Hey guys,
I need your help. I am trying to create a work schedule model for nurses. I'm making good progress so far, but I'm failing with two constraints. I have the variable $x_{ijk}$ which indicates if a doctor $i$ works the shift $k$ on day $j$, it takes the value 1 if he works there. $x_{ij}$ indicates if doctor $i$ works on day $j$. The index goes from $i;j;k \into \{1,...,I;J;K\}$.
I now want to model the following:
1) A nurse must work at least $K_{min}$ days at a stretch. My suggestion would be: \sum_{t=j}^{t+K_{max}}y_{ij}\le K_{max}~\forall i\in I, j\in \{1,\ldots,\mid J\mid -K_{max}\}
2) A nurse may work a maximum of $K_{}$ days at a stretch.
3) A break between work sequences must always be exactly 2 days. How do I model that? As a mathematical formulation
Lorenz Wagner
perhaps this one might help
https://medium.com/walmartglobaltech/automating-shift-scheduling-with-linear-programming-fe1720f13620
specifically, item 6 in "Constraints" section, good luck.
(or, just check on any other online LP job scheduling model formulation)
I cannot see an objective of this problem - what value should be minimized or maximized (if any)?
Anyway, I think that you should consider introducing a period for which scheduling should be prepared (two weeks? three weeks?)
HI,
To model the constraints for creating a nurse work schedule using the variables xijk and xij, as well as additional variables yij, you can use integer programming. I will assume that yij is a binary variable representing whether a nurse starts a work sequence on day j.