Monday, December 15, 2014

No multiple objectives?

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.