Makespan

In operations research, Makespan is the total time that has elapsed from the beginning of a certain project to its end. The term commonly appears in the context of scheduling. There is a complex project that is composed of several sub-tasks. We would like to assign tasks to workers, such that the project finishes in the shortest possible time.

As an example, suppose the "project" is to feed the goats. There are three goats to feed, and there are two children that can feed them: Shmuel feeds each goat in 10 minutes and Shifra feeds each goat in 12 minutes. Several schedules are possible:

1. If we let Shmuel feed all goats, then the makespan is 30 (3*10 for Shmuel, 0 for Shifra);
2. If we let Shifra feed one goat and Shmuel two goats, then the makespan is 20 (2*10 for Shmuel, 12 for Shifra);
3. If we let Shifra feed two goats and Shmuel one goat, then the makespan is 24 (2*12 for Shifra, 10 for Shmuel);
4. If we let Shifra feed all goats, then the makespan is 36 (3*12 for Shifra).

So in this case, the second schedule attains the shortest makespan, which is 20.

Types of makespan minimization problems

• Job shop scheduling - there are n jobs and m identical stations. Each job should be executed on a single machine. This is usually regarded as an online problem.
• Open-shop scheduling - there are n jobs and m different stations. Each job should spend some time at each station, in a free order.
• Flow shop scheduling - there are n jobs and m different stations. Each job should spend some time at each station, in a pre-determined order.