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James R. Holt, Ph.D., PE. Jholt@wsu.edu Jholt@wsu.edu Constraints Management Washington State University’s Engineering Management Program http://etm.wsu.edu/ http://etm.wsu.edu/ The Theory of Constraints: Physical Process Games The Assembly Game: When Things Must Come All Together!

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Another Issue in Operations that Surfaces: Assembly Both Manufacturing and Projects have Assembly; product Joins. There is a place were several things must all be available in order to proceed Typically, someone is late delays the product or project The normal solution is to have a MILESTONE with a significant penalty for being late. But…. The Milestone causes people to be overly cautious. They estimate longer for the Project tasks (to be sure and not be late) or start work much sooner than needed (before the details are clear). The result: The use of milestones creates a slower process that still often messes the milestones!

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The Assembly Game Let’s take six people and give each one two coins. Each person can flip one of his coins each day. To be prepared for the Assembly, each person needs to flip each coin until he has two heads. There are Six Days to get ready for the Assembly. HH HH HH HH HH HH Hum? What are the odds of getting a Head when flipping a fair coin? –50% on the first try! –75% within the first two tries. –87.5% within the first three tries. Hum? But I need to get two head in Six tries. How does that work? Let’s just try!

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The Assembly Game: How to play (First Round). Call out the Days, 1 through 6. Each of the six players flip one coin each day. When a coin results in a Head, shift to the next coin on the next day. When two head are flipped, that person has completed. At the end of Day 6, ask to see if all the players are ready for the Assembly. If all players are ready, record $100,000 profit If all players are not ready, the Assembly cannot take place. In this case, fire all the workers and close the plant! Discuss if this is a fair decision since most people were ready for the Assembly. Why close the plant for just a few poor performers? (From the Binomial Distribution table, the chance of having less than two heads in six rolls is only 11% but for all six to roll at least two is only 50%)

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5 The Assembly Game: How to play (Second Round). For this Round, give everyone an extra day;Seven Days. Count Days 1 through 7. Repeat the same game. Evaluate the assembly on Day 7 If all players are ready, record $50,000 profit (less valuable when late). If all players are not ready, the Assembly cannot take place. In this case, Again, fire all the workers and close the plant! (From the Binomial Distribution table, the chance of having less than two heads in seven rolls is only 6% but for all six to roll at least two is now up to 68%)

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6 The Assembly Game: How to play (Third Round). For this Round, give everyone 8 Days. Count Days 1 through 8. Repeat the same game. Evaluate the assembly on Day 8 If all players are ready, record $25,000 profit (less valuable when late). If all players are not ready, the Assembly cannot take place. In this case, Again, fire all the workers and close the plant! Play Round Three several times (trying to earn the $100,000 they could have if they had promised Six Day Delivery. Most likely, they will have trouble guaranteeing 8 days. (From the Binomial Distribution table, the chance of having less than two heads in eight rolls is only 3.5% but for all six to roll at least two is 80%)

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7 The Assembly Game: A CCPM Approach. CCPM off-sets all task feeding processes to the Critical Chain. To simulate this start five players on Day 1 and one player on Day 4 (This last player is the Critical Chain). This simulates giving a Three-Day Feeder Buffer to the five players. The Constraint also has Six days but starts on Day 4 and ends on Day 9. Assembly occurs on Day 9. (From the Binomial Distribution table, the chance of having less than two heads in nine rolls is only 2% but for all five to all roll at least two is about 90%. With the one person rolling for two heads in six days with an 82% chance of success, the combined system is only 75% probable of a success.) This solution works well for CCPM. About 75% of the time, the system will complete by Day 9. And, with a Project Buffer (protecting the late Constraint) the system is good enough. Still, if the system MUST Assemble, on Day 6, we need a better approach. Let’s try two more ways to improve the assembly.

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8 The Assembly Game: The Bench. For this Round, Start all six players on Day 1 with the Goal to end on Day 6; just like the first round. However, this time, you have a Reserve Bench of two players. The Bench is made up of experts, experts who can flip a coin and get a head 80% of the time. However, for this game, we will have just use two ordinary players to represent those experts sitting on the bench. Each has a single coin. On Days 1, 2 and 3, the six players flip coins normally. If any of the six players does not have two heads by then (half way through), the Bench steps in. On Days 4, 5 (and if necessary 6), one or two from the Bench flip coins along side those players with the least heads. If the Bench person or the regular player get a head, these heads count toward that regular players count.

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9 The Assembly Game: The Bench Results. As a result of having just a little help (the Bench is typically 20%, but for this example, it’s 33% extra capacity), the Bench allows the Assembly to occur on Day 6 better than 90% of the time. And, the Bench only has to roll about 30% of the time. That means that the Experts, can spend 70% of their time thinking about how to make the system work even better, how to improve the processes and to mentor the regular players just at the moment of their need. But if 90% is not good enough? There is another approach….

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10 The Assembly Game: The Full Bench Press. The Bench is a good idea. We used only two regular people as the Reserve Bench with pretty good success. But, if you need certainty of Assembly on Day 6 try the “Full Bench Press”. In the Full Bench Press, there are the two Reserve Bench experts who contribute as in the previous solution. To add to the Bench: When any regular player flips two heads (their regular work is done) prior to the Assembly, they join the Bench and can flip along with other people on the following days as if they too were Reserve Bench Experts. The Full Bench Press delivers Assembly on Day 6 with near Certainty. Keep Thinking! Dr Holt

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