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🦉 10x curiosity - The Dice Game - Make more production!


🦉 10x curiosity

January 29 · Issue #193 · View online

🦉 A weekly sample of links that made me think 🤔

Also published in 10x Curiosity
Understanding how variability impacts production in an industrial plant is critical to understanding where improvement can be made. This is a cornerstone of the TOC and lean manufacturing process philosophy’s. 
Simulations help to explore and develop this understanding without real world implications, making them a great way to learn. The Dice Game provides a hands on simulation for people to explore.
Those familiar with production environments will know how frequently dependent process are managed in silo’s with different teams accountable for delivering their own piece of the production pie —outputs, WIP, and costs. What the dice game helps to highlight is how optimising individual parts of the system can actually create sub optimal outputs for the entire system. This can be compounded when the focus shifts from production output, to cost management which is often achieved through a focus on reducing buffer size (WIP) and cutting compressible costs — normally headcount and maintenance dollars. Without accompanying systems or capital changes to the productionn environment, both of these focus items can actually result in higher variability and lower throughput from the entire system.
Taken from the book “Manufacturing at Warp Speed” The purpose of the Dice Game is threefold: 
  • To demonstrate the impact of variability on a complex system 
  • To understand the compounding effect of variability on a system composed of dependent events 
  • To appreciate the value of constraint management, particularly the first three of the five focusing steps, in successfully managing variability in an environment of dependent events

John McConnell presents a great summary of the dice game in Part 7 — More Tonnes! -The Dice Experiment (p127–132 Analysis and Control of variation — John McConnell)
A most common problem that faces many is finding a way to convince others that a process approach should replace the department by department approach …
The experiment is set up as follows:
  1. A “supplier”, seven “willing workers” and a “customer” are recruited from the audience.
  2. The “supplier”, “willing workers” and “customer” are formed into a “process”, where raw materials or information is fed into the process by the supplier and where each worker passes the job to the next worker once his/her actions on the job are complete.
  3. The supplier has a supply of “widgits”, that represent incoming materials, goods or paperwork.
  4. The customer uses an overhead projector or whiteboard to record the volume of product that reaches him each day. He is interested only in volume. Quality and cost are not important to him in this exercise.
A scenario is set whereby customer research has determined that the customer’s requirement is 35 “widgits” per fortnight (10 days), or an average of 3.5 “widgits” per day. There will always be some degree of variation about the average and so on some days more than average volume will be expected and on other days lower than average output would be anticipated. A playing die is then produced. It is a stable system (although it does not produce a normal distribution) with an average of 3.5. This die will be used to stimulate the output for each step in the process. ..The objective is to provide 35 “widgits” to the customer after 10 days of operation (at an average of 3.5 “widgits” per day). The exercise commences.
The die is thrown for the first step (the supplier). Whatever number appears on the die is the number of “widgits” passed on to willing worker no. 1. The die is then thrown for worker no. 1 and passes on to no. 2 the number of “widgits” that correspond with the number shown on the die, and so on to the customer who records the number of “widgets” that actually reached them on that day.
Sometimes, a worker will throw a number that is lower than the number of “widgits” he holds. After they pass the required number of “widgits” to the next worker, the “widgits” they still holds represents work-in-progress. When a worker throws a number greater than the number of “widgits” in their possession, the situation represents those cases where more work could have been done, but where insufficient feed was available from previous steps.
At the end of ten days work the volume that reached the customer will be much less than 35 “widgits”. Often it is less than 20. Also, work-in progress or inventory is high, resulting in high carrying costs.
This is the basic form of the game, and from this base, variations can be added to try to improve performance.
For the next round why don’t we look at increasing system capacity, but do nothing for the variability. In this scenario when ever a 5 or 6 is rolled, double the production rate — ie produce 10 and 12 widgets. This increases the average capacity of each station to 5.3 so we should expect 53 widgets. Run the 10 rounds and see if the systems achieves this overall capability?
What about if you introduce a bottleneck — on all the work stations bar one, double whatever dice value is rolled. One station remains just with the single dice score — clearly the bottleneck. What happens to overall throughput and WIP in this scenario?
What about reducing system variability (and peak capacity)? In this round whenever a 1,2 or 3 is rolled count it as a 3; and whenever a 4,5 or 6 is rolled it counts as a 4. The overall theoretical average remains at 3.5 (as with the first round) but note how much the through put increases over the 10 rounds and the WIP reduces — despite a reduction in individual work station capability.
Washington State University provides further more advanced variations of the game.
Advanced Game Variations (from WSU)
Variation on the Traditional (Push) game:
Pre-load the line with WIP. Try placing three tokens between each worker before the game starts. Play the game but have individual raise their hand if they roll a number higher than the WIP available. Stop the game when someone raises their hand (probably by day 6). Replay starting with 6 tokens between each worker. Play again. You might make it 20 days. Notice the increased finished goods inventory is really only due to the reduction in WIP as the system approaches steady state. Even starting with 6 tokens between each worker, by day 20, the system appears very close to the same as the system at the end of the first 10 days without any pre-loaded WIP.
Theory of Constraints Approach-DBR (Pull control up front with push everywhere else:
With the TOC approach, you need to create a constraint. In reality, we do this by speeding up everyone but the constraint. To keep things in perspective and make these dice games comparable, we create the constraint by reducing capacity of one of the workers. (as above by doubling the value on all but a single worker). Give the constrained die to a middle worker, say Worker 3). To create the buffer, pre-load the line with 10 tokens right before the constraint worker. This large pile of 10 looks huge, but it is much less than the 24 or 30 used in previous pre-loads.
Begin by Worker 1 rolling the die on day one. No matter what Worker 1 rolls on day 1, no tokens will be moved. Worker 1 only moves in tokens if the amount of WIP between the raw materials and the constraint (WIP between Worker 1 and Worker 2 and WIP between Worker 2 and Worker 3) is less than the buffer amount of 10. So, on day 1, while Worker 1 and Worker 2 will both roll, they will not move any tokens. Worker 3 (the constrained worker) will roll on day 1 and move tokens. Those workers down stream will work as usual. On day 2, Worker 1 will try to replenish the buffer. This means to return the level to 10. On day 2, Worker 1 will move a maximum of what Worker 3 rolled on day 1. If Worker 1 rolls a smaller number, the buffer will be slightly depleted. But, Worker 1 has excess capacity and should be able to catch up. Worker 2 does its best to move available tokens to the constrained Worker 3. Play continues for ten days.
With DBR, the system should out produce all the other systems. EVEN WITH THE CONSTRAINED DIE! The average will be around 30 for the ten days with a range of 27 to 33. If the class is skeptical, play the game over or extend it. You will notice the inventory is very predictable and the production level is calm. It doesn’t matter how long you play, the average production stays at 3 per day.
Discuss what DBR did to improve the system? Was it reduced variability? No. Was it increased inventory? No. Was it increased capacity? No. Then what was it? It was reduced dependency. Having a constraint de-coupled the interdependency of the balanced line. The buffer protected the available capacity. The rope restricted inventory growth.
Assembly Line Models
Rather than a linear assembly line — more complicated dependencies can be set up, for instance where 4 components are required to be assembled in a 5th step into a single final good (FG) or an even more complicated example below where initial production is assembled in an intermediate step before final assembly into 3 finished goods.
Summary of lessons learnt from the dice game.
Across a number of references below a common summary of lessons can be learnt. (Particularly [1] and [9])
On the impact of variability and local optimsation:
  • The system optimum is not the sum of the local optima (efficiencies).
  • Variation and dependency affect all systems. Trying to balance a production process with the same capacity everywhere will reduce capacity of the overall system
  • Measuring and managing complex systems by local efficiencies can hurt the system’s overall effectiveness.
  • The output ratio/buffer size curve is sharply concave. The more variability, the higher the throughput loss.
  • Using the system bottleneck to control the entire systems flow of inventory produces the highest output with the lowest WIP. This need not cost a lot of money.
On the use of Buffers
  • The buffer capacity should be proportional to the squared coefficient of variation of the processing rate.
  • Little work-in-process helps a lot but diminishing returns arise. The rate of diminishing return depends on the level of variability but limiting the buffer space may result in a dramatic output shortfall.
  • Work stations with large variability need to be protected by extra buffer capacity to be. As a result of the propagation of variability buffers need to be allocate to protect the other work stations as well.
By playing the dice game, the Lean Simulations site highlights that you will have a good understanding of Interdependency.
It doesn’t matter if one worker is very efficient, because the previous process may be starving him of parts. The dice game shows how each process is linked and dependent on the processes before and after it. The improvement focus should be on the entire value stream, not just working with each individual process.
  1. MIT Variability simulation. PDF Slides; Excel Simulation; Simulation instructions; Mailroom game
  2. Lean Simulations — A Whole Slew of Dice Games
  3. Manufacturing at Warp Speed — Appendix A: The dice game
  4. Washington State University- Dice Games
  5. Analysis and Control of variation — John McConnell
  6. Dice game simulation and published reference
  7. Robert Boute — THE PRODUCTION DICE GAME -Handling Variability in a Production Environment
  8. Antoine Lagier — Theory of Constraints — Dice Game Simulator (simulator in google sheets
  9. Marc Lambrecht, Stefan Creemers, Robert Boute and Roel Leus — Extending the Production Dice Game
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