Thursday, 13 May 2010

What’s the value of information?

Every weekday I take my car to either drive to the office or visit a customer. Sometimes I work at home first, especial on Tuesdays or Thursdays. On these weekdays the express ways around the village I live are jammed with traffic, but not always. Of course working at home is great and fits the current way of thinking on how to best mix work and social responsibilities. Working at home allows me take my kids to school, while the internet let’s me stay in touch with my colleagues. However, discussions in front off the whiteboard are still hard using web communications. Nothing beats sitting together in the same room to digest and solve the challenges of a customer. So on a Tuesday with a meeting scheduled at 8:30, what should I do? Take my chances and take my kids to school and hope that I’ll arrive in time at the office? Or should I leave early and drop my kids of at the neighbours? Of course this trade-off depends on what happens if I miss the meeting in the office and how many times I asked my neighbours to take my kids to school already. Can some analytics support me in this?

What helps is to structure this decision and pinpoint the uncertainties. The decision I need to make is whether to take the kids to school or leave home early. If I take the kids to school I enjoy the 40 minutes in the car in which we can talk on all kinds of things. When, in that case, there are traffic jams I will be late in the office. Let’s assume that there is 60% chance of a traffic jam causing me to be late by 60 minutes. I need to catch up that time which will cost me an additional 60 minutes. The other option is to leave home early. I won’t enjoy the 40 minutes in the car with the kids and in addition to that, I will have to take my and the neighbours’ kids to soccer practice next Saturday which will cost me 50 minutes in total. When there is a traffic jam I will make the meeting on time, because I left home early. We’ll have an effective meeting saving me 60 minutes that day. When there is no traffic jam however I’ll be much too early at the office and will have to wait for 30 minutes for the guard to open the doors, costing me 80 minutes in total. Based on the assumed 60% chance of a traffic jam the best option is to take the kids to school. The value of the decision is 4 minutes.

Since I do not travel to the office on all Tuesdays, the 60% chance of a traffic jam is just a guess. One way to be certain about it is to do some research on the internet and find out about the frequency of traffic jams on the express ways. Since time is scarce, how much time would I be willing to invest in that? In decision analysis this is called the Expected Value of Perfect Information (EVPI). It is easy to calculate. In this case there is a 60% change of a traffic jam causing me to leave home early. It will cost me 50 minutes next Saturday but 60 minutes of efficiency gain today, net 10 minutes. There is 40% change that I can take my kids to school and enjoy the 40 minutes in the car with them. So in case of perfect information the value of my decision is 60%*10 + 40%*40 or 22 minutes. The EVPI therefore is 22-4 or 18 minutes. So when I am able to find the correct chance of a traffic jam in less than 18 minutes I can improve the value of my decision.

But you know the internet, “you never know what you’re gonna get”. Let’s assume that the internet fails you 25% of the time in predicting a traffic jam. This works in two ways. It could indicate that there is a traffic jam but there isn’t any, or it indicates that there is no traffic jam but there is one. The expected value of the decision to leave home early or not now becomes 5.5 resulting in an expected value of imperfect information (EVIPI) to be equal to 1.5 (5.5-4) minutes. Note that using the internet only improves the value of your decision when it’s ability to estimate a traffic jam or not rises above 72%.

The EVPI en EVIPI measures are not only useful in everyday decisions; they can be used in any business decision. By computing the value (perfect or not) on each uncertainty in a business decision, a trade off can be made on the cost of gathering additional information and the impact it will have on the total value of the decision. It is a perfect guide to decide on how to best use our scarce resources like time and improve the overall value of the decision.

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