Scheduling of Network Television Programs

Maximizing average audience size is a major objective of national television networks. This paper examines the effect of scheduling programs on audience ratings. We determine the predictability of ratings and the major factors which influence ratings. We measure the extent to which ratings can be changed by rescheduling programs, and then test commonly discussed scheduling strategies and propose new strategies. Finally, we ascertain the extent to which the audience's benefit is served by a system of three major networks, each competing to maximize individual ratings. A forecasting model based on five years of historical data estimates ratings for hypothetical schedules. A heuristic fitting procedure yields a model which has consistent estimated parameters and explains about 70% of the variance. The previous year's ratings of a program and competing programs in its time slot are the best predictors of its rating. Also important are the day, time, and lead-in audience. The resulting estimates are incorporated in a combinatorial model, representing the decision of a program scheduler seeking to maximize ratings. A typical sized problem of scheduling 23 programs of various lengths into a week of 40 half-hour time slots can be formulated as a 65 \times 800 assignment-type integer program. The optimizations show that rescheduling programs can, on the average, substantially increase a network's audience size (11.6%) and advertising revenue ($61 million per year). The optimal program scheduling for one network generally decreases the ratings of competing networks. The forecasting and optimization models are then used to evaluate commonly discussed scheduling strategies: Protecting Newcomers, Starting Fast, Homogeneity, Counterprogramming, and Bridging. Of these, Counterprogramming is the only strategy that is presently and optimally used and justified by the model. An additional strategy, termed "Avoidance," is discovered and theoretically justified by subadditivity in ratings. This strategy increases total audience size and benefits the viewing audience.