Transcript Does Goldratt Understand the “Theory” of Constraints?

Does Goldratt Understand the
“Theory” of Constraints?
Evaporating the “Do not
balance”cloud
Agenda
•
•
•
•
•
Originality
Correctness
The correct balance approach
A graphic presentation of economic balance
Conclusion
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
won’t be compromised
MBC and PERT/CPM
4. Elevate the binding 4. Crash the critical
constraint
path
5. Return to Step 1
5. Recalculate the
critical path (return
to step 1)
MBC and PERT/CPM
• For projects, step 3 is too conservative
and not recommended, but that’s 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
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?
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 can’t help but become more
balanced
• “More balanced” means that the bottleneck
shifts over time, randomly [& it’s fine]
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
what’s 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
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”
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
let’s study the correct balance for
throughput maximization
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
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 ΣiCi=1.
Economic Balance
• Assuming continuous capacities, only one
resource can be critical at the same time. Ri
is critical with probability pi and Σipi=1.
• define difference random variables of the
form X=X1-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.
Economic Balance
• We call a difference distribution wellbehaved 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 wellbehaved.
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 system’s throughput.)
Economic Balance
• Theorem 1: In a well-behaved system,
optimal economic balance is achieved when
pi/Ci=1, 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
Graphic presentation
|∆|
p1
C1
|w|
w
0
Figure 0: Calculating the potential benefit by balance
Economic Balance
• The same result, essentially, can be derived
by a linear programming model
n
MaximizeE( T P)= E0  pi i
i =1
n
subject to  C i i = b ; i  - 1
i=1
where Δi=ΔRi/Ri.
Economic Balance
• The marginal gain associated with a small
investment in balance for a resource is
E0|Ci-pi|/min(pi,Ci}, where E0 is the current
value of the system in ΣCj units (a profitable
system implies E0>1, but we’ll assume
E0=1).
Graphic presentation
p1
C1
p2
C2
p3
C3
Figure 1: A Basic Diagram
Graphic presentation
p1
C1
p2
Figure 2: Adding Flags to the Diagram
C2
p3
C3
Goldratt’s “balance”
• Let the main bottleneck resource, R1, have
C1=0.66 (Figure 3). A starvation probability
of 0% on it implies p1=100%. 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.
Therefore…
Figure 3: An Example of Gross Imbalance
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!
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?
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
Conclusion
• The answer to the title question is that he
doesn’t (or at least there is no official
evidence that he does)
• By the way, anybody here in the market for
a used car?
Thank you very much
Any questions?