Scheduling aims at controlling and balancing workload from tasks to resources in a production system. Many of its characteristics and goals are covered in our post Scheduling Problems. Here, we focus on solving the problem and measuring the quality of a schedule plan.

### Sequencing rules

Given a set of orders, how to assign them to a machine? Several rules exist, and their output will definitely influence the quality of the system.

– first in, first out (FIFO): here, the first order to be released will be assigned first to an available machine

– earliest due date: the orders with the earliest due date are scheduled first (even if they are released in a different order)

– shortest processing time: here we prioritize orders that finish quickly, at the detriment of long orders

– minimum slack: we schedule first the orders with a small slack. The slack is measured by the difference between its due date and its processing time (slack = due date – processing time). Smaller slacks will indicate higher priority

### Performance indicators

Given a scheduling output (given by one of the sequencing rules above), a performance indicator measures its quality with respect to an objective.

– waiting time: this indicator measures how much an order waits before it enters production. If orders tend to have a large waiting time, it may be an indicator of lack of resources.

– makespan: this indicator measures the total time needed to complete all orders. In other words, it measures how long it takes to finish a production batch. Typically, one wants to have the makespan within a given limit, but has few advantages of minimizing it further.

– average tardiness: measured by the average lateness of orders according to their due dates. We certainly want this indicator to be as small as possible, ideally zero.

– work in progress: this indicator measures the average number of orders being processed in the system. It serves as an excellent measure of congestion in the workshop.

### Remember these scheduling rules

The shortest processing time rule is optimal for

– minimizing the mean flow time

– minimizing the mean waiting time

The earliest due date rule is optimal for

– minimizing the latest tardiness

Note that all these methods are valid for processes that need only one machine. For two-process flow-shops, other rules apply. Notably, the Johnson’s Rule is optimal to minimize the makespan, but that’s a topic for another post.

With these sequencing rules and all performance indicators described above, all you have to do is measure and select the most appropriate one for your production system.