A Systems Thinking View of Business Analytics, Part III: Making Cause and Effect Measurable

Read - A Systems Thinking View of Analytics, Part I: Introduction to Systems Thinking

Read - A Systems Thinking View of Business Analytics, Part II: Recurring Patterns in Systems

The first article of this series introduces systems thinking as a tool that helps you to understand cause-and-effect relationships. Cause-and-effect is the key to finding root causes and really understanding why things happen. The second article describes recurring patterns in systems known as system archetypes. The combination of causal modeling and system archetypes provides insight into the what and the why of system behaviors—a good beginning, but complete analysis should also look at how much. 

Asking how much actually raises two interesting questions:

  • How much influence does one variable exert on another?
  • How much outcome or result is produced?

Quantifying Influence

Measuring influence is useful when you want to find the strongest levers to effect change—stronger influences providing greater leverage. Quantifying influences is a simple matter of correlation. When a causal model shows one variable influencing another, calculate the correlation coefficient of the two variables. For example, figure 1 shows that hiring influences workforce capacity; when hiring increases workforce capacity increases and when hiring decreases capacity decreases. It also shows that workload influences capacity: increase workload, decrease capacity; decrease workload, increase capacity.

Figure 1. Variables and Influence

Measuring correlation of hiring with workforce capacity quantifies the amount of capacity gain or loss that is achieved when hiring is increased or decreased. Assume that your goal is to increase workforce capacity. You can increase hiring or decrease workload to achieve that goal. Knowing which option has greater influence is one factor in deciding what to do. This type of influence measurement is relatively quick and easy, and it is useful to identify leverage points for management. It is important, however, to recognize correlation coefficient as a point-in-time measurement of influence that does not account for changes over time and the plateau effect of frequent or continuous use.

Stocks and Flows

Causal loop modeling is useful to understand influences among the things in a system, but it does not distinguish between the transient things and things that accumulate. Yet things that accumulate are often the most important to examine when analyzing a system. They are the means by which results are measured. Understanding the dynamics of things that accumulate in a system is central to modeling and simulating system behaviors. Stock and flow models are designed to meet this need.

The things that accumulate in a system are called stocks. A Stock is an accumulation of something in a system – either concrete and tangible things (i.e., dollars or widgets) or abstract and intangible things (i.e., knowledge or morale). Tangible stocks are accumulations of consumable resources. Intangible stocks are accumulations of catalytic resources.

A stock changes through the influences of flows. A Flow is an action that influences a stock by increasing or decreasing the quantity of the stock. Flows are of two kinds:  in-flow that increases the accumulated quantity and out-flow that decreases the quantity.

The relationships of stocks and flows are graphically represented using stock and flow diagrams. Figure 2 shows a simple stock-and-flow diagram for the accumulation of workforce capacity.

 Figure 2. A Basic Stock and Flow Diagram

The diagram notation is as follows:

  • The stock is illustrated as a rectangle – in this example workforce capacity.
  • The arrows indicate two flows: hiring and workload assignment. In-flow and out-flow are designated by the directions of the arrows.
  • The “valves” on the arrows illustrate how each flow is quantified – hiring becomes hiring rate and workload assignment becomes workload assignment rate. 
  • The “clouds” at each end of the diagram mark the boundaries of the problem space. They indicate that the flow hiring rate arrives from someplace beyond the scope of the diagram and that the flow workload assignment rate travels to a place beyond the scope of the diagram.

Throughout this article I’ll continue to build upon the simple example shown in workforce capacity model. It is important to mention, however, that stock-and-flow models are not always as simple as one stock with two flows. Stock and flow models often involve compound sequences as shown in the materials to shipment example shown in figure 3.

 Figure 3. A Compound Stock and Flow Sequence

Measuring Stocks and Flows

Measurement is a key concept of stock and flow modeling. Stocks are always measured as units – dollars, items, etc. In this example the measurement unit for workforce capacity is employee full time equivalents (FTEs). Flows are measured as rate of flow which is expressed as units per time period.  Flow measures for this example might be FTEs hired per week for hiring rate and FTEs assigned per week for workload assignment rate. Consistency of measurement within a stock-and-flow sequence is important. Measuring workforce capacity as FTEs and quantifying flows as headcounts would make little sense. It would be similarly nonsensical to measure the inflow on a weekly basis and the outflow as a monthly amount.

External influences often affect the rate of flow. In stock-and-flow modeling these influences are known as converters. (The term “converter” may seem odd for this concept right now. Bear with me. It is standard stock-and-flow terminology and it will make sense before we’re through.) Connectors link converters to flows as shown in figure 4.

  • Labor budget is a converter that affects the hiring rate.
  • Outstanding orders is a converter that affects workload assignment rate.

Figure 4. Converters in Stock and Flow Models

From Causal Loop to Stock and Flow

Causal loop diagrams will likely be the initial method to analyze system dynamics, with stock and flow modeling used where quantification is needed. A stock-and-flow diagram typically examines a portion of a causal loop model to distinguish stocks from flows and to determine how each is measured. Figure 5 uses a causal loop model from part 1 of this series to illustrate how causal loop extends to become stock-and-flow diagrams.

 Figure 5. From CLD to Stock and Flow

A systematic process of working from a CLD to create stock and flow diagrams uses a sequence of steps described below:

  • Identify critical behaviors of the system – those that are problematic, under study of analysis, or central to the goals and strategies of the organization.
  • Identify the stocks that participate in critical behaviors of the system – those things that are accumulated in the system upon which critical behaviors are dependent.
  • Name each stock with a term that is quantitative but not comparative. The example in figure 5 adds “(FTE count)” to the name “workforce capacity” to make it quantitative. But it does not say “more workforce capacity” which is comparative language.
  • Examine every link to each stock to determine if it becomes a flow. If the influence is one that changes the accumulated quantity of the stock, then it is a flow.
  • Add each flow to the diagram expressing the influence as units-over-time or rate of flow. The example translates “hiring” CLD to “hiring rate” and “workload” to “workload assignment rate.”
  • Examine each flow in context of the system-wide CLD to identify links that are converters – influences that regulate or otherwise affect the rate of flow. Labor budget and outstanding orders are converters in the example.
  • Mark the boundaries – start and end – of the model.
  • The act of creating stock and flow models from causal loop diagrams also serves to test the causal models and make them more complete. It is common, for example, to discover influences previously not modeled when analyzing rate of flow and identifying converters that affect the rate.

Multiple Stocks and Flows 

It is possible – even probable – to derive many stock-and-flow sequences from a single causal loop model. When this occurs, valuable insight can be derived by identifying the interconnections among stock-and-flow sequences. Interconnections occur when a flow in one sequence acts as a converter in another sequence. Figure 6 illustrates an example of interconnected stock-and-flow sequences.

 Figure 6. Multiple Interconnected Stocks and Flows

Labor budget is a stock with the in-flow labor cost allocation rate. The cost allocation rate is a converter that affects hiring rate which is an in-flow to workforce capacity. Similarly, outstanding orders is a stock with the in-flow of order received rate. In both instances the converter link is a flow-to-flow connection. The stock is never used as a converter. The result of this analysis is greater insight that adds understanding and detail to the CLD.

Here we begin to make sense of the term “converter.” The units of measure vary among the three stock-and-flow sequences. Labor budget is measured in dollars. Workforce capacity is measured in FTEs. Outstanding orders is measured as days to complete. A conversion formula is needed to describe the influence of labor cost allocation dollars upon hiring rate FTEs— in other words: How do dollars convert to FTEs? Similarly, we need to know how days to complete is converted to FTEs for the influence of outstanding orders upon workforce capacity.

The Analytics Connection

So, what does all of this have to do with analytics? The obvious connection is stock and flow models as the basis for computer-based simulation. But I believe the connection is much deeper than simulation. The power of analytics is the opportunities for simulation, insight, and understanding to drive innovation. Stock and flow models provide a tool for insight through analysis of system behaviors. Analysis to distinguish stocks from flows, units from rates, and causes from effects, and to understand the dynamics among them increases understanding. Innovation often occurs by combining or connecting existing things in different ways. Stock and flow modeling is a means to study a system in new and different ways and to experiment and look into the future with simulation.

Figure 7. Insight and Understanding through Stock and Flow Modeling

The example shown in figure 7 is identical to that of figure 6 with only one exception. The model in figure 6 does not link order received rate to labor cost allocation rate – the converter that is shown as a dotted line.

This example illustrates:

  • Insight to see that labor cost budgeting is not currently influenced by the rate at which new orders are received,
  • Understanding to recognize that this situation isolates labor budgets from the realities of workload dynamics, which is a fundamental cause of the gap between workload and workforce capacity,
  • Reasoning to conclude that the gap will improve if order received rate becomes an influence to determine labor cost allocations,
  • Planning is required to define a course of action through which labor cost allocations are influenced by orders received,
  • Innovation opportunity to establish a new process through which order received rate influences labor cost allocations, which in turn influences the hiring rate and narrows the gap between workload and workforce capacity.

Final Thoughts 

This series of three articles provides an introduction to systems thinking. There is much more to be learned than what I have written here. I have presented the core concepts that I believe have a real affinity with analytics.

Systems thinking is a mature discipline with roots dating back to 1961 (Industrial Dynamics, Forrester, MIT Press, 1961). It is widely known and practiced in many areas where an understanding of cause and effect really matters—areas such as manufacturing, process control, industrial systems, and organizational dynamics. Analytics has the same critical need to understand cause-and-effect relationships. It doesn’t make sense for us to reinvent the wheel. The analytics community should learn and adopt the practices of systems thinking. The time has come for systems thinking to become a central discipline of business analysis.

Dave Wells

Dave Wells is an advisory consultant, educator, and industry analyst dedicated to building meaningful connections throughout the path from data to business value. He works at the intersection of information...

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