I'm having trouble with the formulation of a linear program constraint, for an aggregate planning problem for 30 months.
Company XYZ wants to maximize profit, and wants to know how many workers the company must have each month, how many workers should the company hire and how many should be laid-off?
The constraint is as follows "Each hired worker must receive a training course, that will last 3 months, and can't be laid-off before the training ends".
Decision Variables are:
a(t)= Number of workers in each day .
b(t) = Number of manufactured units in each day .
c(t)= Number of hired workers in each day.
d(t)= Number of laid-off workers in each day.
The balance constraint is : a(t)=a(t-1)+c(t)-d(t)
I think the constraint would be:
But I'm not sure.