I'm currently handling a project with a problem that is very similar to nurse scheduling problem in many respects. It is a part time workforce scheduling system whereby we need to determine which staff is most suitable to work on that a particular day in a course of 30 days. There are a few constraints:
Hard constraints
- 10 staffs will be hired
- only 5 staffs are required to work in a day
- each staff could only work for a maximum of 20 days
- in a month there will be some days where the staff has indicated that they could not work due to inavailability
Soft constraint
- there will be also some days where the staff is less preferred to work on that day
I was suggested to use linear programming to build this project however I don't see how mathematics can be applied in this case. However, I could be wrong. In that case can anyone point me to the right direction as to what method or techniques should I be using to solve this case?