1. ## Confidence levels

Hi,

I need to calculate the confidence levels that I have enough staff at any point in time to service up to 6 tills in a supermarket. I have a set of data of about 50 days split into 15 mins slots but if I take 1 slot as an example to explain what I'm trying to do.

Between 10 & 10:15 the average number of tools required is 4 but the profile of the data is such that is nearly alwayso 4, a few 5s and a few 1, 2 & 3s. Standard deviation is about 0.4. So for a high confidence level that I'd need enough staff I'd multiple the SD by 2.6ish and add that to the average. This give 5.2 which means I need 6 told tills open. But I know I never experience 6.

As another example, at 17:00 I know I need between 5- 6 tools open. The average is 5.6 with an SD of 0.2. Bit that suggests I need 6.2 tills open, therefore 7, which I simply don't have!!

What is the best way of determining the 95% confidence level that I'll have enough staff?

Many thanks

2. ## Re: Confidence levels

This almost seems like it could be better addressed using business optimization based on your specified constraints. Then giving the solution you could run sensitivity analysis to find the allowable increase, allowable decrease and any slack in the linear program.

Not sure 95% CI buys you much. Perhaps a different approach could also be using some type of time series.

3. ## Re: Confidence levels

I think queuing models from operations research would be the way to go. It is specifically designed to address this type of issue.

4. ## Re: Confidence levels

Here is a simple (or perhaps simplistic) solution until you manage to get a more sophisticated analytic answer (which will probably not be much different).
You want the number of tills to open in a particular time slot that will be sufficient for your customers 95% of the time. You have about 50 cases for each time slot. Rank the 50 numbers for each time slot, and remove the top two. The largest number remaining should be a good estimate of the 95% limit.

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