As the head of an advertising agency, you're faced with either shutting down the offline department or the digital department. What do you do?

I will be fully honest even it will be maybe a bit painfull. If there is really such a question on the table then head of advertising agency should consider to close at all... or to change job him/her self.

I strongly agree that first step is analyze of market and overall situation. If this analyse was done - then there is no space for such questions. If there was not - then hurray to do that...

However results will be my proposal and view in any situation would be to keep both departmets but make their optimization - put effort to more profitable part and keep other one as supporting and complementing. 

On the first sight it can be maybe very temptating to be digital only - as it is trendy, fresh and progressive. But always keep in mind that we all live in physical not virtual reality and there will be always interesting part of customers (users, buyers however you call it) that are not online geeks and prefer more less traditional forms of communitacion and promotion... 

As a head of an advertising agency-it should be no brainer- you should have enough knowledge to review the market analysis data that you spend money collecting; compare that with the past/ present and projected/predicted performances of both departments; then the data will show you which way to take.

Don’t make your feelings toward the team members of either department influence your decision; you are paid well in this position to be heartless; and your focus on the correct path should be based on which direction is more profitable to your company.

As the head of the advertising agency, the decision would need to be calculated based on the following factors:

1) What led me to this point?(In a realistic scenario, well managed agencies can run both effectively)

2) If there are cost associated (TCO) issues driven by a larger interest (group or other shareholders), which division would stand in best interest over the long term?

3) What are the market conditions and consequences that shutting down either division? (client accounts, loss of marketshare etc)

Once I have reasonable evidence and cause from the above 3 points, I would be in a better position to decide. It is all relative to the conditions and environment in which the head of the agency is working under.

If in a primitive market like say Congo, where digital adoption is low and online retail may not be growing or lack of government support for digital,  shutting down the offline division may be wrong. In a market like say Germany, where practically everything is getting centralized and technology is moving fast, keeping a cost center like an offline division would be foolish.

So to answer your question, there is no right or wrong decision. It is completely dependent on market conditions and shareholder interest.