I Maximizing Targeted Reach in Advertising Campaigns: A Statistical Approach

[Singto]

Hey everyone!
I need some help for a work related problem. I am working on a advertising campaign, and I need to optimize my distribution of flyers to reach a specific target of people. Flyers will be distributed randomly in mailboxes by the postal service.
I have a list of neighborhood, along with the total number of mailboxes in the neighborhood, and the targeted population in the neighborood (in this case possessors of vehicles immatriculated before 1997). As I have a limited number of flyers, I need to know the probability that I reach this targeted population in each area.
So for exemple, I have:
-neighborhood 1: 100,000 mailboxes; 5,000 possessors of pre-1997 vehicules
-neighborhood 2: 50,000 mailboxes; 3,000 possessors of pre-1997 vehicules
-neighborhood 3: 4,000 maiboxes; 500 possessors of pre-1997 vehicules

I have 20,000 flyers to distribute at random over these 3 different neighborhood. How do I decide how many fliers to dedicate to each area so as to maximize the number of old-car owners that will receive a flyer in there mailbox?

I know it should be possible to calculate this using a Poisson or normal law maybe? My mathematics got quite rusty since I left high school so I need some advice on that one.

Thanks immensely for your help!

 

[jedishrfu]

Can't you find out who these owners are via public records and then target your campaign to them directly?

Have you looked at the percentages of an owner getting your flyer?

n1 : 5/100 = 5%
n2: 3/50 = 6%
n3: 5/40 = 12.5%

 

[Dale]

Hi Singto, welcome to PF!

Interesting problem. My first instinct would be that you have such a large number of flyers that you won't be able to model this as sampling with replacement, but will need to model it as sampling without replacement.

That means that you will need to use the hypergeometric distribution.

 

[mfb]

How do I decide how many fliers to dedicate to each area so as to maximize the number of old-car owners that will receive a flyer in there mailbox?

If your model is as simple as you describe it: Put a flyer in every mailbox in region 3, put the remaining flyers in mailboxes in region 2. That maximizes your expectation value, median, and every other quantity you might be interested in, simply because you have the largest fraction in region 3 and then the next best fraction in region 2.
I assume "randomly" does not mean that every flyer goes into a random mailbox, i. e. the post service is able to keep track of which mailboxes got a flyer already and which did not.

Different mailbox owners might talk to each other if the flyer is good, if you include coverage beyond the direct mailbox-car relation saving more flyers for region 2 could be interesting - but I don't expect that effect to be large enough to be relevant.