Financial Analytics and the Implications of the Theory of Constraints (TOC)
Value Area: Financial Analytics/Data Science
Theory of Constraints
The Israeli physicist, turned management guru, Elyahu Goldratt (1947-2011) took common industrial production practices to the woodshed in his epic book "The Goal: A Process of Ongoing Improvement" (Elyahi M. Goldratt, Jeff Cox, (1984). North River Press). Goldratt’s view of production systems reminds us all of the underlying consequence associated with statistical fluctuations of dependent events. This reality is virtually a law governing all production systems and many other business processes.
The lead character of the novel, Alex Rogo, learns how the “black box” of his factory is affected by the principle of statistical fluctuations of dependent events. As material flows through his factory, the variations of each of the productions’ processes has a large influence on his factory’s ability to consistently produce completed units at something like a steady flow. After all, the throughput of the factory is the true metric of performance, the goal. In engineering fields, this may be called the “merit function”, in Data Science modeling this is referred to as the “objective function”. This is the figure of merit we seek to optimize.
Alex soon learns that in order to improve the throughput of his factory, his full attention should be focused on those processes which are the bottlenecks (or constraints) of the production flow. He learns surprising things, such as all and any equipment capable of converting units through a bottleneck process, no matter how inefficient, should be utilized. He learns, as do we, that a factory with balanced capacities between dependent events is actually a poorly run factory. Fluctuations will exist, and we need to avoid the effect of fluctuations by expanding the capacity through the bottleneck to exceed demand. The reality of the Theory of Constraints (TOC) push us to balance the flow through the series of dependent events as opposed to balancing capacities.
Thought Experiment (Gedanken Experiment)
To make the concept of TOC clear, let’s do a simple experiment (as did Alex). This is an example of statistical fluctuations of dependent events. We start out with 100 toothpicks from which person number 1 can draw and 9 consecutive people, each having a single die. For this experiment, the dice are specially prepared to only have values of 4,5 and 6. Everyone lines up in a row from left to right.
The first person on the left rolls the die, and moves that number of toothpicks into a small inventory pile to the right of them. This pile become the inventory person 2 can draw from.
The second person does the same, but they can only move a maximum number of toothpicks on the first persons pile matching the corresponding amount on their die throw. If they happen to throw a 6, but only 4 toothpicks are available, they only get to move 4 into their pile.
The first round proceeds through all 10 people.
We repeat the experiment for 10 rounds. It’s easy to write a short program in Python to do this random experiment.
What would be your estimate of the total number of toothpicks in person number 10’s inventory pile at the end of 10 rounds? A reasonable estimate might 49. (The average die roll should 5….maybe the first round we might come up short. We therefore estimate 9 rounds at 5 each, plus 4 for the short first round. Estimate: 49.)
After doing the experiment, we find that the total throughput was only a total of 43. Perhaps that round was just bad luck. After the second time we wind up with a total of only 41. We realize that range of 4,5,6 (statistical fluctuations) is killing us. Now, let’s say we alter the experiment to use values of only 4 or 5. What’s your best guess? To our surprise, the average value is 41 after repeating the whole experiment 10 times.
Keep in mind, the fluctuations created here were completely random (unlike many fluctuations in processes we can influence).
Take away message: Fluctuations significantly reduce the expected throughput of the system.
The solutions presented in Goldratt’s novel were focused on identifying constraints and expanding the capacity of that constraint. One of the 5 TOC paradigms is “an hour lost at a bottleneck is an hour lost for the enitre system”. Know your constraints and manage them carefully.
Extending the Theory of Constraints to Financial Analytics
There are different objective functions to manage in a business context. Which of these are governed by the same TOC principles? How does the presence of fluctuations affect performance data and what can one do to optimize these metrics?
The canonical objective function of any business is the time series of monthly EBITDA. As a first level analysis, let’s consider the functional form of EBITDA time series data. What are the basic characteristics of time evolution of a company’s EBITDA?
The following set of graphs shows the improvements which can be gained from the long term application of TOC. In this case, particular attention was taken to understand the fluctuations at the root of the time series fluctuations.
The above graph is real data from a nominal small company. What are some of the characteristics of the functional form of this example? We see some of the following patterns:
There appears to be a seasonal influence on EBITDA
The baseline year had 3 months of negative EBITDA, the first year only 1 month, the second and third years’ data was only positive.
The average line through each successive year’s data is increasing.
Because EBITDA is composed of revenue patterns and expense patterns, one is inclined to think that sales improved year on year and is responsible for the improved EBITDA. We now take revenue out of the equation and just look at the expense side of the business for the same time periods.
The principles of TOC were applied to the expense side of this business. We see there were substantial gains to be made by understanding the source of the fluctuations, and actively taking action to reduce the fluctuations.
These are some of the characteristic patterns we see in these aggregate expenses:
The baseline year has the most peak to valley transitions (7 transitions)
The cycle for year 1 also had 7 transitions, but the swings were not as large
The overall expenses for cycle year 1 dropped as compared to the baseline year
The cycle for year 2 had fewer transitions (6) and the overall expense continued to drop
The cycle for year 3 had fewer transitions yet (3), albeit the overall cost might have gone up over year 2. (Remember the revenue generated for that year has an effect on expenses too.)
What was the summary effect on expenses year on year applying the method of TOC?
The following diagram summarizes the results
It should come as no surprise that cost reductions were enjoyed, but it will come as a surprise that overall costs could be reduced by an amazing 15%. There will be times of structural change in a business which result in higher costs, but the reason for the added costs IS NOT random fluctuations. It is something planned.
Discussion of Results
One remarkable result of this data is that the managing of fluctuations reduced overall costs. One might well imagine that shifting around expenses should result in the same overall average. In fact, the effects of this kind of management approach work differently.
Principle 1
As experienced in “The Goal”, it was seen that fluctuations in early processes tend to become amplified in later processes. Early management has long term benefits.
Principle 2
Fluctuations in business performance usually have a cause. Quite often the cause is simply not recognized. Once the attention of the staff is brought to the fluctuations, there can be any number of remedies to reduce them.
Principle 3
Fluctuations are usually the symptom of inefficiencies. Identifying and managing fluctuations generally has the effect of making processes more repeatable AND more efficient AT THE SAME TIME.
Conclusion
The lessons of the Theory of Constraints are usually applied to production environments. In that context, an emphasis on expanding bottlenecks over the effects of fluctuations may bring the biggest rewards.
In the context of financial analytics, the second corollary of TOC plays an equally important role in optimizing the objective function of the business, namely EBITDA.
This second corollary of TOC appears to be little understood by TOC practitioners and largely overlooked in most organizations. Here lies the proverbial low-hanging fruits.