# Tag Archives: decision tree

## Should You Hire Security When Tenting Your House?

Last week I had my house tented because of termites. For those of you who don’t know what “tenting” is (I didn’t until about a year ago), it amounts to wrapping an entire house inside a huge tent and filling the tent with a poisonous gas that kills everything inside (and by everything I really do mean everything). Those who have been through this experience know what a hassle it is. We received a to-do list of pre-tenting tasks, which included:

• Remove or discard all food that isn’t canned or packaged in tightly-sealed, never-opened containers
• Turn off all A/C units and open one window in each room of the house
• Open all closet and cabinet doors
• Turn off all internal and external lights (including those operating on a timer)
• Prune/move all outdoor plants away from the house to have a clearance of at least 18 inches
• Soak the soil around the house (up to a foot away from the structure) on the day of the tenting
• Warn your neighbors about the tenting (so that they can keep their pets away from the house)
• etc.

We had to sleep two nights in a hotel, with two dogs, one of which had just had knee surgery. What an adventure!

The main point of concern was that the house would stay vulnerable (open windows) and unattended during the process. On top of that, one of our neighbors told us that he knew of a house that had been robbed during tenting a couple of months ago. So we started to consider hiring a security guard to sit outside the house for 48 hours. Would that be a good idea? Let’s think about this.

Our insurance’s deductible is $2500. I assume that if thieves are willing to risk their lives (wearing gas masks; oh yeah! they do that!) to enter a tented house, they’d steal more than$2500 worth of stuff. Therefore, being robbed would cost us $2500. This doesn’t take into account that one might have irreplaceable items in the house. However, most of the time those can be taken with you (unless they are too big or inconvenient to carry). In my case, I took the external hard drive to which I back up my data, and the mechanical pencil I’ve owned and used since 1991 (yes, you guessed right, the eraser at the end doesn’t exist any more). The security company we called would charge$15 per hour for an unarmed guard to be outside our house. Multiplying that by 48 hours brings the cost of hiring security to $720. Let’s say that the likelihood (a.k.a. probability) of being robbed while your house is tented without a security guard is $p_1$ (in percentage terms; for example, $p_1$ for the White House is pretty close to 0%), and when a security guard is on duty that likelihood is $p_2$. Unless $p_1 > p_2$, there’s no point in having this entire discussion, so I’ll assume that is true. Here’s a pretty neat rule of thumb that you can use: divide the cost of hiring security by your deductible to get a number $n$ between zero and one (of course, if hiring a guard costs more than your deductible, don’t do it!). Unless the presence of the guard reduces your chance of being robbed ($p_1$) by more than $n$, you should not hire security! (Later on, I’ll explain where this rule comes from.) For example, in my case 720/2500 is approximately equal to 29%. If the chance of being robbed without security is 30%, unless hiring a guard brings that chance down to 1% or less, it’s better not to do it. If the value of $p_1$ is less than or equal to 29% to begin with (I live in a reasonably safe neighborhood), the answer is also not to hire security (probabilities cannot be negative). This rule works regardless of the value of $p_1$; what matters is how great the improvement to $p_1$ is. In addition to looking at the numbers, we also took into account the following clause from the security company’s contract: …the Agency makes no warranty or guarantee, including any implied warranty of merchantability or fitness, that the service supplied will avert or prevent occurrences or the losses there from which the service is designed to detect or avert. In other words, if you hire us (the security company) and still get robbed, we have nothing to lose! So what did we do? We chose not to hire security and, fortunately, our house was not robbed. However, even though the tenting instructions say that you don’t have to wash your glasses and plates after returning home, we decided to do so anyway (as they say in Brazil: “seguro morreu de velho”). Disclaimer: The advice contained herein does not guarantee that your house will not be robbed. Use it at your own risk! Details of the Analysis So where does that rule of thumb come from? We can look at this problem from the point of view of a decision tree, as pictured below. In node 0, we make one of two decisions: hire a security guard (payoff = -$720, i.e. a cost), or not (payoff = -$0). For each of those decisions (branches), we create event nodes (1 and 2) to take into account the possibility of being robbed. At the top branch of the tree (node 2), the house will be robbed with probability $p_2$, in which case we incur an additional cost of$2500, and the house will be safe with probability $(1-p_2)$, in which case we incur no additional expense. Therefore, the expected monetary value of hiring security, which we call $EMV_2$, is to spend $720+$2500 with probability $p_2$, and to spend $720 with probability $(1-p_2)$. Hence $EMV_2 = - 3220p_2 - 720(1-p_2) = - 2500p_2 - 720$ Through a similar analysis of the bottom branch (node 1), we conclude that the expected monetary value of not hiring security, which we call $EMV_1$, is to spend$2500 with probability $p_1$ and to spend \$0 with probability $(1-p_1)$. Therefore

$EMV_1 = -2500p_1 - 0(1-p_1) = - 2500p_1$

Hiring security will be the best choice when it has greater expected monetary value than not hiring security, that is when $EMV_2 > EMV_1$, which yields

$-2500p_2 - 720 > -2500p_1$

$\Downarrow$

$2500(p_1 - p_2) > 720$

$\Downarrow$

$p_1 - p_2 > \frac{720}{2500}$

which is the result we talked about earlier (recall that $p_1 > p_2$).

How Does Analytics Fit In?

The Analytics process is composed of three main phases: descriptive (what does the data tell you about what has happened?), predictive (what does the data tell you about what’s likely to happen?), and prescriptive (what should you do given what you learned from the data?). In this problem we can identify a descriptive phase in which we try to obtain probabilities $p_1$ and $p_2$. This could be accomplished by looking at police or insurance company records of robberies in your area. It’s not always possible to get a hold of those records, of course, so one might need to get a little creative in estimating those numbers. Having knowledge of the probabilities, the calculation described above could be classified as a prescriptive phase: what’s the course of action? Hire security if (cost of security)/(insurance deductible) < $p_1 - p_2$. There is no predictive phase here because our analysis does not require the knowledge of any future event (only how likely it is to occur). Operations Research can be used in some or all of these phases. Most of what I do in my research and consulting projects lies in the prescriptive phase (optimization). Recently, however, I’ve decided to broaden my horizons and learn more about the other two phases as well, starting with some self-teaching of data mining.