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Does Goldratt Understand the Theory of Constraints

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Title: Does Goldratt Understand the Theory of Constraints


1
Does Goldratt Understand the Theory of
Constraints?
  • Evaporating the Do not balancecloud

2
Agenda
  • Originality
  • Correctness
  • The correct balance approach
  • A graphic presentation of economic balance
  • Conclusion

3
MBC PERT/CPM
  • 1. Identify the binding constraints
  • 2. Decide how to exploit it (focus on it)
  • 3. Subjugate everything else to that decision
  • 1. Identify the critical path
  • 2. Focus on the critical path
  • 3. Start all non-critical activities early to
    ensure critical path wont be compromised

4
MBC and PERT/CPM
  • 4. Elevate the binding constraint
  • 5. Return to Step 1
  • 4. Crash the critical path
  • 5. Recalculate the critical path (return to step
    1)

5
MBC and PERT/CPM
  • For projects, step 3 is too conservative and not
    recommended, but thats how it was taught and it
    does subjugate
  • For pre-Goldratt sources of a better approach,
    see author. In effect, this talk argues that this
    better approach applies to MBC as well

6
Interim Conclusion
  • When Goldratt discovered that MBC (or however
    he calls it) applies to projects, it was chutzpah
    of a magnitude that even he had not reached
    before
  • When he changed the name critical path to
    critical chain nobody in their right mind
    should have accepted it
  • The chutzpah might be more palatable if we could
    trust the theory. Can we?

7
MBC and Balance
  • Consider Step 4 in MBC Elevate the binding
    constraint
  • Clearly if we repeat it again and again, without
    waste, new bottlenecks arise and the system cant
    help but become more balanced
  • More balanced means that the bottleneck shifts
    over time, randomly its fine

8
MBC and Balance
  • Since it is derived from PERT/CPM, MBC, as
    presented above, is a commendable management
    approach
  • The balance we talk about is similar to whats
    observed in projects during crashing it becomes
    more and more likely that the nominal critical
    path will not prove to be the true critical path
    in the realization

9
MBC and Balance
  • But Goldratt is on record stating that balance
    should be avoided
  • In the book Critical Chain he even proves this
    mathematically
  • The proof is based on his own hallowed principle
    an hour lost on the bottleneck is an hour lost
    to the system

10
MBC and Balance
  • He proceeds to show that it is impossible to
    protect the throughput of the bottleneck without
    excess capacity on all other resources
  • Will this maximize throughput? Goldratt is
    believed to be the throughput guru, so lets
    study the correct balance for throughput
    maximization

11
Economic Balance
  • The correct balance of a system is defined as the
    set of capacities that maximizes the expected
    throughput after taking into account the cost of
    said capacity
  • Assume a system with n resources such that the
    potential capacity of each is an independent
    random variable, Xi

12
Economic Balance
  • The throughput of the system is defined by the
    minimum of these r.v.s
  • Assume that by doubling Ri we also double Xi
  • Let the cost of doubling Ri be Ci
  • In practice we can calculate it as 100 times the
    cost of increasing Ri by 1.
  • WLOG normalize such that SiCi1.

13
Economic Balance
  • Assuming continuous capacities, only one resource
    can be critical at the same time. Ri is critical
    with probability pi and Sipi1.
  • define difference random variables of the form
    XX1-X2. More generally, X1 may be the minimum in
    a subset of resources and X2 is then the minimum
    of the complement of this subset.

14
Economic Balance
  • We call a difference distribution well-behaved if
    it does not change its shape when Ri is changed
    infinitesimally. I.e., a small change in Ri
    involves a small parallel shift along the CDF of
    the difference distribution. E.g., the difference
    between two normal random variables is
    well-behaved.

15
Economic Balance
  • Numerical experience suggests that typical
    systems are approximately well-behaved
  • Otherwise we may require slight modification,
    involving increasing or decreasing Ci by a small
    percentage. (Ci should be decreased if increasing
    Ri reduces the variance of the systems
    throughput.)

16
Economic Balance
  • Theorem 1 In a well-behaved system, optimal
    economic balance is achieved when pi/Ci1, ?i.
  • The proof is by a newsboy argument for any two
    subsets
  • Define the service level of resource i, SLi, as
    the complement of the criticality, 1-pi, then
    SLi, the optimal SLi, is given by 1-Ci

17
Graphic presentation

18
Economic Balance
  • The same result, essentially, can be derived by a
    linear programming model

where ?i?Ri/Ri.
19
Economic Balance
  • The marginal gain associated with a small
    investment in balance for a resource is
    E0Ci-pi/min(pi,Ci, where E0 is the current
    value of the system in SCj units (a profitable
    system implies E0gt1, but well assume E01).

20
Graphic presentation

21
Graphic presentation

22
Goldratts balance
  • Let the main bottleneck resource, R1, have
    C10.66 (Figure 3). A starvation probability of
    0 on it implies p1100. Impossible! So assume a
    1 probability of starving the bottleneck (the
    criticality is 99). This allows all other
    resources combined to be critical 1 of the time.

23
Therefore

24
Calculating the waste
  • In this example, 97 cents out of the last dollar
    invested in the supporting resources was wasted.
    The red flag is 3300 tall (about 15 screen
    sizes). Of course, if the criticality of the BN
    would indeed reach 100 the waste of the last
    dollar would be 100 cents, with an infinitely
    tall flag!

25
Evaporating the cloud
  • Unlike balloon-bursting, which may be done with a
    pin or a cigarette, proper cloud evaporation
    involves exposing erroneous assumptions
  • Where then is the wrong assumption?

26
Evaporating the cloud
  • The culprit here is the rule that an hour lost
    on the BN is an hour lost to the system. It is
    simply wrong if we measure the system by
    throughput

27
Conclusion
  • The answer to the title question is that he
    doesnt (or at least there is no official
    evidence that he does)
  • By the way, anybody here in the market for a used
    car?

28
Thank you very much
  • Any questions?
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