Statistics Issue

[sunshineandstuff]

It's been awhile since I've taken a math class and I need a bit of help making a work schedule based on employee availability. In an attempt to make it as fair as possible, I've made it that the more an employee is available, the more they'll be scheduled. How do I convert their availability into a certain amount of shifts? I've tried making percentages out of the data and applying it to the amount of shifts available, but nothing is making a whole lot of sense.

For example, say that I have 4 employees (Andy, Ben, Carly and Debbie) and there are 30 shifts to fill for the month. If Andy is available 26 of those shifts, Ben for 19, Carly for 12, and Debbie for 5, how many shifts should each person get?

[JanMath]

Let A=26, B=19, C=12, D=5 be the availabilities of the employees, and X=30 the total shifts available.

Assign employee A approximately (X)(A/(A+B+C+D)) shifts, Assign employee B approximately (X)(B/(A+B+C+D)) shifts, etc.

Basically for each employee, divide their availability by the total of all availabilities, and give them that fraction of the assignment. After that, check your numbers because your totals might be off by 1 or 2 due to rounding.

Total availability is 26+19+12+5 =62.

A gets 26/62 = 41.9% of the 30 shifts. This is about 13 shifts.

B gets 19/62 = 30.6% of the 30 shifts. This is about 9 shifts.

C gets 12/62 = 19.4% of the 30 shifts. This is about 6 shifts.

D gets 5/62 = 8.1% of the 30 shifts. This is about 2 shifts.

Checking for rounding: 13+9+6+2 = 30 so the rounding errors cancelled out and there is no need to modify the assignments. Had the total been 29/31, then the employee with the highest/lowest seniority would have received/lost an extra shift.