Scheduling a music rehearsal problem with unequal music piece length

• We schedule music pieces to minimize show-up days and idle time.
• A heuristics is used to generate alternative solutions with minimum show-up days.
• A MIP model then finds the minimal idle time solution from those alternatives.
• The proposed method significantly decreases computational times.

This paper studies a music rehearsal scheduling where music pieces require different sets of players and different rehearsal durations. The rehearsal is arranged in multiple days. The players need to show up only on the day that the pieces they play are scheduled. They must show up before the first piece they involve starts and leave after the last one ends. The objectives are to assign music pieces to the rehearsal days to minimize the total number of days that all players have to show up and sequence the music pieces within each day to minimize the total waiting time of the players. We propose a 2-stage methodology to schedule music pieces, which is a combination of a cell formation technique and an integer-programming model. From 77 test problems, the solutions from the proposed method are as good as the optimal solutions from MIP models and are better than the best founds in all the test problems. The computational time is also significantly less.