I am trying to model a job-shop scenario where - given a certain number of workers (W) and parts (P) such that P>W - each worker spends each shift (k) working on a specific part. Due to reasons of maintaining efficient workflows, it is preferred that a worker keeps working on that same part for the entire week (i.e. all 5 shifts in a week). At the outset, it doesn't matter which part they start on, but once they are scheduled for a part it is preferred they stick to it. I have thought to model it in the following way.
My question is: does this makes sense or if there are any negative consequences to this method of modelling? One thing I do not like is there ends up being many $\delta_{w,p}$ constraints.
$Z_{w,p,k} \in \lbrace 0,1 \rbrace$ = Worker W making part P on shift K
$\delta_{w,p} \in \lbrace 0,1 \rbrace \ge Z_{w,p,k}$ for each k (to check if a worker is working on that part that modelling period or not)
$\delta_{w} = \sum \delta_{w,p} $
And then either minimizing the sum of all $\delta_{w}$ or constraining their maximum.