Optimization is a word that gets thrown around a lot in the marketing industry. Conversations with agencies regarding their optimization strategies rarely touch on the methodology and instead chalk these decisions up to the “secret sauce” of the firm. This is to the detriment of both the agencies (those with a defined methodology are missing an opportunity to show off their quality work) and clients (who are missing an opportunity to vet a firm’s practices as effective). One effective way to present media optimizations is through linear programming.

Linear programming is a process for taking two sets of components: an objective function and a set of constraints and solving for an optimal solution reference. In practical terms, the set of constraints will be all the requirements of a campaign. This can be anything from a certain spend in a specific channel to a limit on total impression volume. The objective function is the key performance indicators (KPIs) we are trying to optimize. In our example, our KPI is sales, but could be any success metric used for the media campaign. The important key, and challenge, to remember when conducting linear programming is translating constraints into mathematical inequalities and to ensure that the term being optimized is consistent across the objective function and constraints. In English, this means that if our question is still “if my campaign has a limited budget, what is the best mix of channel spends to use?” then all constraints and the objective function must be written with channel spends as the x (unknown value) in the equation. An approach based on linear programming optimization is great for a few reasons:

1. Linear programming is a simple to implement

   • The mathematical requirements are low and all statistical software, which is widely available and sometimes open source, include linear programming functionality.

   • Linear programming is also easy to explain to clients; all the constraints and justifications for why optimizations were made in a certain way are all based in the equations, and thus available for scrutiny.

2. Linear programming is flexible due to the objective function/ constraint nature of a linear programming.

   • The constraints of KPIs used can easily change based on needs or new scenarios.

3. Linear programming is reproducible.

   • A defined methodology means consistency across clients, channels, etc. This approach also allows for detailed historical look backs. For example, if I want to explain why certain optimizations were made in Q2 of 2014 for client X I simply review the linear programming code used at that time.

A perfect example of how to implement a linear programming optimization system is presented here. This goes through all the steps of creating an objective function, defining the constraints, and an example of how to code the final solution. The benefits described in this article can be achieved through a similar implementation. With an optimization strategy based on linear programming like the one described, agencies and clients can change the conversation from “we optimize” to “here is how, and why, we optimize”.