# portfolio optimization, with negative KPIs

In portfolio optimization, when having negative KPIs, what does it mean to select a subset of projects with contributions that result in a KPI end value to be less than 0?

For example, if we have below KPI:

• KPI : reduce order to ship time.
• baseline : 5 days.
• end target : 3 days.

and our optimizer selected a subset of projects in which two of them contributed to the above KPIs as follows:

• project A: reduced shipment time by 4 days.
• project B: reduced shipment time by 2 days.

which results in KPI value 5 - 6 = -1.

Is this an acceptable practice "because it is obvious time will always be greater than 0"? Or should we constrain our optimizer to have KPI values above zero but in return select a subset of projects with higher total cost?

• It isn't possible to have an order-to-ship time of -1, as this would mean that you were shipping before the order was placed - unless I am misunderstanding the question. So you can't combine these two projects arithmetically in the way you propose... so I suggest that you need to look at the impact of one project, then see what the second project does to further improve the output from the first one. Does that help? Mar 25 at 11:52
• thank you for your reply. from your experience how can we model KPIs of this type in an optimization process? Mar 28 at 7:00
• Bear in mind that a KPI is a way of measuring achievement against a target, so you need to think about what the expected performance improvement will be, then you have a way to measure whether you have achieved it. I doubt that anyone can tell you explicitly what the figures will be in your specific case, as explained in the various answers: you would have to think about the process and how you expect it to impact on the current performance. Only people within your organisation can define that, I'm afraid. Mar 28 at 11:43
• You’re either using terms oddly, or confusing goals with metrics. Reducing lead time is a goal; your measurable reduction in lead time is a metric. Jun 4 at 1:01

If your baseline is 5, and now one project is now 1 and the other is 3. Seems like your new baseline is 2, the average of your two observations. A metric is the ratio of two measurements. I'd use the savings over baseline = 2/5 = 40%.

• In project portfolio optimization, is it possible to have a variable with limited upper and/or lower value but not as a constraint? Constraint will restrict the choices once the variable limit exceeded. Instead, I want no restrictions in the project mix choice however i want to consider anything achieved beyond this variable limit counts as a zero. Mar 25 at 8:38

TL;DR: the effects of changes can't be added linearly.

It is possible that you have an average effect, as David Espina proposes, or you could have a multiplicative effect, so a change that reduces shipment time by 10% and another one that reduces by 20% could be combined to achieve a reduction by 28% (although that's highly unlikely). In some cases, the application of one change to a system invalidates the assumptions that underly the other change, so it isn't applicable anymore.

It is also possible that both changes require the involvement of the same limited resources (experts, or storage facilities) so that trying to implement them both at the same time results in neither of them getting finished.

The main rule when estimating multiple changes to a system is to see them in conjunction, not separately.

Of course, if the changes are completely separatable (for example, one reduces time from order to warehouse, and another reduces time from shipment preparation to delivery), they might add, but then you need to look at the effects each change has to its relevant process aspects.

• Thank you In your opinion if it is a general case, any variable with a limit (beyond it worth zero) not as a constraint, is it possible? Mar 25 at 18:25