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This article focuses on the sale of a product across channels that are entered sequentially. Using a two-channel model, the authors derive the optimal time to enter the second channel and then obtain a specific parametric solution for movie distributors regarding theater attendance and subsequent sales to video stores. Using data from 35 movies, the authors estimate exponential sales curves for both theater attendance and video rentals and demonstrate how knowledge of the sales parameters in the first channel (theaters) helps predict sales in the second channel (video rentals). Finally, from the movie distributor's perspective, the authors calculate optimal release times based on the model and its estimated parameters. The results suggest that profits would increase if movies were released to video sooner than is the current practice.
Lehmann et al. (Sat,) studied this question.