The cost of reducing costs

Predicting the number of sales representatives on a particular time on a particular store is harder than expected. If you instrument the whole process, you could know the activity of your representatives (number of customers, average time of a transaction, activity rate, …). We could then predict the number of required representatives. We know the cost of having set too much of them but what is the cost of having to few representatives? How to value a missed opportunity, a customer unsatisfaction of the quality of service, the behaviour of a too much stressed employee?

This problem can be extended to other areas where human presence is important (call center, postal services, …) or when dealing with supplies. Having too much item of a product on the shelve is costly, but having too few is costly too as missed opportunities, but hardly measurable. If you have this value, the whole problem is just an optimisation one : find the quality of service which maximize earning while minimize costs.

I have not so much clues right now (happy to hear yours if you have one).  I read that a Telco in New Zealand use 0.001 as the probability for a customer to switch to competitor if can’t have an operator on a call. However finding this magic number is not easy (I don’t know how they achieve it).

An idea is to get data on what happened when the quality of service was disturbed. But you can’t collect so much data. If you can, your business have a big issue. Moreover, such data will be quite complex to handle. For instance, a customer come in your shop and need to wait 15 minutes before having a sales representative. If this customer never shows again, is it because of the quality of service last time he came? Or because of an external factor you can’t catch (like a new ad campaign by your competitor)? Small dataset, huge complexity and external factors, only a thin chance to get something statistically relevant.

Feel free to comment if you have a hint on this problem.