Analysis of Revenue Maximization Under Two Movie-Screening Policies

A few weeks before the start of a major season, movie distributors arrange a private screening of the movies to be released during that season for exhibitors and, subsequently, solicit bids for these movies (from exhibitors). Since the number of such solicitations far exceeds the number of movies that can be feasibly screened at a multiplex (i.e., a theater with multiple screens), the problem of interest for an exhibitor is that of choosing a subset of movies for which to submit bids to the distributors. We consider the problem of the selection and screening of movies for a multiplex to maximize the exhibitor's cumulative revenue over a fixed planning horizon. The release times of the movies that can potentially be selected during the planning horizon are known a priori. If selected for screening, a movie must be scheduled through its obligatory period, after which its run may or may not be extended. The problem involves two primary decisions: (i) the selection of a subset of movies for screening from those that can potentially be screened during the planning horizon and (ii) the determination of the duration of screening for the selected movies. We investigate two basic and popular screening policies: preempt-resume and non-preempt. In the preempt-resume policy, the screening of a movie can be preempted and resumed in its post-obligatory period. In the non-preempt policy, a movie is screened continuously from its release time until the time it is permanently withdrawn from the multiplex. We show that optimizing under the preempt-resume policy is strongly NP-hard while the problem under the non-preempt policy is polynomially solvable. We develop efficient algorithms for the problem under both screening policies and show that the revenue obtained from the preempt-resume policy can be significantly higher as compared with that from the non-preempt policy. Our work provides managers of multiplexes with valuable insights into the selection and screening of movies and offers an easy-to-use computational tool to compare the revenues obtainable from adopting these popular policies.