I have a question related to this question:
The question wasn't answered since it wasn't clear what was asked. However I know what the person tried to ask:
In inventory management, the fill rate is a very common measure of service level. When one wants to calculate a safety stock based on this measure and historical/forecasted data, one has to find the safety factor z for which:
L(z) = EOQ*(1−Target fill rate)/σ
Usually in companies, the target fill rate is determined first, and then the safety factor is calculated, because in contracts there are service level agreements.
However for the Normal loss function L(z), there exist no explicit inverse. So how can I find a value for z that satisfies my target fill rate?
In this table, the vertical axis shows the first integer and decimal of z, and the horizontal axis represents the second decimal.
Another solution I could think of is to try to create some kind of goal-seeking algorithm that uses the Normal loss function and with an arbitrary number of iterations tries to determine z while it approaches the target fill rate. Obviously computation time here is a limiting factor.
Does anyone have any alternative solutions?