Husaria wingLevinson Productivity Systems, P.C.
William A. Levinson, P.E.  Principal
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The Theory of Constraints (TOC)
Important economic considerations

Synchronous Flow Manufacturing

Henry Ford ran a balanced production line at 100% capacity

Ballet, orchestras, and marching bands: you CAN achieve 100% utilization
(SFM) production control

Beyond the Theory of Constraints: NEW BOOK AVAILABLE


Interactive JavaScript simulation of the matchsticks-and-dice experiment from Goldratt and Cox, The Goal

Visual Basic simulation of the matchsticks-and-dice experiment


The Theory of Constraints and Synchronous Flow Manufacturing
Key principle: variation in processing and material transfer times should be taken every bit as seriously as variation in critical-to-quality characteristics.
The Theory of Constraints

A factory's capacity is limited by its constraint operation, or capacity-constraining resource (CCR). The production line described below cannot produce more than 24 pieces per hour. This should be obvious but there are indeed factories that try to run at 30 per hour to "maximize utilization" of the equipment. (Management may even complain that stations 2 and 4 are "consistently underutilized.") Meanwhile, of course, a huge pile of inventory will develop at station 3. Workstation 3 is the constraint, or capacity-constraining resource (CCR).


"OK, you've swallowed the pig; now what do  you do with it?" This is a common problem in push production systems.
  • A production line cannot work faster than the slowest workstation. If it tries, inventory will accumulate. Constrictor snakes such as the one shown at the right are designed to process meals in the indicated manner, and they often sleep for several months while they digest their meals. This is not how we want a factory to operate; pig-swallowing should be left to systems that are designed to handle it.
    • Standard, Charles, and Davis, Dale. 1999. Running Today's Factory: A Proven Strategy for Lean Manufacturing. Cincinnati, OH, Hanser Gardner Publications (1999, 111-112) uses the phrase "pig in a python" to describe large inventory bubbles that move through a factory. "If smaller orders are released more often, the factory resources are loaded much more easily. …This is analogous to the python swallowing dozens of little piglets instead of one large pig. …Surprisingly, many factories prefer to 'stretch the python' so it can swallow an even larger hog!" The reference mentions an explorer who saw an anaconda swallow an adult hog in a Peruvian rain forest. (Dale Davis studied anthropology and specialized in Maya culture.) However, Levinson (editor), Leading the Way to Competitive Excellence (1998, ASQ Quality Press) coined the phrase "pig-swallowing," and even included an actual photo of a recently-fed python from The Serpent's Den in Milford, PA.
  • Goldratt example: a line of soldiers or Boy Scouts cannot march faster than the slowest person (the constraint).
    • If they try, the line will extend in length as the faster people get ahead of the constraint. The distance between them represents inventory.
    • The only way to get more capacity (or go faster) is to elevate the constraint, or improve its performance.


    The Theory of Constraints introduces some very interesting (and important) economic considerations. All of these result from the fact that time lost at the constraint is lost forever: it can never be made up. The cost accounting system does not reflect the true effect of lost time at the constraint accurately. (Remember that accounting statements whose purpose is to satisfy the requirements of the Internal Revenue Service and the Securities and Exchange Commission are rarely suitable for making decisions in the factory!)
     

  • The true loss due to any scrap, rework, or stoppage in the constraint is the marginal profit on the lost unit of production.
    • Rework in the constraint can therefore be worse than pre-constraint scrap!
    • Post-constraint scrap is irreplaceable.
  • Theory of Constraints uses only three performance measurements:
    1. Throughput: finished goods that are shipped to customers. More is better.
      • The marginal profit (sale price minus raw materials) on each transaction is a good measurement.
    2. Inventory: Money that is invested in items the factory intends to sell. Less is better.
    3. Operating Expense: Money spent to convert inventory into throughput. Less is better.


    Note the total absence of considerations like "absorption of overhead," "labor per unit," "equipment time per unit," and other things that might interest the accounting department but which are largely irrelevent to the true economics of running the factory.

    The capacity-constraining resource may change with the product mixture. Linear programming is very useful for assessing these situations.

    • LP Simplex can identify the constraint(s) and quantify the slack capacity (excess capacity) in the non-constraints.
      • It can optimize the product mixture for maximum profit.
      • It can account for market constraints (lack of demand) and contractual obligations as well as capacity constraints.
    • Shadow prices show the marginal effect of increasing a constrained resource, i.e. elevating a constraint.
Synchronous Flow Manufacturing (SFM)
SFM is a pull manufacturing system (like kanban) but it offers some apparent advantages over kanban. In a kanban system, each downstream operation pulls work from the next one upstream. In SFM, the only information transfer is between the capacity-constraining resource (CCR) and production starts. The CCR pulls work into the factory in the form of production starts. It is always desirable to keep a buffer of work in the line upstream of the CCR because a shortage at the CCR means an irrecoverable loss of production time.
  • The constraint operation limits the overall rate of production. This operation "beats the drum" to control the factory's speed.
    • This is achievable by tying the constraint to production releases by a rope.
    • No need for any other production controls, such as kanban!
    • An inventory buffer at (or heading toward) the constraint protects it from upstream stoppages.
  • This gives us Drum-Buffer-Rope (DBR) production control
Achieving Near-100% Utilization of a Balanced Factory
    The matchsticks-and-dice experiment from Goldratt and Cox, The Goal, shows why it is seemingly impossible to achieve 100% utilization in a balanced factory. As a matter of fact, when you try the simulation (below), you'll end up with substantial work-in-process (WIP). Average production will be substantially below 3.5 units per turn even though this is the factory's theoretical capacity.

    Henry Ford said he wanted every employee to have "all the time he needed but not a second more" to perform his or her task. Given the simulation from The Goal and the fact that cycle time in queue is proportional to u/(1-u) where u is utilization, this sounds like a formula for a deranged nightmare in which inventory buries the entire factory.

    The equation (Standard, Charles, and Davis, Dale. 1999. Running Today's Factory: A Proven Strategy for Lean Manufacturing. Cincinnati: Hanser Gardner Publications) allows reconstruction of the technique that Ford used to do the seemingly impossible. The cycle time in queue is also proportional to the variation coefficients for arrivals at the workstation (a function of material transportation in the factory) and effective processing time.

  • Variation in arrival rate at the workstation
    • Batch-and-queue operations aggravate this problem substantially by necessitating the transportation of batches of products. Ford achieved single-unit flow (recognized as highly desirable today).
    • Ford Highland Park plant: Work slides allowed immediate transfer of finished parts to the next workstation.
    • Ford also used work cells (or their equivalent), with all the machines necessary to make a part close together and in sequence of operation.
  • Variation in processing time
    • Automation helped remove human-induced variation from each operation. Consider the following example:
      • Worker using screwdriver ==> considerable variation in assembly times, noting that there is variation in the time it takes the worker to turn his or her wrist. (Also very inefficient, and an invitation to repetitive-motion injury).
      • Worker using powered screwdriver ==> Now most of the variation comes from setup (in the form of placing the screwdriver in the screw's slot) because the screw is driven at a constant rate.
      • Automated multiple-spindle screwdriver (actually used by Ford) ==> Essentially no variation in assembly time.
    • Unitary machines performed many operations between loading the part and unloading it, thus eliminating the variation associated with load/unload.
    • Subdivision of tasks suppressed human-induced variation as well. Example from Rudyard Kipling's Captains Courageous: cleaning cod on a commercial fishing boat
      • Inefficient: One worker does the entire task: pick up knife, slit the fish open, cut off the fish's head, put the knife down, pull out and discard the insides except for the liver, which goes in a separate container, pick the knife up and cut out the fish's backbone. There will obviously be substantial variation in processing time (although there is no downstream operation that suffers as a result, as the cleaned fish goes straight into a tub of salt water). Also, note the waste motions: "pick up knife" and "put down knife."
      • Efficient: Three men working together: the first man, who never puts his knife down, slits the fish and makes cuts at its neck. The second man pulls off and discards the head, removes the entrails, and puts the liver in the cod liver container. The third man cuts the fish's backbone out and tosses the fish into a tub of salt water. Furthermore, tool maintenance is done offline (externalization of setup, per SMED). A fourth person, often a boy or apprentice fisherman, sharpened the knives and exchanged them for the cleaners' dull ones.
Ballet, Orchestras, and Marching Bands show that 100% Utilization is Achievable
    Henry Ford (who repaired watches as a boy) designed his factory to run like a clock. The operations had to keep time with each other almost perfectly to prevent inventory buildup at slower workstations and shortages at faster ones. This brings to mind the concept of a pendulum or metronome, the swing of a conductor's baton, and the beat of a drum.

    Goldratt and Cox's Theory of Constraints suggests that some operations will always have excess capacity, and that the capacity-constraining resource should set the pace for the entire operation. This is absolutely true but three familiar performing arts: ballet, orchestras and bands, and marching bands show that you can successfully run an activity in which no "operation" has any excess capacity. In these performing arts, people (with their built-in variation) constitute the "equipment" or "workstations."

    • Ballet: individual dancers or separate groups will often perform different sets of motions, all of which must coordinate perfectly. In many cases, no one stands around doing nothing (i.e. no one has "excess capacity") while waiting for others to catch up. The music from the orchestra, of course, sets the timing for all the dance movements: a concept very similar to the "drum" in drum-buffer-rope and also takt time.
    • Orchestra or band: This is a little easier than ballet because, although musicians play different instruments, they are using the same set of notes. Again, however, the swing of the conductor's baton or a memorized beat keeps everyone together.
    • Marching bands: Think of a football halftime performance in which a marching band plays music while turning itself into different shapes on the football field. This is much harder than marching in step (which soldiers have done for thousands of years) because everyone is going in the same direction. Elements of the marching band must go off in different directions and then rendezvous at prescribed intervals. The music again sets the pace but the length of the steps and the directions must be carefully prescribed.
    Now go back to factory equipment which, if properly designed, has far less inherent timing variation than even a skilled ballet dancer or member of a marching band. The fact that performing arts can achieve 100 percent utilization of all the performers (who are performing different activities, as opposed to soldiers who are simply marching in a single formation) suggests that a factory also is capable of achieving 100 percent utilization of all of its equipment.

Beyond the Theory of Constraints
The matchsticks-and-dice exercise from The Goal is an excellent way to show the effects of variation in processing and material transfer times. One should not, however, assume from this exercise that the variation is unavoidable and nothing can be done about it. As shown above, it is possible to suppress both forms of variation. The key message, though, is that variation in processing and material transfer times should be taken just as seriously as variation in critical-to-quality characteristics.
Beyond the Theory of Constraints: How to Eliminate Variation and Maximize Capacity (2007, Productivity Press/ Francis-Taylor)
Order from Amazon.com or CRCPress Online

The matchsticks and dice exercise in Goldratt's and Cox's The Goal illustrates the effect of variation--not in product characteristics, but in processing and material transfer times--on a balanced factory that is operating at 100 percent capacity. The Goal asks, "Why do you think it is that nobody after all this time and effort has ever succeeded in running a balanced plant?" More than half a century before The Goal was written, Henry Ford claimed to have run a balanced factory at close to 100 percent capacity: "The idea is that a man must not be hurried in his work— he must have every second necessary but not a single unnecessary second." We conclude from the Kingman Equation (for cycle time in queue as a function of utilization and variation) and detailed examination of Henry Ford's methods that Ford achieved the seemingly impossible by suppressing variation in processing and material transfer times. Beyond the Theory of Constraints explores the methods that Ford, as well as modern lean practitioners, have used to achieve this.

Preface (c) 2007 Producivity Press
Eliyahu Goldratt's and Jeff's Cox's The Goal (1992, 86) asks, "Why do you think it is that nobody after all this time and effort has ever succeeded in running a balanced plant?" Henry Ford (1922, 82) claims to have done so: "The idea is that a man must not be hurried in his work— he must have every second necessary but not a single unnecessary second." Ford's apparent success in doing what The Goal shows to be impossible prompted this book's development.

When manufacturing engineers think of variation, critical-to-quality product characteristics are the first things that come to mind. The concept of variation in product characteristics is in fact central to the quality sciences. This is not, however, the variation that prevents operation of a balanced factory at close to 100 percent capacity. Variation in processing times and material transfer times either wastes capacity or requires large inventories as insurance against its effects. It is therefore necessary to state the following proposition at the outset:
(1)   Variation in product characteristics causes rework and scrap.
o     This is the familiar random or common-cause variation whose effects are shown by measurement histograms. The process standard deviation is the basis of the control limits for statistical process control charts.

(2)   Variation in processing and material transfer times is the root cause of longer cycle times, higher inventories, and inability to run a balanced factory at close to 100 percent capacity.
The matchsticks-and-dice simulation in The Goal illustrates the latter variation's effects. The simulation also shows Ford's proposition to be an obvious formula for a deranged nightmare in which inventory overruns the factory while cycle time in queue becomes infinite. As utilization approaches one hundred percent, cycle time in queue (and hence inventory) will indeed approach infinity— unless variation in processing times and material transfer times approaches zero. Ford's production system was designed explicitly to suppress this kind of variation, and his success demands close investigation of the methods he used. Furthermore, Toyota's heijunka (level scheduling, production smoothing) concept reflects both the need and the ability to suppress the "random" variation suggested by The Goal's matchsticks-and-dice factory simulation.

JIT is also helpless unless downstream production steps practice level scheduling (heijunka in Toyota-speak) to smooth out the perturbations in day-to-day order flow unrelated to actual customer demand. Otherwise, bottlenecks will quickly emerge upstream and buffers ("safety stocks") will be introduced everywhere to prevent them (Womack and Jones, 1996, 58).

It is the author's conclusion that The Goal's matchsticks-and-dice exercise is an excellent device for teaching the effects of variation on throughput and inventory. It may also, however, teach the unintended lesson that the factory is at the mercy of this variation. A die roll suggests unavoidable random variation (also known as common cause variation) but the workstation is nonetheless capable of processing six units. This book's purpose is to teach the reader how to identify and remove the variation, and thereby roll a six every time.

The book is organized as follows:
(1)   Chapter 1 is an overview of the Theory of Constraints, and it also covers the engineering and managerial economic aspects of TOC.
(2)    Chapter 2 covers pull production control methods such as kanban and synchronous flow manufacturing's drum-buffer-rope (DBR) system.
(3)    Chapter 3 illustrates the effect of variation in processing and material transfer times, and shows why this variation prevents achievement of 100 percent utilization.
(4)       Chapter 4 describes methods for reducing variation in processing and material transfer times. Some of the material overlaps with the theme of Chapter 5 because techniques that suppress variation often improve productivity, and vice versa.
(5)        Chapter 5 discusses methods for increasing productivity and reducing cycle time. These are useful for elevating the constraint (increasing its capacity) and they may also reduce variation.


The Theory of Constraints and Synchronous Flow Manufacturing
186 PowerPoint slides (including Notes pages for handouts) $95.00  (Add sales tax for PA delivery)
Download package description as a Word document.
Available on CD-ROM or direct download. Designed as one-day workshop presentations. See licensing terms here
  1. The Theory of Constraints
  2. Performance Measurements (throughput, inventory, and operating costs). Deficiencies of traditional cost models. Concept of marginal costs, revenues, and profits
  3. Production Control: synchronous flow manufacturing (SFM). SFM supports lean manufacturing by reducing cycle times and keeping inventory levels low.
  4. Elevating the Constraint: lean manufacturing techniques for constraint elevation. Introduction to the use of linear programming (simplex method) to identify constraints and slack capacity, and to optimize product mixtures for maximum profit.
  5. Variation Reduction (a unique element of this course).  Henry Ford succeeded in running a balanced factory at close to 100 percent.
  6. Conclusion: TOC and Your Factory


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