| A company wants its advertisements to reach at least 1.5 million people through different media. | |||||
| There is a maximum number of ad impressions considered effective in each medium. How should | |||||
| the company advertise to minimize total cost while satisfying the limits on reach and frequency? | |||||
| Media Requirements | |||||
| TV | Radio | Newspaper | |||
| Audience Size | 50,000 | 25,000 | 20,000 | 15,000 | |
| Cost / Impression | $500 | $200 | $250 | $125 | |
| Max Impressions | 20 | 15 | 10 | 15 | |
| Investments | |||||
| TV | Radio | Newspaper | Total | ||
| Amount | $0 | $0 | $0 | $0 | $0 |
| Impressions | 0 | 0 | 0 | 0 | |
| Audience | 0 | 0 | 0 | 0 | 0 |
| Problem | |||||
| A company wants its advertisements to reach at least 1.5 million people. It is considering advertising | |||||
| through TV, radio, direct mail, and newspapers. Each medium has a certain cost per run of an ad, | |||||
| a certain audience that will see the ad, and a maximum number of ad impressions before response | |||||
| to the ad falls off too much. How should the company advertise in order to reach its target audience | |||||
| at the lowest possible cost? | |||||
| Solution | |||||
| 1) The variables are the amounts of money to spend on each medium. In worksheet Media these | |||||
| are given the name Investments. | |||||
| 2) The constraints are very simple. | |||||
| Investments >= 0 via the Assume Non-Negative option | |||||
| Impressions <= Max_Impressions for each medium | |||||
| Total_Audience >= 1500000 | |||||
| 3) The objective is to minimize total cost. In worksheet Media this is defined as Total_investment. | |||||
| Remarks | |||||
| Often, there are discounts for placing ads with greater frequency in different media. This could be | |||||
| expressed in a model with a 'piecewise-linear' constraint, using binary integer variables. | |||||
