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Management Science (forthcoming)
In live broadcasting, the break lengths available for commercials are not always fixed and known in advance (e.g., strategic and injury time-outs are of variable duration in live sports transmissions). Broadcasters actively manage their advertising revenue by jointly optimizing sales and scheduling policies. We characterize the optimal dynamic schedule in a simplified setting that incorporates stochastic break durations and advertisement lengths of 15 and 30 seconds. The optimal policy is a “greedy” look-ahead rule that accounts for the remaining number of breaks; in this setting, there is no value to perfect information at the scheduling stage, and hence knowing the duration of all breaks would not change the schedule. We present heuristics to help solve scheduling problems of even greater complexity. The performance of these heuristics under various scenarios is tested by running simulations calibrated using industry data. The simple greedy heuristic is shown to perform well except when revenues are concave in ad length, in which case the look-ahead aspect of the optimal schedule becomes more important. Finally, we recommend ways for broadcasters to balance their portfolio of booked ads by determining the optimal overbooking level and mix of ads as a function of their associated revenues generated and penalties incurred.