Break.com is an ad$-$supported video sharing website, which pays users to create quality content. Break$$s editorial staff selects a small number of videos to post to the homepage every day; such curation is Break$$s value proposition. The homepage is a popular destination for males, ages $18$ to $34.$ Break$$s business model is to show advertising to its users. Break puts banner ads at various positions on its homepage. An ad that is shown to a user is called an impression.

Break$$s ability to monetize depends on the total number of ad impressions it can show in a given period of time $($say$,$ a quarter$).$ The number of ad impressions is equal to the total number of user visits to the homepage multiplied by the number of ads shown to each user $($called the $$ad load$).$ To maximize revenue, Break must make its content attractive so that large numbers of users visit its website or increase the ad load. Increasing ad load can deteriorate user experience, so ad load can only be increased so much.

Professor Srikanth Jagabathula, Operations Management.

Homework Assignment Professor Jagabathula

Every quarter, Break forecasts how many impressions it expects to receive for the upcoming quarter. It uses this estimate to enter into what are called reservation contracts with advertisers. Reservation contracts can be quite complex, but at a minimum, they specify the price the advertiser is willing to pay and the number of impressions they want.

As an example, Break might enter into a reservation contract with AT&T$,$ which says that AT&T will pay $$10$ CPM $($cost$-$per$-$mille, i$.$e$.,$ cost per a thousand impressions$)$ if Break promises to show AT&T$$s ads to $1$M of Break$$s users. If Break is able to keep its promise, then AT&T pays Break $$10/(1000)$ x $1$M $=$ $$10$K $($we divided $10$ by $1000$ to obtain cost per impression$).$

If Break fails to keep its promise and shows the ad to only $0\mathrm{.}9$M users $($because Break overestimated how many users are going to visit its homepage next quarter$),$ then Break is charged an under$-$delivery penalty, which is $10\%$ of the under$-$delivery. With only $0\mathrm{.}9$M impressions delivered, AT&T should pay Break $$10/(1000)$ x $0\mathrm{.}9$M $=$ $$9$K$.$ However, Break under$-$delivered $0\mathrm{.}1$M impressions, worth $$10/(1000)$ x $0\mathrm{.}1$M $=$ $$1$K$,$ which results in a penalty of $10\%$ x $$1$K $=$ $$0\mathrm{.}1$K$.$ Therefore, AT&T pays Break only $$9$K $-$ $$0\mathrm{.}1$K $=$ $$8\mathrm{.}9$K$.$

Therefore, every quarter, Break faces the challenge of determining the number of impressions to promise its advertisers through reservation contracts. If it promises too many, then it faces an under$-$delivery penalty. If it promises too little, then it is foregoing a revenue opportunity.

Use the newsvendor framework to determine the optimal number of homepage impressions to promise its advertisers for the next quarter. Assume that advertisers are willing to pay $$10$ CPM under a reservation contract but will impose $10\%$ under$-$delivery penalty. If an impression is not already contracted for, then Break will have to sell it on the Ad Exchange. Break can expect to receive about $$3$ CPM on the exchange. Break forecasts that its next quarter user visits to be normally distributed with a mean of $110$M and a standard deviation of $9$M$.$