Optimal television schedules in alternative competitive environments

We formulate network-television-scheduling problems as integer programs for three different competitive environments – myopic, Nash competitive, and cooperative. To provide input data for the scheduling models, we develop and estimate a regression model in which show-part ratings are regressed on variables that influence television viewership, including day, time slot, show attribute, and competitive effects, as well as lead-in from the previous show part. We apply out models by solving for optimal myopic (noncompetitive) and Nash competitive week-long prime-time schedules for the three major networks for two specific weeks. We find that there are substantial gains to optimization and that those gains are not diminished much by competition. We illustrate the cooperative problem for six time slots and show how the solution differs from the Nash solution. We discuss the use of simple programming heuristics such as counterprogramming.