Below are 2 Theory of Constraints games. The game from The Goal book and the job shop game. Both games do a great job of explaining Theory of Constraints concepts.
Contents
GOLDRATT’S Theory of Constraints GAME from The Goal book – The Dice Game
This activity is a variation of the game Goldratt described in his “novel”, the Goal (North River Press, 1992, pp. 104-112.). This variation can be used to illustrate many concepts in production management. We use it to reinforce the notation that reduction of variation in processes is more efficient and economical than increasing inventory, or work-in-progress in this case.
The game simulates a production line with 5 work stations. The product must pass through each of the 5 work stations in order from 1 to 5. We use pennies to simulate the process. The potential amount of work completed at each station in a given time period is a uniform distribution of 1, 2, 3, 4, 5, and 6. This random potential work is determined each period by the tossing of a die. Hence the average potential amount of work at each station and thus through the system is 3.5 units per period.
If the game is played for 20 periods for example, one might expect an average of 70 completed units. However, the actual work completed at each station is limited by the WIP. The game is played by starting each station with a WIP of 4. At a signal all stations roll their dice to determine their potential work. The actual work forwarded to the next station is of course the minimum of the number on the die and the number of items in the WIP. We use pennies to represent the item being produced (No actual work is done at each station as the pennies move along).
The first station’s WIP is always replenished to the 4 level. As the game is played, WIP begins to vary and eventually in some cases limit the amount of work done. We set up as many lines as we have students available. By the end of 20 periods no line will be near the expected level of 70 finished units. When asked to suggest adjustments that might allow us to reach the target of 70 units on average, many students will suggest increasing the WIP. We re-run the game starting with WIP’s of eight rather than four and production does tend to increase but still often below the 70 level.
Further discussion usually results in a suggestion that better results could be obtained by reducing the variation in the work. The game is played one more time flipping coins to determine potential production levels with heads resulting in 4 units and tails 3 units. The average work done is still 3.5 units. Going back to WIP’s of four, this run is the most successful.
You can download the PDF of the above game here:
Free Game from The Goal by Eliyahu M Goldratt pdf
Video on The Dice Game:
The JOB SHOP GAME, a Theory of Constraints Game
If you run a custom job shop — be sure to visit our Velocity Scheduling System site for tons of free content and to sign up for our coaching program for guidance on implementing The Goal concepts in your shop!
This simple game was developed by
James R. Holt, Ph.D., PE
Associate Professor Engineering Management
Washington State University
Feel free to use this game when you credit to the source.
Instructor Information
Objective of the Theory of Constraints Game
The student will be able to understand how Drum-Buffer-Rope (DBR) scheduling applies to Job Shop environments.
Overview:
The game is played by releasing up to 36 Orders, one at a time, into the shop and sending them through four different Work Centers (A – D) to make the product. The Orders are monitored to determine how long it takes to get an Order processed from start-to-finish (flow time). The flow days are recorded on a chart. The results are analyzed.
Background:
In a Job shop environment, machines are organized in a functional layout (machines with similar processing characteristics are grouped together in a Work Center). Each Order that is released follows a specific outing (a processing sequence) through the Work Centers. With the high variety of routings and loads (setup and run times), you have a complex environment which is extremely hard to schedule. The bottlenecks
(constraints) seem to constantly shift, making it difficult to determine when Orders will be completed. Even though Job Shop environments range from ‘High Variety / Low Volume’ (Unique One-of-a Kind, ex. a tooling shop), to ‘Lower Variety / Higher Volume’ (ex. a production shop where the parts for a set of products are made in batches on a regular basis), this exercise effectively demonstrates the applicability of DBR
to all Job Shop environments.
Work Centers & Capacity:
For this exercise, our Job Shop has four (4) Work Centers (A – D) and each Work Center has one machine. The processing capability of each Work Center is specialized, so you can’t use alternate routings.
Each machine has only enough capacity to perform one operation per day.
Products:
There are 36 Order cards and each Order card has a Product # (1 – 4) on it. For the student who works in a High Variety / Low Volume environment, there are four product TYPES represented by the Product # (1 – 4) [ex. four different types of tools]. Each Order card represents a UNIQUE PRODUCT [tool] within each product type.
For the student who works in a Lower Variety / Higher Volume environment, there
are four different PARTS represented by the Product # (1 – 4). Each Order card
represents a different BATCH of each part.
Routings:
The process Routing, which represents the necessary sequence of Operations (the
Work Center where each operation is to be performed) is on the Order Card.
Orders must be processed by the Work Centers in the same sequence as the
Routing.
Role Requirements:
The Instructor should assign students to the Scheduler, Work Center Operator, and Flow Control Monitor roles. The roles have the following requirements: Scheduler – This game requires the Scheduler to be able to add up the buffer count and determine whether to release an order.
Work Center Operator
– At the end of the day in scenario 3, the students will be required to indicate the number of ‘B’ operations that have not been completed on the orders in their queue. This will be indicated by either a closed fist for none, or the appropriate number of fingers.
Flow Control Monitor
– Must be able to calculate the flow days for each Order card by subtracting the Release Day from the Shop Day. Allow the students to select their own roles.
The Players & Duties:
Scheduler (One):
When the Instructor calls out “Shop Day …”, the Scheduler makes a decision to Release/Not Release an Order card according to the specific scenario instructions. When the Instructor calls out “Write…”, and the Order is going to be released, the Scheduler writes the Shop Day on the ‘Release Day’ line on the Order card. When the Instructor calls out “Pass…”, the Scheduler passes the Order card to the queue of the initial Work Center (the first Operation).
Work Center Operators (Four):
Each Work Center can only process a maximum of one Order per day. When the Instructor calls out “Shop Day …”, the Operator takes ONE Order card from their queue (if there are any Order cards in the queue),
writes the Shop Day in the appropriate ‘Routing Box’ on the Order card. When the Instructor calls out “Pass…”, the Operator passes the Order card on to the next Work Center queue on the routing, or to the Flow Control Monitor if the Order card is complete.
For best results, the Operator should process all Orders in a ‘First-In-First-Out’ (FIFO) sequence [otherwise you end up with a FISH (First-In-Stays-Here) sequence.
Flow Control Monitor (One):
Calculates the flow days for each Order card by subtracting the Release Day from the Shop Day in the last ‘Routing Box’ and writes the flow days on the ‘Total Flow Days’ line on the Order card. When each Scenario is complete, the Flow Control Monitor also plots the data from the Order cards – see Data Plotting instructions.
General Instructions:
The Instructor controls the rate of play and will call out Shop Days until all the Orders have been completely processed. Students will follow the cadence and not work ahead.
Preparing the Students:
In order to have the students perform the exercise correctly, the Instructor must make sure that the students understand what to do and when to do it. Clearly explain the responsibilities of each role and how to properly record data on the ‘Order card’ and Flow Days charts. Also, the students must understand that they are not to work ahead or fall behind. Everyone must be in sync or the exercise will not demonstrate the
desired points. Possibly consider explaining that the Instructor is like a Conductor and everyone must follow the beat or the resulting sound will not be beautiful music – just a lot of noise.
The Queue:
The queue in front of each operator is a piece of 8 ½ x 11 paper with the Work Center Letter written on it. Remind them to keep their orders in First-In-First-Out (FIFO) sequence and give them time, especially operator ‘B’, to stay organized.
The Order Card:
Below is an example of the Order Card. It contains the following items: Product or Part: Labeled 1 – 4, this indicates either 1) which product type is represented (high variety/low volume environments) or 2) a batch of parts numbered 1-4 (lower variety/higher volume environment). Release Day (Shop Day): When the Instructor calls out “Shop Day …”, the Scheduler makes a decision to Release/Not Release an Order card according to the specific scenario instructions. When the Instructor calls out “Write…”, and the Order is going to be released, the Scheduler writes the Shop Day on the ‘Release Day’ line on the Order card.
Routing Box/Shop Day:
When the Instructor calls out “Shop Day …”, the Operator takes ONE Order card from their queue (if there are any Order cards in the queue), writes the Shop Day in the appropriate ‘Routing Box’ on the Order card.
Last Operation Day minus Release Day: When the order is completed, the Flow Control Monitor will calculate the flow days for each Order card by subtracting the Release Day from the Shop Day in the last ‘Routing Box’ and writes the flow days on the ‘Total Flow Days’ line on the Order card.
Scenario Instructions:
This requires that the room remain quiet during the exercise so that all the students can clearly hear the instructions.
Scenarios Overview:
The first two scenarios are run in a Traditional Job Shop scheduling manner. Scenario #2 is a traditional job shop scheduling, but there is an attempt to minimize work in process at Work Center B. Scenario #2 may be skipped if time is short. Scenario #3 is a Drum-Buffer-Rope environment.
Scenario #1 Instructions:
The Scheduler should first shuffle the Order cards. The Scheduler will release one Order card each Shop Day until all Order cards have been released.
For each Shop Day, the Instructor will:
Call out the Shop Day (ex. “Shop Day #7”) Pause, then tell the students to write the number of the Shop Day (ex. “Write #7”) on the next Order card in their queue waiting to be processed (using the FIFO method).
Pause, then tell the students to pass the Order card to the next Work Center on the Routing or to the Flow Control Monitor if the Order is finished (ex. “Pass the Order card”) At completion, record the data. (See ‘Data Plotting Instructions’)
At the completion, discuss with the students:
- Ability to Promise Customer Delivery
- Ability to predict Order Completion
- What’s holding you back?
- How were your Flow Days (Lead Times)?
- What did your Variability look like?
- What changes did you see in your system comparing the beginning to the end?
- Any Growth? Growth of what?
- How would you compare your Capacity to your Workoad?
- Comment on the Inventory in the System
Scenario #2 Instructions:
The Scheduler, with the help of the other members of the team, will use their intuition and the Routings to sequence the Order cards so that the bottleneck Work Center (‘B’) is not so plugged up with Inventory. The Scheduler will release one Order card each day just as in Scenario #1.
For each Shop Day, the Instructor will: Call out the Shop Day (ex. “Shop Day #7”)
Pause, then tell the students to write the number of the Shop Day (ex.
“Write #7”) on the next Order card in their queue waiting to be processed
(using the FIFO method).
Pause, then tell the students to pass the Order card to the next Work Center
on the Routing or to the Flow Control Monitor if the Order is finished (ex.
“Pass the Order card”)
At completion, record the data. (See ‘Data Plotting Instructions’)
At the completion of the second scenario, discuss the amount (insignificant or
lack of) improvement when using intuitive scheduling.
Scenario #3 Instructions:
An explanation of Drum-Buffer-Rope (DBR) is given before the third scenario is
run. Depending on the depth of the knowledge the students have of DBR, they may
be able to analyze the results of the previous exercises and make a
determination of the correct buffer size. If not, the Instructor will have to
give an explanation and guidance. The buffer size should be no less than 4 and
no greater than 6. See the ‘Observations/Results’ for Scenario #3.
The Instructor will ensure that the Scheduler arranges the Order cards in the
same release sequence that was used in the previous Scenario. Explain to the
students that the reason is to provide a direct comparison of results between
the two scheduling methods. The Scheduler will release orders into the shop
based on how much work is in the buffer. The amount of work in the buffer is
defined as the number of Work Center ‘B’ operations which have not been
completed for all Order cards on the shop floor. At the beginning of each Shop
Day, when the Instructor says “Buffer Count”, the Scheduler will count all the
number of ‘B’ operations which have not yet been completed no matter where they
are located (include un-completed B work on cards at the other Work Centers
also). If the number of ‘B’ operations yet to be completed is less than the
buffer size, the Scheduler will plan to release one Order card. If the number of
‘B’ operations is equal to or greater than the buffer size, the buffer is
considered full and no Order card is released.
For each Shop Day, the Instructor will:
Call out “Buffer Count” and the students will raise one finger for each ‘B’
operation which has not been completed on the Orders in their queue – use a
closed fist if they have none. The Scheduler will count the fingers and make
a determination of whether or not to release an order for the day.
Pause
Call out the Shop Day (ex. “Shop Day #7”)
Pause, then tell the students to write the number of the Shop Day (ex.
“Write #7”) on the next Order card in their queue waiting to be processed
(using the FIFO method).
Pause, then tell the students to pass the Order card to the next Work Center
on the Routing or to the Flow Control Monitor if the Order is finished (ex.
“Pass the Order card”)
At completion, record the data. (See ‘Data Plotting Instructions’)
At the completion of the third scenario, compare the results to the first two
scenarios in the same terms used in Scenario #1.
Data Plotting Instructions:
There are two charts for plotting Order card data (see examples below).
I. ‘No. Of Flow Days vs. Orders (in Release Day sequence)’ (top chart)
This chart represents the number of Total Flow Days for each Order card.
A. Arrange the Order cards in sequence by Release Day. Each order will have its
own column.
B. Plot the ‘Total Flow Days’ by putting an ‘X’ in the appropriate column at the
‘Total Flow Days’ height.
C. ex. the ninth Order released had Total Flow Days = 15
II. ‘No. Of Orders vs. Flow Days (Distribution)’ (bottom chart)
This chart represents the number of Order cards that have the same number of
Total Flow Days.
A. For each Order card, put an ‘X’ in the column (starting at the bottom of
the chart and working up) representing the ‘Total Flow Days’ for each order.
B. ex. Six orders had Total Flow Days = 7
Traditional Scheduling Example
Summary
Observations / Results:
Scenario #1: Using the traditional scheduling techniques, the first orders are
processed in 4 days, but as more orders are released, the flow time increases
and becomes highly variable, making order promising a risky proposition and
causing a lot of padding to be added to the expected completion date to avoid
late delivery. This results in lead times for the Customer getting longer and
still missing delivery dates. In addition, WIP inventories continue to increase
in front of the bottleneck Work Center (‘B’).
Traditional Scheduling Example
Scenario #2: Again, the results are about the same as Scenario #1. There will
be no significant improvement and maybe even slightly worse results. (See
‘Data Plotting Instructions – Traditional Scheduling Example’)
Scenario #3: Using the Drum-Buffer-Rope (DBR) scheduling technique, the flow
days range from 4 to about 10 with the most common values (the tallest
columns) of 5 and 6, if the exercise is performed correctly. This results in
short lead times for the Customer and no missed delivery dates, and very
little inventory in the system at any one time. Note: If the buffer size is
set to 4, the Constraint will occasionally run out of work, Throughput is
decreased, and the flow days will be slightly higher. When the constraint runs
out of work, the buffer should be increased by one. If the buffer size is 6 or
higher, the inventory will be slightly higher and the flow days will increase.
If the queue for Work Center ‘B’ never gets below 2, then the buffer is too
big. A correctly sized buffer provides maximum Throughput with minimum Flow
Days and Inventory. If the buffer is too small, Throughput decreases. If the
buffer is too big, both Flow Time and Inventory increase.
DBR Scheduling Example
Conclusion:
DBR is an appropriate technique for scheduling a complex manufacturing
environment.
(Results documented by Chuck Gauthier, Alpha West, Portland, OR, Summer 1998)
Advance Simulations
Luck of the Draw
Shuffle the Cards for Scenario #3: Clever students can spend a lot of time
arranging the cards into a nice sequence. They may think that the performance of
the system is because of their cleverness. Of course, cleverness is not always
possible in real life. Buy shuffling the cards, you see that it is the DBR
control that give the predictable outcome not cleverness (although, cleverness
can give a slightly tighter flow day distribution when used with DBR).
Change Over Inserting DBR on the fly: Often students ask the question, “How can I implement
DBR in our Job Shop?” A fun simulation is to run Scenario #1 for 20 days which
builds up a healthy Queue in the system and THEN implement DBR from Scenario #3.
You have to hold back releasing work until the selected buffer size is reached.
After that, things are smooth again. It shows very nicely on the flow day
visuals.
Variability
Using Dice: After you gain proficiency in using the Job Shop game, you may want
to move forward to some more complex models. The basic game is deterministic.
That is, the only variability is the shuffle of the cards before the start of
the game. This is not realistic. To simulate variability, you can give each
Work Center a single die. Each day the Work Center rolls the die. If the roll
is 2,3,4,5 or 6, the Work Center is productive that day (acts normally). If the
roll is a 1, the Work Center is not productive (cannot do any work at all –
cannot write a number). You may want to play this game yourself before working
with the students. You will find that both Scenario #1 and Scenario #3 perform
almost the same as before only with a bit more variability in the outcomes. The
parallelism is surprising.
Kanban
Just In Time: Doing Kanban flow in a flow line is easy to watch. But, doing
Kanban in a Job Shop is hard and takes a lot of careful control. If you are
brave, you can try to do Kanban with the Job Shop Game as a comparison with DBR.
I suggest using a Kanban size of two cards (one in process and one waiting).
This way, the maximum theoretical work in process would be 8 cards. There are a
lot of different possible outcomes depending upon your control of the system.
In the Job Shop, cards often flow from two Work Centers to one Work Center.
This leads to a decision of who gets to move there and who doesn’t if the Kanban
for the receiving Work Center is full. With students, this often becomes
‘whoever is fastest’. As such, you can get a nice distribution with a few way
out outliers. The key to running Kanban is the release of work. the scheduler
calls out the day but only writes the release date if it is possible to release
work on that day. Since this is similar to the rope in DBR, you will get a
tight distribution of flow times. However, rather than having a safe feeling
buffer, the work in process varies drastically and often approaches zero in Work
Center B’s queue. If you play Kanban with dice, you will surely starve Work
Center B once or twice in 36 cards.
Dynamic Buffering
Advance Buffer Management: In general, buffer sizes are fixed. But, there are
some cases where it is justified to change the buffer size (adjust up and down).
One such incident is when the work load on the system shifts and causes a
non-constraint to become more heavily loaded than the chosen constraint. When
this happens, you have a choice to change the constraint of the company (not the
recommended option since it changes the whole measurement system and
subordination process) or to increase the buffer size to accommodate the
temporary change in product mix. This is a hard thing to teach and difficult
for students to understand, however, with the Job Shop Game, it is easy to demonstrate. Here is how. Create another Product #5 that flows to C->A->C->D.
Take the basic 36 cards and shuffle them to play Scenario #3 as usual. The
scheduler will insert the Product #5 card for the Product #2 card as follows:
After the tenth day (and until the 25th day), every time a Product #2 card comes
up, exchange it for the new Product #5. This will shift the system constraint
to Work Center C temporally. If you have too small a buffer for the real
constraint Work Center B, the buffer will not be enough to assure continued
production on the constraint. Allow the students to determine how to increase
the buffer size during the temporary shift in product mix such that Work Center
B does not run out of work. Encourage them to return the buffer size to its
original size after the day 25.
I hope you enjoy playing the Job Shop Game as much as I do. It is a robust
exercise that really opens the eyes to the necessity of the rope in DBR. The
cleaver instructor can use the Job Shop game (with variabilty) as an effective
introduction to problems with Multi Tasking in Projects and the Critical Chain
Project Management techniques.
Of course, I’m always looking for improvements. Please contribute your
suggestions.
Dr. Holt
Support Materials:
Blank Charts
Basic Jobs (1-4)
Advanced Jobs (5-8)
Copyright Washington State University 2002
You can download the PDF version of the above game here:
Theory of Constraints Job Shop Game – Job Shop Scheduling Game
