Steve Beeler

You have a goal…I have a way to get you there.

Balanced and Dependent Systems

Variation and Waste

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Variation is at the root cause of almost all waste in manufacturing and business systems.  It is no coincidence then that variability reduction is the foundation for the Toyota Production System (Lean Thinking) and its success in continuously reducing waste.  Two games of chance with dice and cards illustrate the linkage between variation and waste.

The first game is a single piece flow system with five machines.  The output of each machine is represented by the total of two dice.

The average of two dice, of course, is 7.  However, our five-machine system only averages 4.3…a 38% loss!  Why?  Variation and waste.  In single piece flow, no machine can outproduce another.  Production is lost through waiting losses (blocks and starves) when the machines interact with each other.  Balanced and dependent systems are surprisingly common.  They never work as expected.  In isolation yes, in combination no is a key lesson from Theory of Constraints.

The second game is a system of three machines feeding an assembly area.  The output of each machine is represented by the draw from a deck of cards.  In order to assemble a product, all three cards must match.

Variation and Waste

Each machine is produces one card per time period.  Jokers represents a defective product and cannot be matched.  The decks are shuffled so the three output sequences are independent.

Variation and Waste

Quite a few cards collect (to the right of the decks) before there are matches for the assembly machine to assemble (to the left of the decks).  Work in process inventory (WIP) and lead time are horrendous.  Throughput suffers as the assembly area waits for matches.  In isolation, each machine is successfully producing cards.  In combination, the system is performing poorly.  Variation and waste again.  This time the variation is in sequence, but the waste is equally dramatic.

Variability reduction is a big part of my day job as a Professional Engineer.  Visit my Operations Engineering page for methods and case studies.  While variation is always present, robust systems can be designed  to minimize the linkage between variation and waste.

Balanced and Dependent Systems

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The ten machine puzzle in my Theory of Constraints blog post is a simple example of the balanced and dependent systems that are surprisingly frequent in the real world. Balanced because all elements have the same capacity. Dependent because events at one element affect the performance of other elements. Frequent because lean thinking drives people and organizations towards them.  None work very well.

balanced and dependent systems

How does this happen? Inventory, conveyance, motion, and over production are wastes that are relatively easily recognized and reduced. When these wastes are removed, waiting losses (blocks and starves) can replace them. In the extreme, system performance deteriorates as lean “improvements” are made. In isolation yes, in combination no is a primary lesson from Theory of Constraints.

There are three options to improving balanced and dependent systems. The first is to improve the reliability of all of its dependent elements. That is lean thinking, but perfection is a high hurdle. In the ten machine puzzle, each machine’s reliability must be improved from 98% to 99.8% to achieve the 98% system availability target.

Cumulative probability predicts that the perfection hurdle gets even higher for larger balanced and dependent systems. Take a process with 100 dependent steps, not unusual in manufacturing or business. If each element has a 98% reliability, the system will only be available 13% of the time. To achieve 98% system availability, the reliability requirement for each element is 99.98%. Ouch!

The second option is to oversize each of the process elements. In the ten machine puzzle, oversizing each machine from 50 to 60 units per hour does the trick. With 100 process steps, each machine would have to be oversized by almost a factor of three…now that is expensive waste!

The third (and by far the best) option is to decouple process elements with buffers and to unbalance capacities to create a distinct constraint. This option trades inventory and conveyance waste against overproduction and waiting. The trick is to find the optimum balance. Is the trick magic? No, not with discrete event simulation…the next blog’s topic.