Play It Again, Sam? Optimal Replacement Policies for a Motion Picture Exhibitor

Every week, motion picture exhibitors must decide whether to keep or replace the movies playing in their theaters in light of the past week’s sales data. This decision is complex because of the dynamic decision environment, the uncertainty of demand, the complex revenue sharing terms between the retailer and the distributor, the need to commit to new movies for several weeks and the competitive release patterns of movies. We formulate this problem as a Markov Decision Process (MDP) model, and use it to obtain optimal replacement policies for the exhibitor. We examine the effect of differences in quality and quantity of available movies, and their respective release dates on the returns from model-based normative solutions. We also show that two practical heuristics are significantly outperformed by the optimal policy for the MDP model. We conclude by applying the model to industry data.