In http://fdahms.com/2014/12/05/objective_functions/ it is argued that we should not fall in the “multi objective trap”. In my experience many practical models have some multi-objective structure. Some examples of models I have been working on are:
- Return vs risk. e.g. portfolio models
- Scheduling: minimize number of late (I should say tardy) jobs vs sum of of tardiness. If only number of late jobs is considered, it does not matter how late a late job is. In practice a job being late a little bit is better. On the other hand the minimizing the sum may deliver a ton of jobs being a little late. Combining these objectives can help.
- Scheduling: adding an extra objective that minimizes the difference between an existing schedule and the new schedule can help preventing wild changes in schedules without having a clear benefit (persistency).
- Cost vs Customer Service Level. If we can improve the CSL when it costs very little we may want to exploit this. On the other hand if a small decrease in CSL delivers a ton of profit then that is also worth considering.
- Tank design: cost vs fire power vs weight.
- Supply chain: cost vs robustness. E.g. keep extra suppliers although reducing the number of suppliers may reduce cost.
- In a typical Cost – Benefit Analysis we also have to consider several criteria.
- Soft and elastic constraints will give rise to extra objectives.
- Etc, etc,
In my view many if not most interesting practical problems have conflicting goals and objectives. To make the client aware of this is an important role of a modeler. Even if we solve this as a single objective model using weights and penalties, the modeler needs to be aware and communicate the multi-objective nature and trade-offs of the underlying model.