On an Optimal Solution to the Film Scheduling and Showtime Staggering Problem

TL;DR

This paper formulates the complex film scheduling and showtime staggering problem as a binary integer linear optimization task, demonstrating that optimal solutions are achievable within clusters of neighboring theaters rather than across all locations simultaneously.

Contribution

It provides an exact mathematical formulation of the scheduling and staggering problem and shows that optimal solutions are cluster-specific, not global.

Findings

Exact binary integer linear programming formulation provided

Optimal scheduling is cluster-dependent, not global

A solved example illustrates the approach

Abstract

The scheduling of films is a major problem for the movie theatre exhibition business. The problem is two-fold: movie exhibitors ideally would like to schedule films to screens in their various locations to maximize attendance and revenue, but would also like to schedule these films such that neighbouring theatre locations play the same films at different times thus giving guests a multitude of showtime options. We refer to this latter problem as the showtime \emph{staggering} problem. We give an exact formulation of this scheduling problem using binary integer linear optimization, and provide a solved example as well. This work further shows that the optimal scheduling of films cannot be done across all theatre locations at once, but rather, must be done for each cluster of neighbouring locations.