The Goal Theory of Constraints

Presented byAdam BogartJay Smith

Chapter 13—Alex Hits the Trail

Alex begins his 10 mile hike to Devil’s Gulch with the scouts.Gaps appear.Alex meets Herbie.What are statistical fluctuations and dependent events?

The Plan

1. Leave at 8:30 in a single file formation with Alex at the leading the way.

2. The average person walks around 2 miles per hour.

3. Allow hour and a half for breaks and lunch.

4. Arrive at Devil’s Gulch at 3:30 “No sweat.”

What Happened was…

Gaps appear immediately in the line. Alex moved to the back of the line. This is where he meets Herbie.

Starts to ponder what Jonah told him about Dependent Events and Statistical Fluctuations.

*Gee, What are dependent events and statistical Fluctuations?

Dependent Events

An event , or a series of events, that must take place before another can begin. The hike to Devil’s Gulch dependent events was the line in which the scouts walked. The first person in line must walk the trail before the person behind them could.

*Well that’s great, but what about statistical fluctuations?

Statistical Fluctuations A task in which the time to

complete the task will vary each time the task is performed. This variance is known as a statistical fluctuation. Alex figured that the boys were walking and average of 2 mph. At times some were walking 2.5 mph and at other times some were walking 1.2 mph. The variance in speeds statistical fluctuations.

* So, What does this have to do with the hike?

Herbie and the Hill

Herbie was slowing everyone behind him down as they were climbing a long steep hill. When Alex got to the top of it he realized the leader was a half a mile ahead of them.

* What happened? How did they get so far ahead?

Putting it Together

The hike was a set of dependent events in combination with statistical fluctuations. Each hiker speed fluctuates at different times. A gap occurs when a slower than average fluctuation happens and the ability to walk faster than the average speed is restricted by the dependent event directly in front of them.

* Ok… (say it like you not sure what I’m talking about)

Putting it Together

However the ability for a hiker to slow down is not restricted. The distance Herbie and Alex had to make up depended on how many dependent events and fluctuations were in front them.

* Oh I see. The fluctuations do not average out, they accumulate. The accumulation of the fluctuations determine the total length of the

lines. Sheesh all this is making me hungry.

Chapter 14 –Lunch Time

The troop stops at noon for lunch.If capacity was perfectly balanced with demand, would excess inventory go away?

* Beats the heck out of me….

Sets up a balanced system using dice, six bowls, and match sticks.

* Match Sticks?…

Behind Schedule At noon the troop was supposed to stop at

Rampage River for lunch. It was still up the trail some and everyone was hungry for lunch. Alex noticed a kid playing with some dice and that sparked an idea to make a perfectly balanced model. * But will it have dependent events and statistical fluctuations? How is that possible.

Dice Bowls and Matches

Dice Determines how many matches can

be moved from one bowl to the next.* Oh ok… they represent the capacity of each resource

or…the bowl.

Bowl The set of six bowls are the

dependent events that must occur in order to produce matches.

Each bowl has the same capacity (*

Which is 6 right?) , but will yield different amounts as numbers fluctuate with the deviation of the rolled number.

Dice Bowls and MatchesProduction Throughput is the speed at

which the matches come out of the last bowl.

Inventory is the total number of matches in the bowls at any given time.

Capacity of the system is 6, the highest number that can be rolled, and the demand is six. * Oh I get it now… Capacity equals demand

making the system a perfectly balanced model.

The Quota is 3.5

Alex and the scouts figure the average matches that can be moved at a time is 3.5 per turn. * Well if that is true then after 10 turns they should have produced 35 matches, and after 20 turns they should have produced 70 matches.

Charting the Results

Rolls of the die1= -2.52= -1.53= -.54= .55= 1.56= 2.5

* I don’t understand…

Numbers on the Graph* After I get done with my graph…Ask “what happened?”

A:\Graph.xls - Graph!A1

76.5

65.5

54.5

43.5

32.5

21.5

10.5

0-0.5

-1-1.5

-2-2.5

-3-3.5

-4-4.5

-5-5.5

-6-6.5

Results From Book's Example

Chapter 15—What Happened

Linear DependencyCovariance Negative DeviationsAlex speeds things upLighten Herbie’s load

Linear Dependency

A mathematical principle that says when there are two or more dependent variables, the fluctuations of the variables down the line will fluctuate around the maximum deviation established by the preceding variables. * Great… that clears thing right up. so how does that explain what happened in the match game model?

Input & Output

Covariance is the input. Negative deviations it the

output.

* Ok that wasn’t the answer we were looking for.

Covariance A statistical measure of

correlation between the fluctuations of two different variables.

* Jay: I guess I don’t understand. And by the looks of our audience… I don’t think I’m alone.

Adam:* Think about it… What were the two variables of the match game?

Jay: Umm The numbers rolled on dice, and only being able to move how ever many matches are in each bowl.

Adam: Exactly and what was the rule of Linear dependency?

Jay: Oh ya… when there are two or more dependent variables, the fluctuations of the variables down the line will fluctuate around the maximum deviation established by the preceding variables.

Jay: But how did all of this make the graph in the book go almost straight down.

Negative Deviations

When covariance is solved the answer is actually the maximum deviation that the two variable revolve around.

*Jay: Oh ok. So in the case of the match game when the covariance is solved, it gave a negative answer, so that’s why the graph was negatively sloped.

Adam: I think you got it. With the variables involved match game, when a statistical fluctuation occurred the maximum deviation was -.2910 for the example in the book, and -.2703 for the model I did. There was no reserve. When the scouts in the match game got behind they had no excess capacity to make up for the loss. And as these negative deviations kept accumulating they got deeper and deeper in the hole.

Jay: Oh ok. The graph makes sense now. But how can knowing that help them on the hike?

Graph!A1

Herbie is the Key

The Hike is a set of dependent events… in combination with statistical fluctuations. Each scout fluctuates differently—some faster, some slower. The ability to go faster than the average speed is restricted by the kid in front of them. But there is no limit on the ability to slow down.

Adam: Of all the dependent events, Herbie is the slowest of the troop. He actually determines how fast the troop moves. Throughput for the troop is when the last person walked the trail. That doesn’t happen until Herbie walks over it. The gaps in the line represented the inventory of the troop. The longer the line the more inventory there is. If it were Alex’s plant in there would be nothing would be being sold and the work-in-process would be through the roof.

Adam: Sometime after lunch he realized the boys had arranged themselves in an order that nobody was being held back. The fastest kid was in the front and the slowest kid, Herbie, was at the back. Everyone was walking at their own pace. If this were the plant, there would be no idle time and every on would be 100% efficient. But what was happening was the line was getting longer and longer—inventory was skyrocketing. Alex stopped the group and moved everyone exactly opposite to where they were in line and now Herbie is at the front and the slowest is in the back. Now each dependent event has the capacity to overcome the statistical fluctuations in front of them as they occur.

Adam: They lighten Herbie’s load and they made the last four miles of the trip in 2 hours. With Herbie at the front of the line, Throughput was up and inventory was down.

Guilt and AccusationsDave gives his Dad a note Adam: Read note

Made to feel that work has taken precedence, Alex can’t find a balanceSharon feels she did something wrongGives standard explanation to both children, not their fault Julies parents: They ask what he has done to her Did he call police? Adam: They knew exactly

where she was. She was there the whole time Moving onto chapter 17: Alex wakes to a difficult morning.

Next Morning

Brief problem with breakfast

Sharon doesn’t want to go to school

Adam: A few hours go by and Alex arrives late to work at the plant.

100 Sub-assembliesHilton Smyth demands 100 pieces by days end States he’ll go to Peach Advised Alex to check

his memos Learns of Smyth’s

promotion: named to Division Productivity Manager, Smyth becomes Alex’s new boss.

By now Alex is thinking “what next, its only Monday!”

Staff MeetingAlex explains hike to staff, nobody grasps it. Alex states as if he’s proven 2+2=4 but they don’t believe himDoubts about source of inspiration – ‘kids on a hike’Points out the statistical fluctuations and dependent events as proof of what he’s foundBob states statistical fluctuations not possible with robots, they were bought for consistency Adam: I beg to differ its very possible

Goal to make the “system” productiveMeeting interrupted attention returns to 100 sub assemblies

Time Constraint 5 hours remain

Simple schedule, each group will record output / hour until 5(insert example here???)Output has to be at least 100 pieces no lessPete’s dept supposed to be at rate of 100 pieces/hour but will have statistical fluctuations. Some times short a few pieces, sometime extra pieces. A few ahead, a few behind. Dependant events: occur because the robots can’t start until it has received materials from Pete’s department$10.00 bet is initiated

Ideal Output of Sub AssembliesAdam : That looks like a good schedule to me. I see the dependent events, but where are the statistical fluctuations?

Jay: I glad you asked that., Hold on to that thought.. Before we go on, I thought we’d check back in with Alex

Time Constraint5 hours remain

Two remaining departments to complete sub-assemblies

Adam: Let me get this straight. They have five hours to make 100 pieces that have to go through two departments and one of them is a robot. Sounds like dependent events to me.

Time constraint until 5:00 pm to catch the truckPer quotas they feel they can meet the deadlinePete’s dept to send parts for 25 units/hour to robotsRobots capable of welding 25 units every hourAdam: This sounds like a good way to way for Alex to show what he learned on his hike.Jay: That is exactly what he does.

Implements changes to show what he has ‘discovered’

Alex has time to reflect

Consults his secretary on how she handles a child in reference to workConsiders looking for Julie. Asks his mom to come and stay until things settle

Jay: Did anyone notice what Alex’s Mom did when she came to stay with Alex? Call on Roberto

Roberto:Ya. She brought over all of her pots and pans.Jay: Nice job Roberto. You’re pretty sharp I noticed the

same thing.Adam: Well I guess I missed the whole thing. Why did

she do that?

Pots and Pans This and other signs show that

people are resistant to change and things different than what they are comfortable with.

Moment of truthPete’s people had statistical fluctuation 19 complete, 1st hour

Short 6 units 40 complete by 2nd

hour Short 10 units

68 complete by 3rd hour Short 7 units

100 complete by 4th hour 0 units short, work

flow increased, all 100 units complete.Adam: Oh I see the fluctuations (Walk to the

screen and point) Pete’s people need to make 25 but they only made 19. That’s just like rolling a 6 but only passing 4 matches. Negative deviations

Round of coffeeAlex compares two sheets- shows that the robot capacity is only 25 units/hour

Pete’s group brought 19 in 1st hour, 21 in second hour: these became capacity

3rd hour brought 28 to robot and in 4th hour 32 to robot. Machines maximum capacity is 25/hour.

Bob looses the $10 bet, Alex tells Bob to buy coffee for his employees as thanks for the extra efforts. After 5 o’clock machine is still working on sub assembliesRobot’s capacity based on what the prior work group completes

machine is only capable of 25/hour, machines constraint was met and could not be exceeded.

Time lost can not be made up, thus machine was still going after 5th hour.

Adam: Look it has it all, Linear dependency, covariance, and negative deviation..

Jay: It sure does

Jonah’s Next StepFeel they know what is causing late orders: dependency and statistical fluctuationsDebate is sparked

Bob says longer lead times? Adam: Won’t that will lead to a larger inventory which is against the goal.

Control all variables? Adam: How can they do that? Jay: Good question, They can’t, there is way to many.

Jonah is called in: Optimize the whole system by balancing

the flow of products through the plant. Find the bottlenecks and the non-

bottlenecksJay: A bottleneck is any resource whose capacity is equal to or

less than the demand placed upon it.Adam: So would that make a Non bottleneck is when capacity

is greater than the demand placed on it.Jay: That is exactly right?

Adam: Aren’t Bottlenecks bad?Jay: They are not necessarily bad or good

The Search Is OnDebate on how to find bottlenecks

Look at resources, compare against market demand Find demand greater

than capacity, they will find the bottleneck?

Adam: Well if this were true, couldn’t they just go out to the shop and look for a giant pile of Work in progress in front of a machine. The kids piled up behind Herbie is how Alex knew he was the problem on the hike.

Jay:That is exactly what they do.

Good Afternoon HerbieRalph provided computer data and calculationsTime to simplify, they walk through factory taking observationsHello Herbie, the NCX-10

Proof is stack of WIP Inventory, backlog inventory Reason for the change with loss of old machines

Herbie #2: Heat treat, only 2 available Not running full batches Some parts must wait Some batches to small, some to big

Sequence of operations must stay the sameAdam: Ah… you mean a set of dependent eventsJay: you got it

Increase resources to increase capacities which increases throughput and decreases inventory.

Adam: Just like they did with Herbie and lightening his load?Jay: You got it. The idea is balance the flow of the product through the

plant. Only then, when this happens, can “The Goal” be met.

Question, Comments, or Insults

Audience participation time!

The End