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 constraint

5. Return to Step 1

4. Crash the critical path

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 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.

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

|∆|

|w|

C1

p1

0w

Figure 0: Calculating the potential benefit by balance

Economic Balance

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

ii

n

1=i0 p E = TP)E( Maximize

1- ; b = C to subject iii

n

=1i

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

Figure 1: A Basic Diagram

p1

p2

p3

C1

C2

C3

Graphic presentation

Figure 2: Adding Flags to the Diagram

p1C1

p2C2

p3C3

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?