This entry describes KPIs (Key Performance Indicators) for production planning, i.e. job sequencing, and gives you a list of priority rules which can support you in achieving your planning objectives. Priority scheduling rules generally lead to detrimental plans and often cannot be implemented because the complexity of real production planning cannot be catered for. This blog entry will show that these disadvantages can be overcome by means of mathematical optimization (the methods of Prescriptive Analytics).

## Priority scheduling rules in production planning

Priority scheduling rules are a rough calculation of production planning. Those who deploy more precise methods will reach their targets better.

Production planning is commonly known as job sequence planning. Its task is to determine the sequence in which jobs are to be performed, i.e. in which order the required stations  should do their jobs. The quality of the production plans can be measured in different KPIs. The typical KPIs for evaluation are:

• the completion time of a job: when the final work stage of this job has been completed.
• the flow time of a job: the time span for one particular job – from the start of the first job stage to the end of the final one
• delay: The length of time that a job is performed beyond its scheduled completion time; in the event of early completion, 0 is accepted
• The make span: The time spanning the entire production plan, from the start of the first work stage and the end of the last one for all jobs.

The KPIS must be recalculated every time a change is made to the jobs, such as completing an order or accepting a new one. Due to the recalculation of KPIs, it makes no sense to compare them across different job quantities/volumes as they have different bases. KPIs, however, are a suitable planning goal and ideal to compare priority rules.

Priority scheduling rules are often used in practice since they are easy to implement and easy to understand at the same time. The following rules are typically used in planning:

• FCFS (First Come First Serve): Jobs are processed by order of their arrival; that is, what comes in first is processed first.
• SPT(F) (Shortest Processing Time First):  The next job selected is the job in the queue which has the shortest execution time
• EDDF (Earliest Due-Date First: The next job selected is the job in the queue which has the earliest due date.
• Moores Algorithm: Because the priority rules really only lead to acceptable results in the most straightforward cases, Moore devised an algorithm which takes both the delay and the processing time into consideration.[4].

Thonemann [1] shows that each rule leads to plans with varying degrees of good KPIs:

• FCFS results in coincidental plans and is used as a comparable instance
• SPTF results in a minimum average completion time
• EDDF results in the shortest delay
• Moores Algorithm leads to a minimum number of delays.[4]

Diagram 1: Achieving KPIs by means of priority rules, in alignment with Thonemann et al. .[1]

An advantage of priority rules is that they are easy to understand. Planners can check the plans and – depending on the software – they can compare the plans of different priority rules.

## Mathematical optimization in production planning

Several challenges can complicate planning with priority rules but these challenges can be overcome if your use of priority rules is smart:

• Jobs can be made up of different items, each of which require different manufacturing steps and stations.
Solution: When planning, each item can first be processed as an individual job but when calculating the KPIs, all items must be taken into consideration (completion time: the latest date for all items, the flow time, the time span between the earliest start and latest completion time for all items)
• Usually no planning is made before the first job begins and therefore it has to be made with jobs that are already underway. Therefore, jobs which have already begun occupy stations.
Solution: The standrad procedures can be adjusted so that they accept the jobs that have begun as fixed jobs. These jobs are scheduled first without giving any consideration to their priority. All jobs can then be done in accordance with their rule priority.

Even if these solutions mean that the rules can be deployed for more complex planning, they seldom yield good results. The results of the priority rules shown above only apply to jobs at an individual station. Therefore, while the use of priority rules is indeed a possibility in more complex planning cases, it is seldom feasible. We certainly advise against using priority rules in the following situations:

• The moment jobs are completed at several stations or when jobs cannot be completed at every station or have different completion times at different stations, then priority rules will seldom produce the best possible results.
• More complex target requirements may be needed. For instance:„We have agreed a delay of one day with a customer; we are allowed to use this to keep our Work-In-Pr0ogress ( note:analogous to flow time) at as low a level as possible.“ or:“Going by calculations, a €1000 penalty is to be imposed on orders that are delayed by more than 5 days.  Which plan is the most cost-effective if we consider installation costs, energy costs and capital binding for the work in progress?

In these cases, mathematical optimization is an alternative. Thonemann describes the procedure  very basically as a branch- and- bound algorithm [1]  (and refers interested readers to Domschke et al.[2] and Pinedo und Chao[3]). This procedure is more complex in his calculation. On the other hand, though, from a mathematical point of view, it leads to the best results. And even if it is considerably more complex, this doesn’t mean that the calculation needs a great deal longer. OPTANO production offers you a way to make these calculations quickly and easily.

A lot of the information in this blog is based on the following:

[1]: Thonemann, Ulrich et al. „Operations-Management: Konzepte, Methoden und Anwendungen“, Pearson Studium, München, 2010

[2]: Domschke, Werner et al. „Produktionsplanung – Ablauforganisatorische Aspekte“, Springer, Berlin, 1997

[3]: Pinedo, M. et al. „Operations Scheduling with Applications in Manufactoring and Services”, McGraw-Hill, New York, 1999

[4]: Beweis der Anzahl minimaler Verspätungen: https://www.win.tue.nl/~wscor/OW/2P450/MooreHodgson.pdf und http://pubsonline.informs.org/doi/abs/10.1287/mnsc.17.1.116?journalCode=mnsc