Auto Populate 'on call' schedule for year? Is this possible?

Is this for a 7 day workweek? Can more than 1 employee be scheduled at the same time?

Taking a chance I used quite a few helpers columns to do multiple sorts on random numbers.
The columns in the file labelled Rand 1, Rand 2, Rand 3 used this formula starting in C2 and filled down to give random numbers. In order to sort properly and use the RANK function I copied and pasted values to keep the values but get rid of the formulae.

Formula:

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Once that was completed I used the RANK function to rank in order the random values

Formula:

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I did this 3 times and then sorted on the final ranking.

Before doing this, I used several formulae to copy the Employee names the number of reps for each. They are still on the worksheet.

Further explanation. (had to leave the question before I wanted)
The small table on the worksheet located at O3:Q6 is used to get the rows required for each employee in column A the middle column is the running total of the list for the employees.
A2 has this formula filled down. This lists each employee the number of times that they will appear during the year.

Formula:

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This list was then copied and paste values into column B which was used for sorting using the calculation from column C to J.
This isn't perfect and the complicating factor was that 2 employees used more than half the days.
Column B is the final order for you to use in your calendar.

A lot depends upon how the calendar is produced. I don't think it will be easy with formulae...but who knows. Upload your calendar file and we can take a look at it for a possible solution.

The final listing can be exported by copy and paste values. The calculations are not necessary to be included in a new workbook.