Solving Talent Scheduling with Dynamic Programming

We give a dynamic programming solution to the problem of scheduling scenes to minimize the cost of the talent. Starting from a basic dynamic program, we show a number of ways to improve the dynamic programming solution by preprocessing and restricting the search. We show how by considering a bounded version of the problem, and determining lower and upper bounds, we can improve the search. We then show how ordering the scenes from both ends can drastically reduce the search space. The final dynamic programming solution is orders of magnitude faster than competing approaches and finds optimal solutions to larger problems than were considered previously.