Scheduling is the process of developing a list of tasks for some system, e.g. the sequence of jobs which a machine is to process. Scheduling problems arise in all areas of production and distribution and also in less obvious areas such as television advertising.

Scheduling problems tend to have these characteristics:

• they relate to the near future (1 day - 1 month ahead);
• there is an enormous number of potential solutions;
• many solutions are similar but some are definitely better than others;
• finding the best solution is very difficult.

Mathematical models can be of immense use in tackling scheduling problems. They consist of a mathematical representation of the system together with a mechanism for valuing solutions and algorithms for finding good solutions and improving them. In some cases it is possible to find the "best" solution (i.e. the one which scores highest using the valuation mechanism). In others the number of potential solutions is so large (greater than the number of atoms in the universe!) that a good solution is all that can be achieved.

Often the process of developing a scheduling model is itself a valuable exercise. It forces the people concerned to analyse what they are doing and why they prefer one solution to another. This leads to a greater understanding of the issues involved and can lead to improvements even before the scheduling model is brought into use.

The design of the user interface for a scheduling model is often of as much importance as the algorithms. There are often aspects of a scheduling problem which a human scheduler knows about but which have not been represented in the mathematical model. The human scheduler needs to be able to reflect these issues in the solution, either by controlling which solution is selected or by modifying the solution which the model has selected.