Sunday, 31 January 2010

Risky Business


No, this is not yet another review of Tom Cruise’s breakthrough movie. It is about how decision makers in governments and business make their decisions, especially when the dynamics of the challenge they are facing is misunderstood. Understanding the dynamics of a system requires mastery of concepts like stocks, flows, delays, nonlinearities, feedback loops and uncertainty. Lack of understanding these concepts causes decision makers to make the wrong decisions. With the use of simple and easy to grasp models an analytical consultant can help government and business to make better decisions supporting them to get better understanding of real world challenges.

The concept of stocks and flows is often misunderstood, leading to hard to resolve problems in controlling the performance of supply chains. An example of such lack of control is the bullwhip effect which describes the magnification of fluctuating demand in a supply chain. A very simple example already shows how complex and counterintuitive flows and stocks can get. Let’s take a simple inventory model, in this case a bathtub with water. In the example the bathtub is first filled with water at a varying rate starting from 100 litres/minute reduced to 0 and than up again (see illustration). Next, the bathtub is emptied using the same flow rate profile. Question is how much water will be in the bathtub overtime? Can you draw the picture? What will be the maximum water in the tub? Sent me your answers, I am curious on what you can come up with. Many people draw a picture mimicking the saw tooth profile of the flow rates and use it to estimate the size of the bathtub to contain all the water. As a result they will underestimate it. In practice this would mean that for example the required stock space will be estimated to small or the wrong counter measures are taken to reduce for example carbon emissions to meet certain maximum levels.

The importance of understanding the dynamics of a decision even becomes more important when uncertainty is introduced. To return to our example, assume the rate at which water enters the bathtub now is uncertain and the above figure depict the average rate at which water enters or leaves the bathtub. For simplicity assume that the actual rate is 10 litres/minute higher or lower than average with a 50% change. Now try to estimate what the water level at the end of the time period. What is the chance that it will be less than 100 litres? What will be the change of the bath to overrun if the maximum capacity of the bath is 510 litres and the starting level 100 litres?

In business and government many times average rates are used to cover this kind of challenges. Using that same approach, the average total amount of water flowing into the bath will be 400 litres. With a starting level of a 100 litres the bath will never overrun, so the probability of overruns is 0. Using the same kind of reasoning the water level at the end of the experiment will on average be 100 litres. I have encountered this kind of reasoning a lot and it is wrong, very wrong. The correct answer requires some more work that just adding up averages, but it happens all the time. Together with misunderstanding the dynamics of the system this leads to very poor decisions.


The answer is to apply a mathematical model; in this case a simple model can show you what will happen to the water level in the bath tub. Using a small Monte Carlo model helps you include the uncertainty on the actual rate at which the water enters or leaves the bath tub. The MC model creates insight into the influence of the uncertainty on the flow rates and also warns you about the spread of the water level. The model will tell you that the chance of overrun is arround 25% and that the change of less than 100 litres is arround 50%. Did you guess that upfront? A mathematical model or more general an analytical approach therefore gives you the opportunity to make better decision like buying a bigger bath or a tap that you can control better, otherwise even managing the water level in your bath becomes risky business.
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