Coordination of quantity and shelf-retention timing in the video movie rental industry

How should a video rental chain replenish its stock of new movies over time? Any such policy should consist of two key dimensions: (i) The number of copies purchased; and (ii) when to remove a movie from the front shelves and replace it by a newly released one. We first analyze this bi-variate problem for an integrated chain. As for decentralized chains, we show that a (wholesale) price-only contract cannot coordinate such a chain. We then consider a price-and-revenue-sharing contract. Such a contract can achieve coordination, but the unique price and share which are needed may not provide one of the parties with its desired profit (i.e., it will violate individual rationality). This situation has been reported in the case of Blockbuster Video and has led to litigation between Blockbuster and Disney Studios. We thus propose adding a third lever: A license fee (or subsidy) associated with each new movie. Such a contract can coordinate the channel and satisfy the individual rationality requirements. In fact, all our results hold true irrespective of whether or not the rental store is allowed to sell surplus copies of movies. We are able to compare the optimal decision variable and coordinating lever values, as well as the optimal profits, for the "rental only" and "sales + rental" models. Our numerical examples, which utilize empirical demand data have significant managerial implications in terms of increasing the effectiveness of the video rental industry.