measures are related to the operational measures. How?

8. Define Throughput, Inventory and Operating Expense in your process’ terms




Chapter 9 – 11

1. Express the "goal" in terms of throughput, inventory, and operational expense.

2. What is the result of high efficiencies on a non-constraint machine?

3. Do high efficiencies necessarily imply higher profit?

4. Why is it important that throughput be defined in terms of sales rather than production?

5. What causes a balanced plant to fail?

6. What are the type of operational operating expenses?

7. What is the equation for Productivity?




Chapters 12 – 19

1. Why does the spread of the line of boy scouts discussed on page 100 always become longer

as time goes on?

2. What characteristics of the hiking troop relate to the production characteristics of

Throughput, Inventory, and Operational Expense?

3. Using the hike analogy on page 113, what happens in a plant if the fastest operations are put

at the beginning of the production process, the slowest operations are put at the end, and all

workers produce at a high efficiency?

4. What is Herbie in terms of TOC?

5. In terms of TOC what has been done when Herbie goes to the front of the line?

6. In terms of TOC what has been done when items are removed from Herbie's pack?

7. Why was Pete so happy even through the order was not delivered on time?

8. Define a bottleneck

9. Why does Jonah say “balance flow not capacities”?



Chapters 20 – 25

1. Why does Jonah say a plant should have bottlenecks?

2. What does lost time at a bottleneck cost?

3. What two things can be done to optimize a bottleneck?

4. What is the effect of the "efficient" operation of non-bottleneck machines?

5. What determines the level of utilization of a non-bottleneck machine?

6. What are the combinations of production flow through a bottleneck and non-bottleneck?

7. What is the difference between activating a resource and utilizing a resource?

8. Which resources in the system should we seek to optimize?

9. What does Jonah suggest is the actual constraint in the system?

10. What do you think is the solution Jonah is proposing?



Chapters 26 – 31

1. What is the function of the drum and rope if used on a hike?

2. What is the drum for the production facility?

3. What is the rope for the production facility?

4. Why is a rope needed for assembly operations?

5. What is the next logical step after establishing the drum and rope for the production process?

6. What does cutting batch sizes in half for non-bottleneck operations accomplish?

7. How can the time material spends in plant be classified into four types?

8. What is time saved on a non-bottleneck machine?



Chapters 32 – 40

1. What are the 5 Focusing Steps?

2. What is the Process of Change?

3. Alex and his team have moved from the _______________ world to the _____________

world.

4. In each world, what is the relative importance of Inventory (I), Operating Expense (OE) and

Throughput (T) and why?

____________ World _______________ World

1. 1.

2. 2.

3. 3.

5. What are your most important learnings?


Author Bio

Eli Goldratt is an educator, author, scientist, philosopher, and business leader. But he is, first and

foremost, a thinker who provokes others to think. Often characterized as unconventional,

stimulating, and "a slayer of sacred cows," Dr. Goldratt exhorts his audience to examine and

reassess their business practices with a fresh, new vision.

He obtained his Bachelor of Science degree from Tel Aviv University and his Masters of

Science, and Doctorate of Philosophy from Bar-Ilan University. In addition to his pioneering

work in Business Management and education, he holds patents in a number of areas ranging

from medical devices to drip irrigation to temperature sensors


Further Reading

Theory of Constraints

“It’s Not Luck” by Eli Goldratt

Applying TOC to sales and marketing

“Critical Chain” by Eli Goldratt

Applying TOC to project management

“What is this thing called Theory of Constraints” by Eli Goldratt

Further explanation of the Five Focusing Steps, the Process of Change and implementing

TOC

“Breaking the Constraints to World-Class Performance” by H. William Dettmer

Very in-depth discussion of the Theory of Constraints

Lean

“Gemba Kaizen” by Masaaki Imai

Applying the principles of lean production and continuous improvement

“Office Kaizen” by William Lareau

Applying the principles of lean production and continuous improvement to office and

administrative functions